Mapping mental states into propositional planning
TED英语演说-可能的未来,来自自然,技术和社会的交集
可能的未来，来自自然、技术和社会的交集Possible futures from the intersection of nature, tech and society00:09In 1998, my friends and I won a national art competition. The prize was a week in Disneyland Paris, with hundreds of other children from across the world, as delegates to UNESCO's International Children's Summit. Now this was no ordinary trip to Disneyland. Between running riot in the park and making friends, we workshopped the future of this planet. How could we overcome the problems of pollution and their threats to human and environmental health? How could we guarantee universal human rights of equality, justice and dignity?00:40Towards the end of the summit, we created a 20-year time capsule, with each country planting a vision of the future they hoped for. But as I look around today, it's clear to me that those visions have not come true yet. We're confronted by the same crises, made infinitely worse through decades of geopolitical inaction. We now face global existential risks as a result of the climate emergency, with the world's least-resourced and most disenfranchised made more vulnerable despite having contributed least to the problem. That trip to Disneyland taught me that art and design had the power to imagine other possible futures. The question is: "How do we actually build them?"01:21Today, I lead a design agency called Faber Futures, and my team and I design at the intersection of biology, technology and society. Through research and development collaborations, partnerships, and other strategies, we model a future in which both people and planet can thrive and where the role that biotechnology plays is shaped through plural visions.01:42Our design work prototypes the future. We have developed toxin-free, water-efficient textile dye processes with a pigment-producing bacterium, pioneering new ways of thinking about circular design for the textile and fashion industries.01:57You've probably already heard of data surveillance, but what if it was biological? Using open-source data on the human microbiome, we’ve created experiential artworks that engage with the ethics of DNA mining. How can we embed a culture of multidisciplinary codesign from within the industry of biotechnology? To find out, we designed the Ginkgo Creative Residency, which invites creative practitioners to spend several months developing their own projects from within the Ginkgo Bioworks foundry. We also generate and publish unique and expansive dialogues between people with different types of knowledges -- Afrofuturists with astrobiologists, food researchers with Indigenous campaigners. The stories that they and others tell give us the tools we need to imagine other biological futures.02:46Design deeply permeates all of our lives, and yet we tend to recognize things and not the complex systems that actually produce them. My team and I explore these systems, connecting fields like culture and technology, ecology and economics. We identify problems, and where value and values can be created. We like to think about a design brief as an instruction manual, mapping the context of the problem, and where we might find solutions.03:13Getting there might involve establishing new networks, building new tools,and even infrastructure. How all of these pieces interact with one another can determine research and development, material specification, manufacturing and distribution. Who ultimately benefits, and at what environmental cost. So you can start to imagine the kinds of systems that might drive the design of your smartphone or even a rideshare service. But when it comes to the design of biology, things become a little bit more abstract.03:45Organism engineers design microbes to do industrially useful things, like bioremediate toxic waste sites or replace petroleum-based textiles with renewable ones. To architect this level of biological precision and performance at scale, tools like DNA sequencing, automation and machine learning are essential. They allow the organism engineers to really zoom in on biology, asking scientific questions to solve deep technical challenges.04:14Successful solutions designed at a molecular scale eventually interact with those at a planetary one. But if all of the research and development focuses on the technical question alone, then what do we risk by excluding the broader context? We've all spent over a year now living at an unprecedented intersection between biology, technology and society. We've witnessed, with the rapid development of the COVID-19 vaccine, that although techno-fixes offer us a critical remedy, they don't always provide a panaceum, and that’s because the real world is a complex social and economic one, where dominant systems determine the distribution of benefits.04:54It will be another two years before hundreds of millions across the world receive their emergency vaccines, which, in a globalized world, risks undermining its efficacy on all our communities.05:05Scientific endeavors have long been considered separate to real-world contexts, an idea that places profound limitations on the promises of biotechnology. By missing the full scope of design, we may think we’re solving problems and realize later that actually, not much has changed.05:22And a similar logic is emerging in biotechnology for consumer goods and industry. So far, it offers innovations for commodities markets, drop-in replacements that change problematic ingredients, and yet sustain prevailing mindsets and dynamics of power. Again, technically sound solutions that unwittingly reinforce social and ecological inequities.05:44Addressing these asymmetries requires us to take a more revolutionary approach, one that begins by asking "What kind of a world do we wish for?" So what if we could do both? What if we could design at the molecular scale, with the real world in mind? A more integrated approach to designing with biology requires us to ask more nuanced questions; not "What will people buy," but "What if we put communities, rather than commodities, first." "Could distributed biotechnology enable people to find local solutions to local problems?" "Can we move beyond a biotechnology that creates monocultures to one which, like nature itself, embraces a multiplicity of adaptations?" "How do we equip the next generation with the tools, spaces and communities they need to broaden their skills, knowledge and ideas?" An incredible amount of work that begins to address these questions is already underway.06:40The Open Bioeconomy Lab, which has nodes in the UK, Ghana and Cameroon,designs open-source research tools to expand geographies of innovation into resource-constrained contexts. Over thousands of years, we've domesticated plants to make them edible, creating nutrient-rich, diverse and delicious food cultures. MicroByre wants to do the same, but for microbes. The San Francisco based start-up assembles diverse microbial libraries for a more resilient biological toolkit. Imagine the expanded color palettes and different applications, from different types of pigment-producing bacteria. And from London's famed art school, Central Saint Martins, students from different disciplines are generating new sustainable design practices from biological medium. You'll find them at work in a wet lab, nested between historic fashion textiles and architecture departments, a radical reunification of the arts and sciences in education. Many examples of this type of systemic design work in biotechnology exist -- piece them together, and you start to glimpse different visions of our biological futures.07:49I don't know what happened to the time capsule we left behind in Paris, but I do remember wishing for a more just and meaningful world, where all of nature can thrive. In their own significant ways, technology and design have played their role in denying us this, but it's in our power to change that. Fundamentally, this means recognizing that the design of, with and from biology is designing systems and not stuff, and that with a truly ambitious design proposition, one that’s based on values that center flourishing, caretaking and equity. We have the opportunity to build truly transformative systems, systems that open up holistic measures of value and impact, and how we think about scaling innovation and doing business for the futures we now need.--END--。
数学专业英语 第2章课后答案
2.12.比:ratio 比例:proportion 利率:interest rate 速率:speed 除:divide 除法:division 商:quotient 同类量:like quantity 项:term 线段:line segment 角:angle 长度:length 宽:width高度:height 维数:dimension 单位:unit 分数:fraction 百分数:percentage3.(1)一条线段和一个角的比没有意义,他们不是相同类型的量.(2)比较式通过说明一个量是另一个量的多少倍做出的,并且这两个量必须依据相同的单位.(5)为了解一个方程,我们必须移项,直到未知项独自处在方程的一边,这样就可以使它等于另一边的某量.4.(1)Measuring the length of a desk, is actually comparing the length of the desk to that of a ruler.(3)Ratio is different from the measurement, it has no units. The ratio of the length and the width of the same book does not vary when the measurement unit changes.(5)60 percent of students in a school are female students, which mean that 60 students out of every 100 students are female students.2.22.初等几何:elementary geometry 三角学:trigonometry 余弦定理:Law of cosines 勾股定理/毕达哥拉斯定理:Gou-Gu theorem/Pythagoras theorem 角:angle 锐角:acute angle 直角:right angle 同终边的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全等:congruence 夹角:included angle 三角形:triangle 三角函数:trigonometric function直角边:leg 斜边:hypotenuse 对边:opposite side 临边:adjacent side 始边:initial side 解三角形:solve a triangle 互相依赖:mutually dependent 表示成:be denoted as 定义为:be defined as3.(1)Trigonometric function of the acute angle shows the mutually dependent relations between each sides and acute angle of the right triangle.(3)If two sides and the included angle of an oblique triangle areknown, then the unknown sides and angles can be found by using the law of cosines.(5)Knowing the length of two sides and the measure of the included angle can determine the shape and size of the triangle. In other words, the two triangles made by these data are congruent.4.(1)如果一个角的顶点在一个笛卡尔坐标系的原点并且它的始边沿着x轴正方向，这个角被称为处于标准位置.(3)仰角和俯角是以一条以水平线为参考位置来测量的,如果正被观测的物体在观测者的上方,那么由水平线和视线所形成的角叫做仰角.如果正被观测的物体在观测者的下方,那么由水平线和视线所形成的的角叫做俯角.(5)如果我们知道一个三角形的两条边的长度和对着其中一条边的角度,我们如何解这个三角形呢?这个问题有一点困难来回答,因为所给的信息可能确定两个三角形,一个三角形或者一个也确定不了.2.32.素数:prime 合数:composite 质因数:prime factor/prime divisor 公倍数:common multiple 正素因子: positive prime divisor 除法算式:division equation 最大公因数:greatest common divisor(G.C.D) 最小公倍数: lowest common multiple(L.C.M) 整除:divide by 整除性:divisibility 过程:process 证明:proof 分类:classification 剩余:remainder辗转相除法:Euclidean algorithm 有限集:finite set 无限的:infinitely 可数的countable 终止:terminate 与矛盾:contrary to3.(1)We need to study by which integers an integer is divisible, that is , what factor it has. Specially, it is sometime required that an integer is expressed as the product of its prime factors.(3)The number 1 is neither a prime nor a composite number;A composite number in addition to being divisible by 1 and itself, can also be divisible by some prime number.(5)The number of the primes bounded above by any given finite integer N can be found by using the method of the sieve Eratosthenes.4.(1)数论中一个重要的问题是哥德巴赫猜想,它是关于偶数作为两个奇素数和的表示.(3)一个数,形如2p-1的素数被称为梅森素数.求出5个这样的数.(5)任意给定的整数m和素数p,p的仅有的正因子是p和1,因此仅有的可能的p和m的正公因子是p和1.因此,我们有结论:如果p是一个素数,m是任意整数,那么p整除m,要么(p,m)=1.2.42.集:set 子集:subset 真子集:proper subset 全集:universe 补集:complement 抽象集:abstract set 并集:union 交集:intersection 元素:element/member 组成:comprise/constitute包含:contain 术语:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:least upper bound 完备性公理:completeness axiom3.(1)Set theory has become one of the common theoretical foundation and the important tools in many branches of mathematics.(3)Set S itself is the improper subset of S; if set T is a subset of S but not S, then T is called a proper subset of S.(5)The subset T of set S can often be denoted by {x}, that is, T consists of those elements x for which P(x) holds.(7)This example makes the following question become clear, that is, why may two straight lines in the space neither intersect nor parallel.4.(1)设N是所有自然数的集合,如果S是所有偶数的集合,那么它在N中的补集是所有奇数的集合.(3)一个非空集合S称为由上界的,如果存在一个数c具有属性:x<=c对于所有S中的x.这样一个数字c被称为S的上界.(5)从任意两个对象x和y，我们可以形成序列（x，y），它被称为一个有序对，除非x=y，否则它当然不同于（y，x）.如果S和T是任意集合，我们用S*T表示所有有序对（x,y),其中x术语S，y属于T.在R.笛卡尔展示了如何通过实轴和它自己的笛卡尔积来描述平面的点之后，集合S*T被称为S和T的笛卡尔积.2.52.竖直线:vertical line 水平线:horizontal line 数对:pairs of numbers 有序对:ordered pairs 纵坐标:ordinate 横坐标:abscissas 一一对应:one-to-one 对应点:corresponding points圆锥曲线:conic sections 非空图形:non vacuous graph 直立圆锥:right circular cone 定值角:constant angle 母线:generating line 双曲线:hyperbola 抛物线:parabola 椭圆:ellipse退化的:degenerate 非退化的:nondegenerate任意的:arbitrarily 相容的:consistent 在几何上:geometrically 二次方程:quadratic equation 判别式:discriminant 行列式:determinant3.(1)In the planar rectangular coordinate system, one can set up aone-to-one correspondence between points and ordered pairs of numbers and also a one-to-one correspondence between conic sections and quadratic equation.(3)The symbol can be used to denote the set of ordered pairs（x，y）such that the ordinate is equal to the cube of the abscissa.（5）According to the values of the discriminate，the non-degenerate graph of Equation （iii） maybe known to be a parabola， a hyperbolaor an ellipse.4.（1）在例1，我们既用了图形，也用了代数的代入法解一个方程组（其中一个方程式二次的，另一个是线性的）。
Mind mapping applications in special teaching
Procedia Social and Behavioral Sciences 1 (2009) 2274–2279Available online at Ali Gunay Balim.E-mail address ; agunay.balim@.trWorld Conference on Educational Sciences 2009Mind mapping applications in special teaching methods courses for science teacher candidates and teacher candidates’ opinionsconcerning the applicationsErtug Evrekli a , Ali Gunay Balim a* , Didem ønel aaFaculty of Buca Education, Dokuz Eylul University, 35150-Izmir, TurkeyReceived October 10, 2008; revised December 11, 2008; accepted January 02, 2009AbstractIn this research, the examples of mind maps, prepared by science teacher candidates, about the different subject of Science and Technology are given. In addition, six open-ended questions about the using of mind mapping in constructive science and technology education were asked to science teacher candidates (n=25, male=9; female=16) and then, the data gained from this research was analyzed. In the result, according to science teacher candidates, mind mapping can be used in constructive science and technology effectively and help students in different stages; however, some science topics is not suitable for using mind mapping.© 2009 Elsevier Ltd. All rights reservedKeywords: Constructivism; mind mapping and science teacher candidates;1. I n troductio nIn the constructivist approach, individual sets connections between their background and new information to construct the knowledge in their mind so that learning takes place. Therefore, it is important to elicit students’ pre-knowledge, and if there are, to detect their misconceptions or insufficient comprehension. Two dimensioned visual techniques and tools are being used to elicit students’ pre-knowledge and the new information they learn during the learning process. One of the visual techniques that are used with the stated objectives is mind mapping. According to Zhao (2003), teachers can understand if students understood the subject and if they could construct an appropriate structure for the new information by examining their mind maps. In addition, the mind map helps students assimilate new information, to think and to develop their conceptual schema. So, it is considered that mind maps could be used in constructivist science lessons. To Mento, Martinelli and Jones (1999), mind mapping is a technique which enhances creativity and promotes individuals’ learning. They assure individuals to recall knowledge and to show the relations between different thoughts and concepts (Buzan ve Buzan, 1995; Buzan, 2002; Buzan, 2005). So, mind mapping could provide teacher with a feedback about students’ mental structure and development of their mental structure, could facilitate students’ recalling the knowledge by the assistance of using visual elements and could be used as an activity that makes the students participate the lesson. In recent years, there have been a load of studies aiming to identify the efficiency and limits of mind maps in the literature (Williams, 1999; Brinkmann, 2003; Ling,1877-0428/$–see front matter © 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.sbspro.2009.01.400Ertug Evrekli et al. / Procedia Social and Behavioral Sciences 1 (2009) 2274–227922752004; Amma, 2005; Treviño, 2005). When the features of mind maps are taken into consideration, it is proposed that using mind maps in the constructivist science and technology education might be efficient. For this reason, in the special teaching methods course implementations science teacher candidates were given samples of activities devoted to using mind maps in the constructivist science and technology education and then the candidates made implementations. Two samples of mind maps which were done in the course are given in figures 1 and 2 in the last page. F urthermore, opinions of the teacher candidates concerning the using mind maps in science education can provide feedback for the investigators about utility and limits of using mind maps. Thus, a need was felt for making a search intended for determining science teacher candidates’ opinions about mind maps. The interrogation sentence of the research was determined as “What are the Opinions of the Science Teacher Candidates about Mind maps and Using Mind maps in the Science Lessons?”.2. Methodology, Research Group and Data Collecting ToolThe research is a kind of descriptive one. 25 Science Teacher Candidates (female 16, male 9) who did the special teaching method course in 2007-2008 education period constitute the research group. The lessons of the special teaching methods were carried out along with the teacher candidates and they were given information about mind mapping. Activities devoted to using mind mapping in the Science and Technology Curriculum basing on the constructivist approach were implemented and teacher candidates prepared samples of activities which include mind mapping. In the research, a questionnaire consisting of six open ended questions was applied. These six questions were intended for identifying opinions of Science teacher candidates relating to mind maps and using mind maps in science teaching. In the process of developing the questionnaire, the main problem which was aimed to explain was determined and then, the open-ended questions were written concerning the problem. 3. FindingsThis part includes the findings of the research and interpretations of the findings. The first open ended question intended for identifying opinions of Science teacher candidates relating to applications of mind maps was: “Do you think that mind maps will be useful in Science and Technology Teaching?” The percent –frequency rates relating to answers given to this open ended question by the teacher candidates are given place in Table 1.Table 1. Opinions of the teacher candidates relating to the first open ended question.Do you think that mind maps will be useful in Science and Technology Teaching? Why?Codes f % Sample Expressio ns f %Assures the information to be permanent/ Facilitatesstudents’ recalling.20 48.8 Assures the relations between the concepts and thoughts to be seen / to be interrelated. 9 21.9Facilitates learning.4 9.8Enhances the interest of the students toward the lesson.2 4.9 Prevents the information from being memorized. 2 4.9 Assures the acquired knowledge and misconceptions to be identified2 4.9 Y e s (n =25), b e c a u s eM i n d m a p s ;Assures mental development of the students/ Assures students to gain time.2 4.8When the mind mapping technique is usedthe student can see the concepts and the relations between concepts visually……Assures to determine to what extend students assimilated the concepts and to reconcile this knowledge with experienceand background knowledge …In my opinion, it is useful to understand the interrelations of the concepts about the subject unit and to keep the concepts inmind longer41 100At the end of the analyses of the first open ended question it was detected that all the teacher candidates stated that mind maps would be useful in Technology and Science Teaching. Besides, teacher candidates stated with % 48.8 frequency that mind maps assure the knowledge to be permanent and facilitate recall it; they stated with the %21.9 frequency that mind maps assure the relations between the concepts and thoughts to be seen and to be interrelated. The other opinions of the teacher candidates are demonstrated in Table 1.2276 Ertug Evrekli et al. / Procedia Social and Behavioral Sciences 1 (2009) 2274–2279F or the purpose of determining the opinions of teacher candidates concerning mind mapping applications the following open ended question was inquired: “Do you think that mind maps will be useful in Science and Technology Teaching?” The percent –frequency rates relating to answers given to this open ended question by the teacher candidates are given place in Table 2.Table 2. Opinions of the teacher candidates relating to the second open ended question.Do you think that mind maps are appropriate for studying every subject in Science and Technology Teaching? Why? Codes f % Sample Expressio ns f %Yes, I do. 8 32 I am not sure 13 52 No I don’t.416Because every subject includes relations and terms each one canbe studied by using mind maps…Maybe we can not adapt each subject to mind maps…It is not possible for each subject to be explained by shapes…25 100At the end of the analyses of the second open ended question, teacher candidates stated with %32 frequency thatmind maps can be used for each subject in science and technology teaching; with %52 frequency that they are not sue and with %16 frequency they stated that mind maps can not be used with every subject.F or the purpose of determining the opinions of teacher candidates concerning mind mapping applications the following open ended question was inquired: “What can be the effects of using mind maps in Science and Technology teaching on students?” The percent –frequency rates relating to answers given to this open ended question by the teacher candidates are given place in Table 3.Table 3. Opinions of the teacher candidates relating to the third open ended question.What can be the effects of using mind maps in Science and Technology teaching on students? Explain with your reasons. CodesF % Sample Expressio ns f %Creates an environment that students will have fun/Attracts attention/Motivates 11 26.8 Assures permanent learning 7 17.1 Facilitates recalling7 17.1 Helps to understand learn the subject/Assures to set interrelations between concepts.6 14.7 Assures to express the subject with main lines andvisually/Displays how much students learned the concepts 5 12.1 It might bore the students in some circumstances. 3 7.3 U s e o f m i n d m a p s ;Assures to reveal students’ skills/Enhances creativity24.9Assures permanent learning. Because it isconspicuous and facilitates to makeconnections and transitions between concepts. It is important for students to express how much they have learned the concepts... Keeps the students’ attention awake… Makes the lesson more fun. It might bore the students who don’t likedrawing and picturing…41 100 At the end of the analyses of the third open ended question the teacher candidates stated with %26.8 frequency that mind maps would create a learning environment which students will like and which will motivate the students and attract their attention. With %17.1 frequency they stated that it assured a permanent learning, again wit the same %17.1 frequency they stated that it will facilitate recalling. The results of analyses about their other opinions are given place in Table 3.F or the purpose of determining the opinions of teacher candidates concerning mind mapping applications the following open ended question was inquired: “In which stage do you think that it will be true to use mind maps in learning process?” The percent –frequency rates relating to answers given to this open ended question by the teacher candidates are given place in Table 4.Ertug Evrekli et al. / Procedia Social and Behavioral Sciences 1 (2009) 2274–22792277Table 4. Opinions of the teacher candidates relating to the fourth open ended questionIn which stage do you think that it will be true to use mind maps in learning process? Codes f% Sample Expressionsf%Evaluate 926.6 Elicit 411.8 Elaborate 12.9 Engage 1 2.9 Explore 1 2.9 7E M o d e lExplain 1 2.9 17 50At the end of the subject or the unit720.6 At the beginning of the subject or the unit 720.6 P r o c e s sEvaluation of students38.8In my opinion it must be shown in the first stage… Just before the subject was demonstrated…To me, mind map should be used in the evaluation stage.…This technique can be used by teachers to understand if learning took place in point of evaluating students…It should firstly be used to reveal background knowledge… What does the student know about that subject? And later it should be used in evaluation stage. 17 50At the end of the analyses of the fourth open ended question the teacher candidates stated with %26.6 frequency thatmind maps should be used in evaluation stage which takes place in 7E learning model; with % 20.6 frequency that they should be used at the end of the subject or the unit and again with %20.6 frequency that at the beginning of the subject or unit. The results of analyses about other opinions are given place in Table 4. F or the purpose of determining the opinions of teacher candidates concerning mind mapping applications the following open ended question was inquired: “Do you think that mind maps are appropriate tools for constructivist approach?” The percent –frequency rates relating to answers given to this open ended question by the teacher candidates are given place in Table 5.Table 5. Opinions of the teacher candidates relating to the fifth open ended questionDo you think that mind maps are appropriate tools for constructivist approach? Why / Why not?Codes F % Sample Expressio ns f %Helps to learn the subject better / Assures to interrelate the knowledge 8 29.7 Assures efficient teaching 6 22.2 Helps to determine and repair misconceptions and missing knowledge 5 18.5 Moves creativity forefront 2 7.4Assures knowledge to be permanent 2 7.4Y e s (n =25) b e c a u s e ,Yes, because it is student-centered and depends on creativity…Yes, because at the stage of forming this map, students reflect the knowledge on the map as they have constructed it intheir mind…Absolutely yes, because when the student interrelate the map in their mind, it will be much better for them to assimilate the subject …27 100At the end of the analyses of the fifth open ended question it was determined that all of the teacher candidatesstated that mind maps are appropriate visual tools for constructivist approach. Besides, as the reason of the mind maps being appropriate visual tools for the constructivist approach, they stated with %29.7 frequency that it helped to learn the subjects better and assured to inter-relate knowledge; with %22.2 frequency that it assured students’ active participation, attracted students’ attention and assured an efficient learning. The other opinions of the teacher candidates relating to the question and percent –frequency rates relating to these opinions are displayed in table 5. F or the purpose of determining the opinions of teacher candidates concerning mind mapping applications the following open ended question was inquired: “Would you like to use the mind maps during your teaching practice in the future?” The percent –frequency rates relating to answers given to this open ended question by the teacher candidates are given place in Table 6.2278 Ertug Evrekli et al. / Procedia Social and Behavioral Sciences 1 (2009) 2274–2279Table 6. Opinions of the teacher candidates relating to the sixth open ended questionWould you like to use the mind maps during your teaching practice in the future? Why / Why not?Codes f % Sample Expressio n s f %To determine students’ knowledge andmisconceptions/ To evaluate7 24.2To make students join the lesson/ to arouse interest 6 20.7 For students to learn easier and more efficiently5 17.2 To set relations between subjects and daily life 3 10.4 For subjects to be recalled/ permanent knowledge 3 10.4 For students to speculate on the subject 2 6.9 Y e s , I w o u l d l i k eb ec a u s e ; (n =23).To improve creativity1 3.4 27 93.2It might make a mess in the classroom 1 3.4 R a r e l y ;(n =2)It should be used with some of the subjects13.4Yes, I would of course, to understand howstudents comprehend and construct the subject. Definitely I would, since it is easier to assure learning with an activity which draws students’ attention…Yes, to make the subject comprehended better…I would like because it is an efficient technique for determining misconceptions of the students and knowledge they have learnt in a wrong way…Yes but not quite often. Using it with appropriate subjects will be more useful.2 6.8According to answers given to the sixth open ended question it was determined that 23 teacher candidates stated that they want to use the mind maps in the future and two of them would like to use them in some contexts. The teacher candidates who declared that they would like to use the maps in the future stated with %24.2 frequency that they would use mind maps to unfold students’ background knowledge, to determine misconceptions and evaluate students; with %20.7 frequency that they would use mind maps to get students to participate the lesson and to draw their attention. As to the teacher candidates who declared that they would sometimes like to use the mind maps, they stated as the reason of their reason that during the stage of forming the maps the class might get into mess and for some subjects these tools might not be appropriate.4. Conclusion, Discussion and RecommendationsIn the analyses carried out at the end of the study; all of the teacher candidates declared that using mind maps inScience and Technology Education will be useful. As the reason of this they stated with % 48.8 frequency that mindmaps assure knowledge to be permanent and facilitated students’ recalling; with % 21.9 frequency that they assure the relations between conceptions and thoughts to be seen and they assure these concept-thoughts to be interrelated. Science teacher candidates stated with %32 frequency that mind maps can be applied to every subject; with % 52 frequency that they are not sure and with frequency of %16 that they can not be applied to every subject. Relating to effects of using mind maps in science and technology teaching upon students, science teacher candidates stated with %26.8 frequency that they would create an environment that the students will enjoy (and similar statements); with % 17.1 frequency that they would assure permanent learning and again with % 17.1 frequency that they would facilitate students’ recalling. Science teacher candidates stated with %26.6 frequency that mind maps should be used in the evaluation stage which take place in 7E model; with % 20.6 frequency that they should be used at the end of the subject or unit and again with % 20.6 frequency that they should be used at the beginning of the subject or unit. All of the science teacher candidates stated that mind maps are appropriate tools for constructivist approach. As a reason of that they stated with %29.7 frequency that they would help students to learn the subject better; with %22 frequency that they would assure students’ active participation, draw their attention and ensure efficient learning. 23 of the science teacher candidates stated that they would like to use mind maps during their teaching practice in the future and as for two of them stated that they would like to use them with some of the units. % 24.2 of the teacher candidates who declared that they would like to use mind maps stated that they would do this to reveal students’ knowledge, to determine their misconceptions and to evaluate. Two of the teacher candidates expressed that they would use the mind maps with some of the units for the reason that the class might get into mess whenErtug Evrekli et al. / Procedia Social and Behavioral Sciences 1 (2009) 2274–22792279 using them and they are not appropriate for every unit. At the end of the interpretations of teacher candidates’ opinions the following conclusions are adopted.Mind maps can be prepared and used appropriately for some Science and Technology subjects and this can be done by taking students’ peculiarities into consideration.Mind maps can help to determine students’ pre-knowledge and deficiencies or misconceptions in their pre-knowledge. It can facilitate to recall knowledge and conceptions and the interrelations set between them.Mind maps can be effective to create learning environments in which students feel desirous to learn and used in different stages of learning process.AcknowledgementsThis study is supported by TUBITAKReferencesAmma, C. (2005). Effectiveness of Computer based Mind Maps in The Learning of Biology at the Higher Secondary Level. New Delhi: ICDE International Conference (November, 19-23, 2005).Brinkmann, A. (2003). Graphical Knowledge Display-Mind Mapping and Concept Mapping as Efficient Tools in Mathematics Education.Mathematics Education Review. 16. 35-48.Buzan, T. and Buzan, B. (1995). The Mind Map Book. London: BBC Books.Buzan, T. (2002). How to Mind Map. London: Thorsons.Buzan, T. (2005). Mind Map: The Ultimate Thinking Tool. London: ThorsonsLing, C. W. (2004). The Effectiveness of Using Mind Mapping Skills in Enhancing Secondary One and Secondary Four Students’ Writing in a CMI School. The University of Hong Kong: Unpublished Master Thesis.Mento, A. J., Martinelli, P. and Jones, R. M. (1999). Mind Mapping in Executive Education: Applications and Outcomes. Journal of Management Development. 18(4). 390-416.Treviño, C. (2005). Mind Mapping and Outlining: Comparing Two Types of Graphic Organizers for Learning Seventh-Grade Life Science.Texas Tech University: Unpublished PhD Thesis.Williams, M. H. (1999). The Effects of a Brain-Based Learning Strategy, Mind Mapping, On Achievement of Adults in a Training Environment with Consideration to Learning Styles and Brain Hemisphericity. University of North Texas: Unpublished PhD Thesis.Zhao, Y. (2003). The Use of a Constructivist Teaching Model in Environmental Science at Beijing Normal University. The Chine Papers. 2. 78-83.Figure 1. The Mind Map about System in Our Body (Huri Didem) Figure 2. The Mind Map about World and Its Structure (Hilal)。
评价理论简介
Appraisal TheoryIt is within the general theoretical framework of SFL that Martin and White‟s (2005) Appraisal Theory evolved. The basic idea of SEL is that “language i s a resource for mapping ideational, interpersonal and textual meaning onto one another in virtually every act of communication” (Martin and White, 2005: 7). Appraisal Theory focuses on interpersonal meaning at the discourse level for three reasons. Firstly, the realization of an “attitude tends to splash across a phase of discourse, irrespective of grammatical boundaries - especially where amplified”; secondly, a given attitude can be “realized across a range of grammatical categories and we need to move out of lexicogrammar to generalize the evaluative meaning common to this kind of scatter”; and finally, there is grammatical metaphor “whereby meaning is not cooked twice as it were, introducing a degree of tension between wording and meaning” (Martin and White, 2005: 10). As Martin and White suggest, appraisal can be located as an interpersonal system at the level of discourse semantics. At this level it co-articulates interpersonal meaning with two other systems of negotiation and involvement, as can be shown in the following figure:Figure3.4Interpersonal semantic systems and tenor variable(Martin and White,2005:34)solidaritypowernegotiationappraisalAs can be seen from the figure, appraisal is one of three major discourse semantic resources construing interpersonal meaning (alongside involvement and negotiation). In this sense, we can firmly say that appraisal is mainly concerned with semantic sources for construing evaluative meaning in the interpersonal dimension at the discourse level.The notion of appraisal is used to cover the “resources for modalising, amplifying, reacting emotionally (affect), judging morally (judge-ment) and evaluating aesthetically (appreciation).” (Martin 1995b: 28). In SFL terms, the appraisal system realises tenor at the level of discourse semantics and is constituted by three semantic categories: ATTITUDE, ENGAGEMENT, and GRADUATION, with further sub-divisions:Figure3.5An overview of appraisal resources(Martin and White2005:38)monoglossENGAGEMENTheteroglossAPPRAISALAFFECT…ATTITUDEJUDGEMENT …APPRECIATION …FOCUSFORCEATTITUDE is concerned with “values by which speakers pass judgements and associate emotional/affectual responses with participants and processes” (W hite 2001a: 1). APPRAISAL system holds the view that evaluations can be divided into three basic kinds – (i) the value of things, (ii) people‟s character and (iii) people‟sfeelings (Martin and White, 2005). Accordingly, ATTITUDE system involves three semantic regions which are termed AFFECT, JUDGEMENT and APPRECIATION.AFFECT construes emotion with the person experiencing the emotion being the Emoter and what evokes the emotion being the Trigger (Martin and White, 2005). JUDGEMENT construes attitude about character and is subdivided into two broad categories: judgements of social esteem (normality, capacity, tenacity) and judgements of social sanction (veracity, propriety) APPRECIATION construes attitudes about texts, performances or natural phenomena and is organised around three variables: Reaction, Composition, and Valuation. Reaction concerns the impact of the text/process on our attention (reaction: impact) and its emotional impact (reac-tion: quality). Composition concerns perceptions of proportionality/balance (composition: balance) and detail (composition: complexity) in a text/process. Valuation has to do with our assessment of the social significance of the text/process (Martin and White, 2005).GRADUATION is concerned with gradability and is divided into force and focus. Focus applies most typically to categories which are not scalable and functions to sharpen or soften the specification to indicate strong or weak sense of prototypicality. Force is divided into intensification and quantification. Assessments of degree of intensity can operate over qualities (e.g. slightly foolish), over process (e.g. It greatly hindered us), or over the verbal modalities of likelihood, usuality, inclination and obligation (e.g. it’s very possible that). The term …quantification‟ is employed to indicate assessment of amount that applies to entities. The system of GRADUATION can be shown in figure 3.6.Figure3.6System of GRADUATION(Martin and White,2005:154)ENGAGEMENT system adjusts a speaker‟s commitment to what he or she is saying (Martin 2000), and is related to what has traditionally been described as epistemic modality. Under the system, the following options are seen as enabling the textual voice to vary the terms by which it engages with alternative voices and alternative positions.Dialogic Contraction includes resources for disclaiming and proclaiming. Disclaim covers “mean ings by which some dialogic alternative is directly rejected or supplanted, or is represented as not applying ” (Martin and White, 2005: 117) and is accordingly divided into two sub-types: deny (negation) and counter. According to Martin and White (2005), Proclaim includes the formulations which act to limit the scope of dialogistic alternatives by representing a proposition as valid or plausible in order to rule out alternative positions. Proclaim is divided into three sub-types: concur, endorsement, pronounce. The category of c oncur involves formulations which “overtly announce the addresser as agreeing with, or having the same knowledge as, some projected dialogic partner” (Martin and White, 2005: 123). Endorsement refers numbermass/presencetimeQUANTIFICATIONPROXIMITYspacetimeDISTRIBUTIONspacequalityINTENSIFICATIONFORCE processisolatinginfusingFOCUSEXTENTto those formulations by which “propositions sourced to external sources re-construed by the authorial voice as correct, valid, undeniable or otherwise maximally warrantable” (Martin and White, 2005:126). Pronounce covers formulations which involve “authorial emphases or explicit authorial interventions or interpolations”(Martin and White, 2005:127).Dialogic Expansion includes those resources for entertaining and attributing a proposition. Entertain means that the writer “represents the proposition as one of a range of possible positions” (White, 2002a:2). Under this sub-system the term attribution mainly deals with those formulations which “disassociate the proposition from the text‟s internal voice by attributing it to some external source” (Martin and White, 2005: 111) and is further divided into the two sub-categories of acknowledge and distance. Acknowledge covers those locutions which have no overt indication as to “where the authorial voice stands with respect to the proposition” (Martin and White, 2005: 112. Distance, in contrast, involves formulations by which there is an “explicit distancing of the authorial voice from the attributed material” (Martin and White, 2005: 113).Figure3.7The ENGAGEMENT System(Martin and White,2005:134)denydisclaimcountercontractaffirmconcurconcedeproclaimpronounceendorseentertain。
英语数学词汇E
数学专业词汇对照以字母 E 开头eccentric angle 离心角eccentric angle of an ellipse 椭圆的离心角eccentric anomaly 离心角eccentricity 离心率eccentricity of a hyperbola 双曲线的离心率echelon matrix 梯阵econometrics 计量经济学eddy 涡流旋涡edge 边edge connectivity 边连通度edge homomorphism 边缘同态edge of a solid 立体棱edge of regression 回归边缘edge of the wedge theorem 楔的边定理editcyclic markov chain 循环马尔可夫链effective area 有效面积effective convergence 有效收敛effective cross section 有效截面effective differential cross section 有效微分截面effective divisor 非负除数effective interest rate 有效利率effective number of replications 有效重复数effective variance of error 有效误差方差effectively computable function 能行可计算函数efficiency 效率efficiency factor 效率因子efficient estimator 有效估计量efficient point 有效点egyptian numerals 埃及数字eigenelement 特摘素eigenfunction 特寨数eigenspace 本照间eigenvalue 矩阵的特盏eigenvalue problem 特盏问题eigenvector 特镇量eigenvector of linear operator 线性算子的特镇量einstein equation 爱因斯坦方程einstein metric 爱因斯坦度量elastic coefficient 弹性常数elastic constant 弹性常数elastic deformation 弹性变形elastic limit 弹性限度elastic modulus 弹性模数elastic scattering 弹性散射elasticity 弹性elastodynamics 弹性动力学electrodynamics 电动力学electromagnetism 电磁electronic computer 电子计算机electronic data processing machine 电子数据处理机electronics 电子学electrostatics 静电学element 元件element of area 面积元素element of best approximation 最佳逼近元素element of finite order 有限阶元素element of surface 面元素elementary 基本的elementary chain 初等链elementary circuit 基本回路elementary conjunction 基本合取式elementary divisor 初等因子elementary divisor theorem 初等因子定理elementary event 简单事件elementary formula 原始公式elementary function 初等函数elementary geometry 初等几何elementary matrix 初等阵elementary number theory 初等数论elementary operation 初等运算elementary path 有向通路elementary set 初等集elementary subdivision 初等重分elementary symmetric function 初等对称函数elementary theory of numbers 初等数沦elevation 正视图eliminant 结式eliminate 消去elimination 消去elimination by substitution 代入消元法elimination method 消元法elimination of unknowns 未知数消去elimination theorem 消去定理ellipse 椭圆ellipse of deformation 变形椭圆ellipsograph 椭圆规ellipsoid 椭面ellipsoid of inertia 惯性椭球ellipsoid of revolution 回转椭面ellipsoid of rotation 回转椭面ellipsoidal 椭面的ellipsoidal coordinates 椭球面]坐标ellipsoidal harmonics 椭球低函数elliptic catenary 椭圆悬链线elliptic coordinates 椭圆坐标elliptic curve 椭圆曲线elliptic cylinder 椭圆柱elliptic cylinder function 椭圆柱函数elliptic differential operator 椭圆型微分算子elliptic equation 椭圆型微分方程elliptic function 椭圆函数elliptic function of the second kind 第二类椭圆函数elliptic function of the third kind 第三类椭圆函数elliptic geometry 椭圆几何elliptic integral 椭圆积分elliptic irrational function 椭圆无理函数elliptic modular function 椭圆模函数elliptic modular group 椭圆模群elliptic motion 椭圆运动elliptic orbit 椭圆轨道elliptic paraboloid 椭圆抛物面elliptic point 椭圆点elliptic quartic curve 椭圆四次曲线elliptic space 椭圆空间elliptic surface 椭圆曲面elliptic system 椭圆型方程组elliptic type 椭圆型ellipticity 椭圆率elongation 伸长embedding 嵌入embedding operator 嵌入算子embedding theorem 嵌入定理empirical curve 经验曲线empirical distribution curve 经验分布曲线empirical distribution function 经验分布函数empirical formula 经验公式empty mapping 空映射empty relation 零关系empty set 空集end 端end around carry 循环进位end device 输出设备endless 无穷的endomorphism 自同态endomorphism group 自同态群endomorphism ring 自同态环endpoint 端点energetic inequality 能量不等式energy 能量energy barrier 能量障碍energy distribution 能量分布energy integral 能量积分energy level 能级energy method 能量法energy momentum tensor 能量动量张量energy norm 能量范数energy operator 能量算子energy principle 能量原理energy space 能量空间energy surface 能面enlarge 扩大enneagon 九边形enriques surface 讹凯斯面ensemble 总体entire 整个的entire function 整函数entire modular form 整模形式entire rational function 整有理函数entire series 整级数entire transcendental function 整超越函数entrance angle 入射角entropy 熵enumerability 可数性enumerable 可数的enumerable set 可数集enumerate 列举enumeration 列举enumeration data 计数数据enumeration problem 列举问题enumerative geometry 枚举几何envelope 包络线envelope of holomorphy 正则包enveloping algebra 包络代数enveloping ring 包络环enveloping surface 包络面epicycle 周转圆epicycloid 外摆线epicycloidal 圆外旋轮线的epimorphic 满射的epimorphic image 满射像epimorphism 满射epitrochoid 长短辐圆外旋轮线epitrochoidal curve 圆外旋轮曲线epsilon chain 链epsilon function 函数epsilon map 映射epsilon neighborhood 邻域epsilon net 网epsilonnumber 数equal 相等的equal set 相等集equal sign 等号equality 等式equality constraint 等式约束equalization 平衡化;同等化equally possible event 相等可能事件equate 使...相等equation 方程equation of a circle 圆方程equation of a curve 曲线方程equation of continuity 连续方程equation of heat conduction 热传导方程equation of higher order 高阶方程式equation of jacobi 雅可比方程equation of mixed type 混合型方程equation of motion 运动方程equation of state 状态方程equation of the straight line 直线方程equation root 方程的根equation with integral coefficients 整系数方程equatorial coordinates 赤道座标equatorial radius 赤道半径equi asymptotic stability 等度渐近稳定性equi luminosity curve 均匀光度曲线equiangular 等角的equiangular spiral 对数螺线equiareal 保积的equiconjugate diameter 等共轭直径equicontinuity 同等连续性equicontinuous 等度连续的equicontinuous functions 等度连续函数equicontinuous set 等度连续集equiconvergence 同等收敛性equidimensional ideal 纯理想equidistant 等距的equidistant curve 等距曲线equilateral 等边的equilateral cone 等边锥面equilateral hyperbola 等轴双曲线equilateral triangle 等边三角形equilibrium 平衡equilibrium concentration 平衡浓度equilibrium conditions 平衡条件equilibrium constant 平衡常数equilibrium diagram 平衡图equilibrium point 平衡点equilibrium principle 平衡原理equilibrium state 平衡状态equipartition 匀分equipotent 等势的;对等的equipotent set 等势集equipotential 等势的equipotential line 等位线equipotential surface 等位面equivalence 等价equivalence class 等价类equivalence problem 等价问题equivalence relation 等价关系equivalent 等价的equivalent equation 等价方程equivalent fiber bundle in g g 等价纤维丛equivalent form 等价形式equivalent functions 等价函数equivalent knot 等价纽结equivalent mapping 保面积映射equivalent matrix 等价阵equivalent metric 等价度量equivalent neighborhood system 等价邻域系equivalent norm 等价范数equivalent point 等价点equivalent proposition 等值命题equivalent states 等价状态equivalent stochastic process 等价随机过程equivalent terms 等价项equivalent transformation 初等运算equivariant map 等变化映射erasing 擦除ergodic chain 遍历马尔可夫链ergodic hypothesis 遍历假说ergodic markov chain 遍历马尔可夫链ergodic property 遍历性ergodic state 遍历态ergodic theorem 遍历定理ergodic theorem in the mean 平均遍历定理ergodic theory 遍历理论ergodic transformation 遍历变换ergodicity 遍历性error 误差error analysis 误差分析error band 误差范围error coefficient 误差系数error component 误差分量error curve 误差曲线error equation 误差方程error estimation 误差估计error function 误差函数error in the input data 输入数据误差error law 误差律error limit 误差界限error mean square 误差方差error model 误差模型error of estimation 估计误差error of first kind 第一类误差error of measurement 测量误差error of observation 观测误差error of reading 读数误差error of second kind 第二类误差error of the third kind 第三类误差error of truncation 舍位误差error originated from input 输入误差error probability 误差概率error sum of squares 误差平方和error variance 误差方差escribe 旁切escribed 旁切的escribed circle 旁切圆essential 本性的essential boundary condition 本质边界条件essential convergence 本质收敛essential epimorphism 本质满射essential extension 本质开拓essential homomorphism 本质同态essential inferior limit 本质下极限essential infimum 本性下确界essential parameter 本质参数essential point 本质点essential singular kernel 本性奇核essential singularity 本性奇点essential spectrum 本质谱essential strategy 本质策略essential superior limit 本质上极限essential supremum 本性上确界essential undecidability 本质不可判定性essentially bounded 本质有界的essentially convergent sequence 本质收敛序列essentially self adjoint operator 本质自伴算子estimable function 可估计函数estimable hypothesis 可估计假设estimate 估计estimation 估计estimation of error 误差估计estimation of parameter 参数的估计estimation region 估计区域estimation theory 估计论estimator 估计量etale neighborhood 层邻域etale space 层空间etale topology 层拓扑etalon 标准euclid factorization theorem for rational integers 因子分解定理euclid lemma 欧几里得引理euclid parallel postulate 欧几里得平行公设euclidean algorithm 欧几里得算法euclidean domain 欧几里得整环euclidean geometry 欧几里得几何euclidean metric 欧几里得度量euclidean norm 欧几里得范数euclidean plane 欧几里得平面euclidean ring 欧几里得整环euclidean space 欧几里得空间euclidean vector space 欧几里得向量空间euler characteristic 欧拉示性数euler class 欧拉类euler constant 欧拉常数euler criterion 欧拉判别准则euler differential equation 欧拉微分方程euler formula 欧拉公式euler identity 欧拉恒等式euler number 欧拉数euler poincare formula 欧拉庞加莱公式euler poincare relation 欧拉庞加莱公式euler polyhedron theorem 欧拉多面体定理euler polynomial 欧拉多项式euler summation formula 欧拉总和公式eulerian angle 欧拉角evaluate 求...的值evaluation 计算evaluation of functions 函数值计算evaluation of integrals 积分计算even 偶数的even function 偶函数even number 偶数even parity 偶数同位even permutation 偶置换evenness 偶数性event 事件everywhere convergent sequence 处处收敛序列evidence 迷evident 迷的evolute 缩闭线evolute surface 渐屈面evolution 开方evolution equation 发展方程evolvent 渐伸线exact cohomology sequence 正合上同凋列exact differential equation 全微分方程exact division 正合除法exact homotopy sequence 正合同伦序列exact solution 精确解exact square 正合平方exactitude 精确度exactness axiom 正合性公理example 例exceed 超过excenter 外心exceptional curve 例外曲线exceptional jordan algebra 例外约当代数exceptional point 例外点exceptional value 例外值excess 超过excess function 超过函数excess of nine 舍九法exchange 交换exchange integral 交换积分exchange lattice 交换格exchange theorem 交换定理excircle 旁切圆excision 切除excision isomorphism 切除同构exclude 排除exclusion 排除exclusive disjunction 不可兼析取exclusive events 互斥事件exclusive or 不可兼的或executive program 执行程序exist 存在existence 存在existence conditions 存在条件existence of extremum 极值的存在existence theorem 存在定理existence theorem for roots 根的存在性定理existence theorem of implicit function 隐函数的存在性定理existential quantifier 存在量词exogenous variable 局外变量exotic space 异种空间expactation vector 期望值向量expand 展开expansion 展开expansion coefficient 展开系数expansion in series 级数展开expansion in terms of eigenfunction 本寨数展开expansion of a determinant 行列式的展开expansion theorem 展开定理expectation 期望值expected gain 期望增益expected payoff 期望增益expected value 期望值expected value vector 期望值向量experiment 实验experimental 实验的experimental error 实验误差explicit difference scheme 显式差分格式explicit differential equation 显式微分方程explicit function 显函数exponent 指数exponent notation 指数记法exponent of convergence 收敛指数exponential 指数函数exponential curve 指数曲线exponential distribution 指数分布exponential equation 指数方程exponential family 指数族exponential form of complex number 复数的指数形式exponential fourier transformation 指数型傅里叶变换exponential function 指数函数exponential integral 积分指数exponential law 指数定律exponential map 指数映射exponential p adic valuation 指数p 进赋值exponential process 指数过程exponential series 指数级数exponential sum 指数和exponential type 指数型exponential valuation 指数赋值exponentially asymptotic stability 指数式渐近稳定exportation 输出express 表示expression 式exradius 外圆半径extend 扩大extended commutator 广义换位子extended complex plane 扩张平面extended ideal 广义理想extended mean value theorem 广义均值定理extended plane 扩张平面extended point transformation 开拓的点变换extended predicate calculus 广义谓词演算extended riemann hypothesis 广义黎曼假设extended unitary group 广义酉群extension 扩张extension module 扩张模extension of a field 域的扩张extension of the residue field 剩余域的扩张extension principle of propositional logic 命题逻辑的外延性原理extension theorem 扩张定理extensionality 外延extensive quantity 外延量extent 范围exterior 外exterior algebra 外代数exterior angle 外角exterior approximation 外逼近exterior boundary problem 外边界问题exterior derivative 外导数exterior differential 外微分exterior differential form 外微分形式exterior differentiation 外微分法exterior domain 外域exterior interior angles 同位角exterior multiplication 外乘exterior normal 外法线exterior point 外点exterior power 外幂exterior problem 外边界问题exterior product 外积exterior product of tensors 张量的外积external 外部的external composition 外部合成external composition law 外部合成律external direct sum 外直和external division 外分external law of composition 外部合成律external memory 外存储器external program 外部程序external ratio 外分比external store 外存储器externally stable set 控制集externally tangent 外切的extract 开方extraction of a root 开方extraneous root 额外根extrapolate 外推extrapolation 外插extremal 极值曲线;极值的extremal element 极值元素extremal function 极值函数extremal length 极值长度extremal point 极值点extremal property 极值性质extremal surface 极值曲面extreme 外项extreme form 极型extreme point 极值点extreme term 外项extreme value 极值extreme value distribution 极值分布extreme value problem 极值问题extremity 端extremum 极值extremum conditions 极值条件extremum problem with subsidiary condition 附加条件极值问题extremum with a condition 条件极值extremum with a constraint 条件极值。
打算的作文英语
打算的作文英语Here is an English essay with more than 1000 words, without a title and without any extra punctuation marks in the body of the text.The power of planning cannot be overstated when it comes to achieving one's goals and aspirations. Whether it's a personal endeavor or a professional undertaking, having a well-thought-out plan can make all the difference in determining the ultimate outcome. In this essay we will explore the importance of planning and how it can be effectively applied to various aspects of our lives.At its core planning is the process of identifying a desired end result and then systematically mapping out the steps necessary to reach that outcome. This involves careful consideration of the resources available time constraints and potential obstacles that may arise along the way. By taking the time to plan meticulously one can increase the likelihood of success and minimize the risk of unexpected setbacks.One of the primary benefits of planning is that it provides a clear roadmap to follow. When we have a detailed plan in place it becomes much easier to stay focused and on track towards ourobjectives. Without a plan it's all too easy to become sidetracked or to lose sight of the bigger picture. A well-crafted plan serves as a constant reference point keeping us oriented and ensuring that we make steady progress.Moreover planning allows us to anticipate and prepare for potential challenges. By thinking through various scenarios in advance we can develop contingency plans and identify strategies for overcoming obstacles. This proactive approach helps to mitigate risk and ensures that we are equipped to handle whatever comes our way. Rather than being caught off guard and forced to react in the moment we can take a more measured and strategic response.Another key advantage of planning is that it fosters a greater sense of control and confidence. When we have a clear plan in place we feel more empowered and self-assured in our ability to achieve our goals. This sense of agency can be incredibly motivating spurring us on to put in the necessary effort and persevere through difficulties. Conversely without a plan we may feel overwhelmed and uncertain about the path forward which can undermine our motivation and self-belief.Of course the planning process itself requires a significant investment of time and mental energy. It can be tempting to simply jump right into action without taking the time to carefully map out astrategy. However the upfront effort involved in planning is more than offset by the benefits it provides in the long run. By taking the time to plan thoroughly we can avoid costly mistakes and setbacks and maximize our chances of success.It's important to note that effective planning is not a one-size-fits-all proposition. The specific approach that works best will depend on the nature of the task at hand as well as individual preferences and working styles. Some people may prefer a more detailed and structured planning process while others may favor a more flexible and iterative approach. The key is to find a planning method that aligns with your own strengths and preferences.Regardless of the specific approach taken planning can be applied to a wide range of contexts from personal goals like saving for a down payment on a house or training for a marathon to professional objectives such as launching a new product or expanding a business into a new market. In each case the underlying principles of planning remain the same identifying the desired outcome mapping out the necessary steps and anticipating potential challenges.One area where planning is particularly crucial is in the realm of personal finance. Creating a detailed budget and savings plan for example can help individuals to achieve their financial goals whether that's paying off debt building an emergency fund or saving forretirement. By mapping out their income and expenses and prioritizing their spending individuals can ensure that they are allocating their resources in a way that aligns with their long-term objectives.Similarly in the realm of health and wellness planning can play a vital role. Developing a comprehensive fitness and nutrition plan for instance can help individuals to achieve their health and wellness goals. By mapping out a structured program of exercise and healthy eating individuals can stay motivated and on track even in the face of setbacks or temptations.Ultimately the power of planning lies in its ability to provide focus direction and a sense of control. By taking the time to thoughtfully map out a course of action we can increase our chances of success and minimize the risk of costly mistakes. Whether it's a personal goal or a professional objective careful planning is an essential ingredient for turning our aspirations into reality.。
语言测试的目标构念
世界上的所有事物都是系统 系统由子系统构成，构成要素既各自独立又相互依存 所有系统都具有共同特征、普遍联系、一般规律 System
世 界 系观 统和 论方 ：法 论
Element (Attribute)
Structure (Relation)
Function (Procedure)
既具有类别本质［属性］，又拥有个体区别性［特征］ 既具有内在结构［关系］，又与外部系统普遍［关联］ 既处于相对静止［状态］，又经历绝对的变化［过程］
STRATEGIC COMPETENCE
PSYCHOPHYSIOLOGICAL MECHANISMS
CONTEXT OF SITUATION
1. 交际语言能力观（Communicative Language Ability－CLA）
LANGUAGE COMPETENCE
ORGANIZATION COMPETENCE
Ideat. Functs.
Manip. Functs.
Heur. Functs.
Imag. Functs.
Sensit. to dial. or variety
Sensit. to reg.
Sensit. to nat.
词汇、词法、句法、语音/字系；词语连接、修辞结构；表意、控制、教诲、想象；方言及变体、语域、地道语言、 文化含义/比喻
数学专业英语词汇
横坐标Abscissa 横轴Abscissa axis 绝对值Absolute value Absolutely convergent Absolutely convergent series Acceptance region Acute angle 绝对收敛绝对收敛级数接受区域锐角锐角三角形加法Acute triangle Addition 伴随矩阵代数Adjoint matrix Algebra 角Angle 圆心角Angle at the centre Angle in a circular segment Anti-clockwise Anti-symmetric matrix Arc cosecant 圆周角反时针方向反对称矩阵反余割反余弦Arc cosine 反余切Arc cotangent Areal element Argument 面积元素幅角算术中项结合律Arithmetic mean Associative law Asymptote 渐近线渐近线Asymptotic line Augmented matrix Auxiliary line Average 增广矩阵辅助线平均值轴Axis 横坐标轴纵坐标轴对称轴Axis of abscissas Axis of ordinates Axis of symmetry Basis 基贝叶斯定理伯努利试验二元Bayes’ Theorem Bernouill’s trial Binary 二项分布二项式定理二元正态分布分块对角矩阵旋转体Binomial distribution Binomial Theorem Bivariate normal distribution Block diagonal matrix Body of rotation Bounded 有界的上有界的下有界的有界区域 Bounded above Bounded below Bounded region有界变量无限的Bounded variable Boundless 微积分Calculus 消去律Cancellation law Canonical form Casual 标准型随机的圆心Center of a circle Central limit Theorem Central moment Certain event 中心极限定理中心矩必然事件链式法则基变换Chain rule Change of base Characteristic equation Characteristic root Characteristic value Characteristic vector Chybyshev inequality Chi square distribution Circle 特征方程特征根特征值特征向量切比雪夫不等式2 分布 圆 圆锥 Circular cone圆柱 Circular cylinderCircular ring圆环 圆周 CircumferenceClass interval组距 组限 Class limits组平均 组中值 顺时针的 闭区间 闭集 Class meanClass midpointClockwiseClosed intervalClosed set系数 Coefficient相关系数 余子式 列 Coefficient of correlationCofactorColumn列秩 Column rank列向量 公分母 公差 Column vectorCommon denominatorCommon differenceCommon divisorCommon factorCommon logarithmCommon multipleCommon ratioCommutative lawComplement minor 公约数 公因子 常用对数 公倍数 公比 交换律 余子式补集Complementary set Complex number Composite function Composition 复数复合函数 复合复合事件 复利Compound event Compound interest Concave 凹凸Convex 条件收敛 条件概率条件概率密度 条件概率分布 条件概率函数 置信区间 置信水平 共轭复数 连通域常数Conditional convergence Conditional probability Conditional probability density Conditional probability distribution Conditional probability function Confidence interval Confidence level Conjugate complex number Connect domain Constant 约束条件 连续性左连续右连续连续点连续分布连续随机变量 收敛Constraint condition Continuity Continuity from the left Continuity from the right Continuity point Continuous distribution Continuous random variable Converge 收敛性收敛域依概率收敛 收敛半径 逆命题卷积Convergence Convergence domain Convergence in probability Convergence radius Converse proposition Convolution 坐标Coordinate 坐标轴坐标平面 坐标系坐标变换 共面Coordinate axis Coordinate planes Coordinate system Coordinate transformation Coplane 互素Coprime 推论Corollary 相关系数 余割Correlation coefficient Cosecant 余弦Cosine 余切Cotangent 可列 Countable可列可加性 协方差协方差矩阵 准则Countable additivity Covariance Covariance matrix Criterion 临界值立方体立方根立方Critical value Cube Cube root Cubic 三次插值 立方根三次样条函数 曲线Cubic interpolation Cubic root Cubic splines Curve 曲线Curve line 曲面Curve surface Cusp 尖点曲线的尖点 柱Cusp of a curve Cylinder 柱面Cylindrical surface D’Alembert’s criterion Data procession Decade 达朗贝尔准则 数据处理 十进制推论Deduction 定积分定二次型 定义Definite integral Definite quadratic form Definition 退化双曲线 次数Degenerate hyperbola Degree 置信度多项式的次数 密度函数 分母Degree of confidence Degree of polynomial Density function Denominator Denumerable Derivative 可列的导数左导数右导数行列式偏差Derivative on the left Derivative on the right Determinant Deviation 对角线对角阵矩阵的对角化 直径Diagonal line Diagonal matrix Diagonalization of matrix Diameter 菱形Diamond 差、差分 差分方程 可微的 Difference Difference equation Differentiable微分Differential 微积分Differential and integral calculus Differential coefficient Differential equation Differential equation of first order Differential equation of higher order Differential of area Differential operation Differentials of higher order Differentiate 微商微分方程一阶微分方程 高阶微分方程 面积元素 微分运算 高阶微分 求微分微分积分方程 数值逼近 维Differention integral equation Digital approximation Dimension 有向直线最速下降方向 狄利克雷函数 不连通的 不连续点第一类不连续点 第二类不连续点 离散Directed line Direction of steepest descent Dirichlet’s function Disconnected Discontinuity point Discontinuity point of the first kind Discontinuity point of the second kind Discrete 离散分布离散随机变量 判别式Discrete distribution Discrete random variable Discriminant 不相交事件 相异根Disjiont events Distinct root 分布Distribution 分布函数 分配律Distribution function Distributive law 发散Diverge 发散级数多项式相除法 因子Divergent series Division algorithm for polynomial Divisor 域Domain 收敛域Domain of convergence Domain of definition Domain of integration Dot product 定义域积分区域 内积二重积分 二重极限 双精度Double integral Double limit Double precision 二重根Double root 对偶Dual 对偶律Dualization law 有效估计 Efficiency estimation有效估计量特征多项式特征值Efficiency estimator Eigenpolynomial Eigenvalue特征向量弹性Eigenvector Elasticity元素Element柱的母线面积元素矩阵的元素集合的元素基本事件初等函数初等数学初等变换消元法Element of cylinder Element of area Element of matrix Element of set Elementary event Elementary function Elementary mathematics Elementary transformation Elimination椭圆Ellipse 椭球Ellipsoid椭圆柱面经验方差经验分布函数空集Elliptic cylinderEmpirical variance Empirical distribution function Empty set端点Endpoint 总体Ensemble总体均值可数Ensemble average Enumerable可数无穷等概率Enumerable infinite Equal probability Equal ratio等比等可能事件方程Equally likely event Equationn次方程等腰三角形相似变换等边三角形等价Equation of n-th order Equicrural triangle Equiform transformation Equilateral triangle Equivalence等价变换等价关系误差Equivalence transformation Equivalent relationError误差分析误差检验测量误差估计Error analysisError checkError of measurement Estimate区间估计相关的估计量回归系数估计Estimate by a interval Estimate of correlation Estimate of regression coefficient总体比例估计 总体方差估计 估计量Estimate of population proportion Estimate of population variance Estimator 欧几里德空间 偶数Euclidean space Even 偶函数Even function 偶数Even number 事件Event 小概率事件 幂级数展开 期望Event of small probability Expansion into power-series Expectation 试验Experiment 显函数Explicit function Exponent 指数指数曲线 指数曲线 指数分布 指数函数 开立方Exponent curve Exponential curve Exponential distribution Exponential function Extraction of cubic root Extraction of square root Extremal 开平方极值极值点Extreme point 极值Extreme value 因子Factor 阶乘Factorial 因式分解 曲线族Factoring Family of curve Fiducial interval Fiducial limit 置信区间 置信限定义域Field of definition Field of rational numbers Finite 有理数域 有限的有限区间 有限开区间 一阶矩Finite interval Finite open interval First moment 拟和Fitting 曲线拟和 多项式拟和 直线拟和 浮点运算 焦点Fitting of a curve Fitting of a polynomial Fitting of a straight line Floating point operation Focus 公式Formula 四则运算 分数Four arithmetic operation Fraction 分数线 Fraction stroke相对误差 分数Fractional error Fractional number Frequency 频率边界点Frontier point 满秩Full rank 函数Function 一元函数 一次函数 多元函数 n 元函数 基本函数 基本解Function of a single variable Function of first degree Function of many variables Function of n-variables Fundamental function Fundamental solution Fundamental system of solutions Fundamental theorem Gamma distribution Gamma function 基础解系 基本定理 分布函数高斯分布 母线Gaussian distribution Generator 几何平均 几何分布 几何平均 几何级数 几何级数 几何Geometric average Geometric distribution Geometric mean Geometric series Geometrical series Geometry 空间几何 黄金分割 拟和优度拟和优度检验 斜率Geometry of space Golden cut Goodness of fit Goodness of fit test Gradient 图示法Graphical method Great circle of a sphere Greatest common factor Greatest lower bound Greatest value 球的大圆 最大公因子 下确界最大值分组误差区间分半搜索 调和级数 高阶导数 高阶差分高阶微分方程 高阶微分 高阶Grouping error Half interval search Harmonic series Higher derivative Higher difference Higher differential equation Higher differentiation Higher order 高次项Higher term 高阶导数高阶常微分方程 Higher-order derivative Higher-order ordinary differential equation高阶偏微分方程高阶偏导数直方图Higher-order partial differential equation Higher-order partial derivative Histogram齐次Homogeneous齐次微分方程齐次方程齐次函数齐次线性微分方程齐次线性方程齐次多项式n次齐次多项式水平渐近线水平线Homogeneous differential equation Homogeneous equation Homogeneous function Homogeneous linear differential equation Homogeneous linear equation Homogeneous polynomial Homogeneous polynomial of degree n Horizontal asymptoteHorizontal line水平面Horizontal plane 双曲线Hyperbola双曲面Hyperboloid单叶双曲面双叶双曲面超几何分布假设Hyperboloid of one sheet Hyperboloid of two sheets Hypergeometric distribution Hypothesis假设检验幂等矩阵单位元素单位矩阵病态Hypothesis testing Idempotent matrix Identical element Identity matrixIll-condition病态方程病态矩阵虚轴Ill-conditioned equation Ill-conditioned matrix Imaginary axis虚数Imaginary number 虚根Imaginary root虚数单位隐式Imaginary unit Implicit隐函数Implicit function不可能事件广义积分广义二重积分倾角Impossible event Improper integral Improper double integral Inclination angle夹角Included angle集合的包含不相容Inclusion of sets Incompatible不相容事件不定积分不定二次型独立Incompatible event Indefinite integral Indefinite quadratic form Independence随机变量独立性Independence of random variable独立事件独立随机事件 独立随机变量 自变量 Independent event Independent random event Independent random variable Independent variable Indeterminate form Index of a quadratic form Index of inertia 未定式二次型的指数 惯性指数 不等式Inequality 无限自由度 无穷间断点 无穷区间 无穷极限 无穷级数 无穷集 Infinite degree of freedom Infinite discontinuity Infinite interval Infinite limit Infinite series Infinite set 无穷大量 无穷小量 拐点Infinitely large quantity Infinitely small quantity Inflection point 固有误差 非齐次 Inherent error Inhomogeneous Initial condition Initial value 初始条件 初值内点Inner point 内积Inner product 向量内积 内径Inner product of vector Inradius 内切圆 Inscribed circle 瞬时Instantaneous 整数Integer 可积的 Integrable 积分Integral 整式Integral expression Integral mean value Integration 积分中值 积分法部分分式积分法 分部积分法 换元积分法 截距Integration by partial fraction Integration by parts Integration by substitution Intercept 内点Interior point 内积Interior product Intermediate value theorem Interpolation 介值定理 插值插值多项式 交Interpolation polynomial Intersection 集合的交 交点 Intersection of sets Intersection point区间Interval 区间估计收敛区间反三角函数 反函数Interval estimation Interval of convergence Inverse circular function Inverse function Inverse interpolation Inverse logarithm Inverse mapping Inverse matrix 逆插值反对数逆映射逆矩阵倒数Inverse of a number Inverse operation Inverse proposition Inverse sine 逆运算逆命题反正弦反对称Inverse symmetric Inverse theorem Inverse transformation Invertible 逆定理逆变换可逆可逆矩阵无理数Invertible matrix Irrational 无理数Irrational number Irrelevance 不相关不可逆Irreversible 等腰直角三角形 等腰梯形等腰三角形 累次积分迭代Isosceles right triangle Isosceles trapezoid Isosceles triangle Iterated integral Iteration 雅可比行列式 联合密度联合分布联合分布函数 联合概率密度 联合概率分布 约当标准型 约当矩阵跳跃间断点 拐点Jacobian Joint density Joint distribution Joint distribution function Joint probability density Joint probability distribution Jordan canonical form Jordan matrix Jump discontinuity Knee 已知Known 拉格朗日方程 拉格朗日乘数 拉格朗日插值 结合律Lagrange equation Lagrange multiplier Lagrange interpolation Law of association Law of commutation Law of distribution Law of large number交换律分配律大数定律主对角线首项元素最小公倍数 最小二乘法 左连续Leading diagonal Leading element Least common multiple Least square method Left continuous Left derivative 左导数左极限Left limit 左乘法Left multiplication Leibniz’s formula Lemma 莱布尼兹公式 引理弧长Length of arc 线段长度峰度Length of segment Leptokurtosis 显著水平似然方程似然函数极限Level of significance Likelihood equation Likelihood function Limit 极限分布线段Limiting distribution Line segment 线性代数线性相关线性相关线性微分方程 线性方程线性表示线性函数线性无关线性回归线性表示线性空间线性变换线性相关线性无关局部极大值 局部极小值 对数Linear algebras Linear correlation Linear dependence Linear differential equation Linear equation Linear expression Linear function Linear independence Linear regression Linear representation Linear space Linear transformation Linearly dependent Linearly independent Local maximum Local minimum Logarithm 对数函数对数的底纵轴Logarithm function Logarithmic base Longitudinal axis Lower bound 下界下三角矩阵 最小公倍数 菱形Lower triangular matrix Lowest common multiple Lozenge 马克劳林级数 长轴 Maclaurin series Major axis优化Majorization 尾数Mantissa 多值函数映射Many-value function Map 边缘密度边缘分布临界值Marginal density Marginal distribution Marginal value 数学期望数学归纳法 乘方Mathematical expectation Mathematical induction Mathematical power Mathematical statistics Matrix 数理统计矩阵二次型的矩阵 系数矩阵矩阵的迹最大的Matrix of a quadratic form Matrix of coefficients Matrix trace Maximal 最大值Maximal value 最大Maximum 最大似然最大似然估计 最大点Maximum likelihood Maximum likelihood estimate Maximum point 平均值Mean 平均数Mean number 均方差Mean square deviation Mean square error Mean value 均方误差平均值均值向量平均速度精确度Mean vector Mean velocity Measure of precision Median point 中点、重心 配方法Method of completing the square Method of geometry Method of iteration Method of least squares Method of maximum likelihood Method of minimum squares Method of moment Method of optimization Method of parabolas Method of random sampling Method of steepest descent Method of substitution Method of variation of constants Method of weighted mean Metric space几何方法迭代法最小二乘法 最大似然法 最小二乘法 矩法最优化方法 抛物线法随机抽样法 最速下降法 置换法常数变异法 加权平均法 度量空间中点Middle point 中点Mid-point 中值Mid-value 最小的Minimal 最小点Minimal point 最小值Minimal value 最小值Minimum 最小方差估计 子式Minimum variance estimation Minor 子行列式次对角线减、负Minor determinant Minor diagonal Minus 负无穷大带分数Minus infinity Mixed fraction 混合偏导数 众数Mixed partial derivative Mode 模Moduli 模Modulo 模Modulus 复数的模矩Modulus of complex number Moment 矩函数Moment function Moment generating function Moment method of estimation Monodrome function Monogamy 矩母函数矩估计法单值函数一一对应单项式Monomial expression Monotone 单调单调收敛定理 单调递减单调递增单调序列单调数列单调减少单调函数单调增加单调减少函数 单调增加函数 单调性Monotone convergence theorem Monotone decreasing Monotone increasing Monotone sequence Monotone sequence of numbers Monotonic decreasing quantity Monotonic function Monotonic increasing quantity Monotonically decreasing function Monotonically increasing function Monotonicity 单值函数可去奇点可去奇点m 次样条函数 多维的Monotropic function Movable singular point Moving singularity m-splines Multidimensional Multidimensional normal distribution多维正态分布多值函数多项式Multiform function Multinomial 复合Multiple 多重特征值 多重积分多重极限重数Multiple eigenvalues Multiple integral Multiple limits Multiple numbers 重根Multiple root 多值函数矩阵乘法乘法定理特征值的重数 根的重数多值函数多元正态分布 多元样条函数 互不相容互逆的Multiple valued function Multiplication of matrices Multiplication theorem Multiplicity of eigenvalue Multiplicity of root Multivalued function Multivariate normal distribution Multivariate splines Mutually exclusive Mutually inverse 自然对数自然对数n 维正态分布 n 维概率分布 n 维空间Napierian logarithms Natural logarithm n-dimensional normal distribution n-dimensional probability distribution n-dimensional space Necessary and sufficient condition Necessary condition 充分必要条件 必要条件负的Negative 负相关Negative correlation Negative definite matrix Negative definite quadratic form Negative number 负定矩阵负定二次型 负数半负定二次型 负号Negative semidefinite quadratic form Negative sign 邻域Neighborhood 牛顿插值公式 n 重极限Newton’s interpolatio n formula n-fold limit 幂零矩阵不可数集不可微函数 不可数集非齐次的非齐次微分方程非齐次线性微分方程 非齐次线性方程 非线性的非线性方程 Nilpotent matrix Non-denumerable set Non-differentiable function Non-enumerable set Non-homogeneous Non-homogeneous differential equation Non-homogeneous linear differential equation Non-homogeneous linear equation Nonlinear Nonlinear equation非线性回归非线性回归分析非负定矩阵非奇异的非奇异线性变换非奇异矩阵非零向量正态分布法线Nonlinear regression Nonlinear regression analysis Nonnegative definite matrix NonsingularNonsingular linear transformation Nonsingular matrixNon-vanishing vectorNormal distributionNormal line标准正交基正态总体零因子Normal orthogonal basis Normal populationNull divisor零矩阵Null matrix零点Null point零解Null solution零向量Null vector排列数Number of permutationsNumerable可数的分子Numerator数值分析数值计算数值计算数值计算数值积分组合Numerical analysis Numerical calculation Numerical computation Numerical evaluation Numerical integration Combination观测值Observed value 钝角Obtuse angle钝角三角形事件的出现奇函数Obtuse triangle Occurrence of event Odd function奇数Odd number奇排列Odd permutationOdd-even奇偶奇偶性Odevity一维概率分布一一映射单侧One-dimensional probability distribution One-one mappingOne-sided单侧导数单侧极限一一对应一一映射单值函数开区间One-sided derivativeOne-sided limitOne-to-one correspondence One-to-one mappingOne-valued function Open interval开邻域Open neighborhoodOpen region开区域开集Open set 运算法则 最优解 Operational rule Optimal solution Optimize 最优化 最优解 Optimum solution Optimum value Order of a differential equation Order of a matrix Order of infinitesimal Order of infinity Ordinary differential Ordinary differential equation Origin 最优值微分方程的阶 矩阵的阶 无穷小的阶 无穷大的阶 常微分常微分方程 原点初始值 Original value 垂心Orthocenter 正交的 Orthogonal 正交基 Orthogonal basis Orthogonal transformation Orthogonal vectors Orthogonalization Orthonormal basis Oscillatory series Outer diameter 正交变换 正交向量 正交化标准正交基 振荡级数 外径外点Outer point 无顺序 Out-of-order 外径Outside diameter Pairwise independence Pairwise independence events Pairwise orthogonal Parabola 两两独立两两独立事件 两两正交 抛物线 抛物柱面 悖论Parabolic cylinder Paradox 平行Parallel 平行直线 平行四边形 参数Parallel straight lines Parallelogram Parameter 参数估计 总体参数 参数方程 参变量 Parameter estimation Parameter of population Parameter equation Parametric variable Parenthesis 圆括号 奇偶性 Parity 奇偶数字 部分相关 偏导数 Parity digit Part correlation Partial derivative偏微分Partial differential Partial differential equation Partial fraction expansion Partial sum 偏微分方程 部分分式展开 部分和 特解Particular solution Partitioned matrix Peak 分块矩阵 峰值百分数 Percentage 周长Perimeter 周期Period 循环小数 容许误差 排列Periodic decimal Permissible error Permutation 垂线Perpendicular 垂直Perpendicularity Piecewise 分段分段函数分段线性插值 分段多项式插值 枢轴元素 旋转Piecewise function Piecewise linear interpolation Piecewise polynomial interpolation Pivotal Pivoting 平面图形 平面Planar graph Plane 平面几何 极坐标 Plane geometry Plane polar coordinates Plumb-line 铅垂线 正无穷大 点估计 Plus infinity Point estimation Point of discontinuity Point of inflection Point of intersection Point of tangency Point slope form Poisson distribution Polar axis 间断点 拐点交点切点点斜式 泊松分布 极轴极坐标 Polar coordinates Polar radius 极半径 极点Pole 极坐标的极点 多边形 Pole of polar coordinates Polygon 多项式Polynomial 多项式插值函数 n 次多项式 总体Polynomial interpolating function Polynomial of degree n Population 总体中心矩 Population central moment总体分布总体均值总体矩Population distribution Population mean Population moment Population parameter Population variance Positive总体参数总体方差正的正定的Positive definite正定矩阵正定二次型正定对称矩阵正整数Positive definite matrixPositive definite quadratic form Positive definite symmetric matrix Positive integer正数Positive number半正定的半正定矩阵半正定二次型正平方根正项级数正定矩阵可能性Positive semi-definitePositive semi-definite matrix Positive semi-definite quadratic form Positive square rootPositive term seriesPositively definite matrix Possibility后验概率右乘Posterior probability Postmultiplication Postulate公设幂Power幂函数Power function幂数Power of a numberPower series幂级数幂级数展开原函数Power series expansion Primary function素数Prime number主对角线主子式Principal diagonal Principal minor微分算子的主部主值Principal part of a differential operator Principal value先验概率概率模型概率Prior probability Probabilistic model Probability依概率收敛概率分布概率论Probability convergence Probability distribution Probability theory Process of iteration Product event迭代法积事件乘积公式集的交Product formula Product of sets右导数Progressive derivativeProlate axis长轴反证法 归纳证明 真分数 真子集 真包含 连续性 命题Proof of contradiction Proof of induction Proper fraction Proper subset Proper include Property of continuity Proposition 伪码Pseudo code 纯虚数 二次的 二次曲线 二次型 二次函数二次齐次多项式 平方根 平方和 二次曲面 二次项 求积分 二次曲线 二次柱面 二次型 二次曲面 分位数 拟牛顿法 商Purely imaginary number Quadratic Quadratic curve Quadratic form Quadratic function Quadratic homogeneous polynomial Quadratic root Quadratic sum Quadratic surface Quadratic term Quadrature Quadric curve Quadric cylinder Quadric form Quadric surface Quantile Quasi-Newton method Quatient 弧度Radian 根号Radical 被开方数 开方Radicand Radication 半径Radius 小数点 随机的 随机事件 随机试验 随机变量 随机向量 随机性函数的值域 秩Radix point Random Random event Random experiment Random variable Random vector Randomness Range of function Rank 稀疏Rarefaction 比率Ratio 等比Ratio of equality Rational fraction Rational number 有理分式 有理数射线Ray瑞利分布实的Rayleigh distribution Real实轴Real axis实数Real number实二次型倒数Real quadratic form Reciprocal互逆矩阵矩形Reciprocal matrix Rectangle直角坐标直角坐标系递推公式接受域收敛区域拒绝域回归Rectangular coordinates Rectangular coordinate system Recurrence equationRegion of acceptance Region of convergence Region of rejection Regression回归分析回归方程相关系数等价关系相对导数相对误差剩余Regression analysis Regression equation Related coefficient Relation of equivalence Relative derivative Relative error Remainder可去间断点累次积分累次极限重根Removable discontinuity Repeated integral Repeated limits Repeated root Residual残差残差平方和弹性Residual sum of squares Resilience可逆的菱形Reversible Rhomb直角Right angle右连续性右导数直角三角形罗尔定理根Right continuous Right derivative Right triangle Rolle’s theouem Root开平方根均方根舍入误差行RootingRoot-mean-square Round off error Row行秩Row rank行向量鞍点Row vector Saddle样本Sample样本均值样本相关系数样本均值样本矩Sample averageSample correlation coefficient Sample meanSample momentSample point样本点样本容量样本空间样本标准差样本方差抽样Sample sizeSample spaceSample standard deviation Sample variance Sampling抽样检验斯密特正交化法正割Sampling inspection Schmidt’s orthogonalization Secant次对角线分段连续扇形Secondary diagonal Sectionally continuous Sector半轴Semi-axis 半圆Semi-circle半定二次型半正定型序列Semi-definite quadratic form Semi-positive definite form Sequence事件序列数列Sequence of events Sequence of numbers Series级数级数展开函数级数集合Series expansion Series of functions Set方程组Set of equationsSet union集的并符号差Signature显著水平有效数字相似矩阵相似三角形相似性Significance level Significant figure Similar matrices Similar triangles Similarity相似变换简单平均简分数Similarity transformation Simple averageSimple fractionSimple root单根联立方程正弦Simultaneous equations Sine奇异的Singular奇异矩阵正弦曲线Singular matrix Sinusoidal curve斜率Slope解向量空间Solution vector Space稀疏矩阵球形Sparse matrix Sphere球冠Spherical cap 球冠Spherical crownSpline样条样条函数迹Spline function Spur矩阵的迹平方Spur of matrix Square方阵Square matrixSquare root 平方根残差平方和标准差标准正态分布标准化随机变量初始值统计Square sum of residues Standard deviation Standard normal distribution Standardized random variable Starting valueStatistic统计假设最速下降算法步长Statistical hypothesis Steepest descent algorithm Step length随机的直线Stochastic Straight line严格单调严格单调递减严格单调递增子集Strictly monotoneStrictly monotone decreasing Strictly monotone increasing Subaggregate子块Subblock子行列式子矩阵子集Subdeterminant Submatrix Subset代换Substitution充分条件充分估计量充分统计量并集Sufficient condition Sufficient estimates Sufficient statisticsSum aggregateSum of squares of deviations Supremum离差平方和上确界补集SupplementarySymmetric对称对称矩阵系统误差坐标系Symmetric matrix System error System of coordinates方程组System of equations System of fundamental solutions System of linear equations System of nonlinear equations Tangent 基础解系线性方程组非线性方程组 正切切线Tangent line 曲线的切线方程 切线Tangential equation of a curve Tangential line 泰勒级数泰勒公式t 分布Taylor series Taylor’s formula t-distribution 逐项微分多项式的项级数的项假设检验检验统计量假设检验立方Term by term differentiation Term of a polynomial Term of a series Test of hypothesis Test statistics Testing of hypothesis Third power 三维空间全微分Third-dimensional space Total differential Total differentiation Total probability Totality 全微分全概率总体迹Trace 矩阵的迹变换Trace of a matrix Transform 变换Transformation 变换矩阵坐标变换转置Transformation matrix Transformation of coordinates Transpose 矩阵的转置转置矩阵横截面Transpose of a matrix Transposed matrix Transversal surface Triangle 三角形三角函数三角行列式三角矩阵截短误差二维空间二重极限两点分布双侧检验无偏的Triangle function Triangular determinant Triangular matrix Truncation error Two-dimensional space Two-limit Two-point distribution Two-sides test Unbiased 无偏估计无偏估计 Unbiased estimate Unbiased estimation无偏性Unbiasedness Underdeterminant Uniform distribution Uniformly minimum variance unbiased estimation Unilateral limit Union 子行列式均匀分布一致最小方差无偏估计 单侧极限并集合的并唯一解Union of sets Unique solution Unit circle 单位圆单位长度单位向量未知数Unit length Unit vector Unknown number Unsymmetrical Untrivial solution Upper bound 不对称的非零解上界上三角矩阵有效性Upper triangular matrix Validity 趋于零Vanishingly 变量Variable 方差Variance 方差分析变量Variance analysis Variant 簇Variety 向量Vector 向量范数向量积Vector norm Vector product Vector space 向量空间铅垂渐近线竖轴Vertical asymptote Vertical axis 弱收敛Weak convergence Weak law of large numbers Weight 弱大数定律权加权平均值加权平均值无偏性Weighted average Weighted mean Without bias 零一分布 Zero-one distribution。
胡壮麟《语言学教程》第一章-第六章重难点
名词解释Syntactic function/ predicate/ performance/ tone/ semi-vowels/ minimal pairs/ intonation/ competence/ proposition/ cognitionMinimal pair, semi vowels, tone, intonation, competence, performance, predicate, syntactic function, proposition, cognition, conceptual metaphors, image schemas, hyponymy, endocentric construction, inflection Minimal pair refers to a pair of words, as pin and bin, or sheep and ship, differing only by one sound in the same position in each wordSemi-vowels The segments are neither vowels nor consonants but midway between the two categories.Intonation the occurrence of recurring fall-rise patterns, each of which is used with a set of relatively consistent meanings, either on single words or on groups of words of varying length. Tone a set of fall-rise patterns affecting the meanings of individual words.Predicate refers to a major constituent of sentence structure in binary analysis in which all obligatory constituents other than the subject were considered together.A language user’s underlying knowledge about the system ofrules is called his linguistic competence.Performance refers to the actual use of language in concrete situation.Syntactic function shows the relationship between a linguistic form and other parts of the linguistic pattern in which it is used. Cognition In psychology it is used to refer to the mental processes of an individual, with particular relation to a view that argues that the mind has internal mental states and can be understood in terms of information processing, especially when a lot of abstraction or concretization is involved, or processes such as involving knowledge, expertise or learning for example are at work. In cognitive linguistics, cognition refers to the conceptualization of linguistic structures and patterns.A proposition is what is expressed by a declarative sentence when that sentence is uttered to make a statement.Chapter 1Design feature of languageArbitrariness1.bowwow 汪汪2.Syntactic level 有句法顺序3.Convention 约定俗成为什么树叫树而不是别的Duality1.底层构建上层Creativity/productivity1.duality 不同地层结构可以组成很多上层结构2.Recursiveness 句子可以无限长Displacement1.不受限制，可以谈论过去/未来，真的/假的Functions of languageHalliday —— ideational，interpersonal，textual◆Informative function 语言用于表达一个概念或内容◆Interpersonal function◆Performative function （change social status如结婚词，定罪词，表达动作，我让你去关门）◆Emotive function 感叹词（damn it）◆Phatic communion 寒暄功能（问你吃了吗，并不真的问吃了没）◆Recreational function 写诗陶冶情操◆Metalingual function 用语言解释语言（词典中，一个词下很多释义）Important distinctions in linguistics◆Descriptive VS prescriptive尊重语言事实，客观描述约定俗成的现在更关注descriptive◆Langue & Parole （更倾向于parole）Saussure 提出（社会角度）Langue 语言（抽象）parole 从小生活在某个社区影响的语言◆Competence & performance （心理角度）Chomsky提出天生具备的语言能力依据参数规则转化出所说所写A knowledge of grammar, to incorporate the pragmatic communicative competence --communicative competenceChapter 2Gesture -- movements of the tongue and the lipsVoiceless consonants-- air can pass through easilyvoiced consonants -- airstream causes them to vibrate against each otherConsonants and vowels 区别（obstruction of airstream）元音不受阻P32, 33 图（⚠）例如：voiceless bilabial stopVoiced bilabial stopVoiceless alveolar fricativeVoiceless velar stopGlottal, palatal, lateral, affricative, approximant例如：high front tense unrounded vowelHigh back lax rounded vowelPhonemes: refers to a unit of explicit sound contrast; the existence of a minimal pair automatically grants phonemic status to the sounds responsible for the contrasts.Allophones 音位变体「p」「ph」都是/p/的音位变体，且二者为互补分配（complementary distribution）Assimilation 同化（受周边影响）Nasalization （cap-can）Dentalization （tent-tenth）Velarization （since-sink）Regressive Assimilation （逆同化，后者受前者影响）progressive Assimilation （相反）Rule ordering冠词规则：The elsewhere conditionThe more specific rule supplies first （最特殊的规则最先用）SyllableNucleus 一般为元音Maximal onset principle (MOP) 最大节首原则如：telling /l/ 划分到节首(ling 的节首)Intonation and toneIntonation-- fall-rise tonesChinese is tone language.Tone sandhi 连续变调你好（你变三声）Obligatory contour principle (OCP) {identical adjacent elements are not allowed}Chapter3Morpheme◆Free Morpheme 可以独立存在◆Bound Morpheme 不可以Stem=root+（Bound Morpheme）如：cat 的stem和root都是catRoot：nature stem：naturalAffix - prefix，suffix，infix（-um-），circumfix（gr--t）Allomorphs同位异形体in-，ir-，im-都有表示否定，但因为phonological requirement 而区别开Lexeme 词位Walk - lexeme；walked，walking - word formContent words（open class words）and function words（closed class words）◆Derivation （lexeme+affix）◆Compounding （lexeme+lexeme）Attributive compound（windmill）wind修饰millCoordinative compound （teacher-student）并列Subordinative compound （truck-driver）左名词，右动词变形存在（drive变driver）即synthetic compound；不存在即root compoundInflection 曲折构词曲折词缀主要是表达不同的语法关系或语法范畴，如数、时、格等。
语言学定义
1.Cohort model交股模型model for he perception of spoken words proposed in the mid-1980s.It assumes a “recognition lexicon" in which each word is represented by a full and independent “recognition element”. When the system receives the beginning of a relevant acoustic signal, all elements matching it are fully activated, and, as more of the signal is received, the system tries to match it independently with each of them, Wherever it fails the element is deactivated; this process continues until only one remains active.2. Cohort theory:it refers to hypothesizes that auditory word recognition begins with the formation of a group of words at the perception of the initial sound and proceeds sound by sound with the cohort of words decreasing as more sounds are perceived.3. Interactive model交互模型It holds that in recognizing the spoken words higher processing levels have a direct, “top-down” influence on lower levels. Lexical knowledge can affect the perception of phonemes. There interactivity in the form of lexical effect on the perception of sublexical units. In certain case, listeners’ knowledge of words can lead to the inhibition of certain phonemes; in other cases, listeners continue to hear phonemes that have been removed from the speech signal and replaced by noise.4.Construal识解The ability to conceive and portray the same situation in different ways (through specificity, different mental scanning, directionality, vantage point figure- ground segregation )5.Construal operations识解操作Are conceptualizing process used in language process by human beings. That is, construal operations are the underlying psychological processes and reasons employed in the interpretation of linguistic expression.6.Figure- ground alignment seems to apply to space with the ground as the propositional object and the proposition expressing the spatial relation configuration. It also applies to human perception of moving objects.7. Trajector射体means a moving or dynamic figure.8. Landmark路标means the ground provided for a moving figure.9. Basic level category: is the most economical level at which you can find the most relevant information. The information on our interaction with subjects in the real world is stored at this level. It is at this level that we conjure up the general gestalt of the category10. Subordinate level 下属层次Is the level at which we perceive the differences between the members of the basic level categories.11. Image schema is a recurring, dynamic pattern of our perceptual interactions and motor programs that gives coherence and structure to our experience.12.Conceptual Metaphor is a conceptual mapping, not a linguistic one, from one domain to another, not from a word to another13.Blending theory；also known as the integration theory, A cognitive operation whereby elements of two or more “mental space” are integrated via projection into a new, blended space which has its unique structure.14.SPEAKING交际民族学的研究模式A mnemonic way of summarizing certain components of speech which make possible for the description and analysis of communication behavior: situation, participants, ends, act sequence, key instrumentalities, norms and genres.15 Speech community言语社团A group of people who form a community and share the same language or a particular variety of language.16 Sapir-Whorf Hypothesi: Our language helps mould our way of thinking and different languages may probably express our unique way of understanding the world. In a loose sense, this term can be interchangeably used with linguistic relativity and linguistic determinism.17 linguistic relativity语言相对性similarity between languages is relative, the greater their structural differentiation is, the more diverse their conceptualization of the world will be. For this reason, this hypothesis has alternatively been referred to as linguistic determinism and linguistic relativity-----a view which “was first expounded by the German ethnologist, Wilhelm von Humboldt”. 18 linguistic determinism is a theory which believes that our language will influence or decide our way of looking at the world19 The strong version of the theory:refers to the claim the original hypothesis suggests, emphasizing the decisive role of language as the shaper of our thinking patterns.20 The weak version :is modified type of its original theory , suggesting that there is a correlation between language, culture, and thought, but the cross-culture differences thus produced in our way of thinking are relatives, rather than categorical.21 Pidgin 皮钦语Is a special language variety that mixes or blends languages and it is used by people who speak different languages for restricted purposes.22 Creole: When a pidgin has become the primary language of a speech community, and is acquired by the children of that speech community as their native language.23 Diglossia双言制First used by Ferguson. Two distinctive varieties of the same languages are used, side by side, for two different sets of functions. It is a matter of formality in nature.24Bilingualism双语现象In some speech communities, two languages are used side by side with each other having a different role to play, and language switching occurs when the situation changes.25Speech act theory: “Speech act theory” was proposed by John Austin and has been developed by his student J. Searle. Basically, they believe that language is not only us ed to inform or to describe things, it is often used to “do things”, and to perform acts. While making an utterance, a speaker is performing three acts simultaneously: an illocutionary act, an illocutionary act, and a perlocutionary act.26 illocutionary act言内行为the act of uttering words, phrases, clauses. It’s an act of conveying literal meaning by means of syntax, lexicon, and phonology. Namely, the act of saying something: the utterance of a sentence with determinate sense and reference. 27 illocutionary act言外行为the act of expressing the speaker’s intention; it is the act performed in saying something; its force is identical with the speaker’s intention. The making of a statement, offer promise, etc, in uttering a sentence, by virtue of the conventional force associated with it. The act of using a sentence to perform a function such as command, request, etc28 Perlocutionary act言后行为the act performed by or resulting from saying something, it's the consequence of, or the change brought about by the utterance; it is the act performed by saying something, the bringing about of effects on the audience by means of uttering the sentence, such effects being special to the circumstances. the results or effects that are produced by means of saying sth.29Constative叙事话语Constatives are statements that either state or describe, and are thus verifiable and constatives bearing the truth-value.30 Performative行事Are statements used to perform an action, it has no truth value.31 conversational implicature会话含义the extra meaning not contained in the literal utterances, understandable to the listener only when he shares the speaker’s knowledge or knows why and how he violates intentionally one of the four maxims of the cooperative principle. Is a type of implied meaning, which is deduced on the basis of the conversational meaning of words together with the context, under the guidance of the cp and its maxims.32the cooperative Principle( cp)合作原则Make your contribution such as is required at the stage at which it occurs, by the accepted purpose or direction of the exchange in which you are engaged. Proposed and formulated by P.Grice, a pragmatic hypothesis, is about that the participants must first of all be willing to cooperate; otherwise, it would not be possible for them to carry on the talk.33 Entailment 蕴含This is a logical relationship between two sentences in which the truth of the second necessarily follows from the truth of the first, while the falsity of the first follows from the falsity of the first.34 Presupposition预设Is that shared background information. In essence, presupposition is a pragmatic notion, because it is the speaker who presupposes by means of an utterance, rather than the sentence or the utterance itself.35 Ostensive communication明示推理交际From the speaker’s side, communication should be seen as an act of making clear one’s intention to express something. They maintain that inference has only to do with the hearer.36Relevance: a property that any utterance, or a proposition that it communicates, must, in the nature of communication, necessarily have. •Relevance is a comparative concept, so they also have an extent-conditions format:•Extent condition 1: an assumption is relevant in a context to the extent that its contextual efforts in this context are large.Extent condition 2: an assumption is relevant in a context to the extent that the effort required to process it in this context is small37 Euphemism: A euphemism, then, is a mild, indirect or less offensive word or expression substituted when the speaker or writer fears more direct wording might be harsh, unpleasantly direct, or offensive.38 Speech variety, also known as language variety, refers to any distinguishable form of speech used by a speaker or group of speakers. Thedistinctive characteristics of a speech variety may be lexical, phonological, morphological, syntactic, or a combination of linguistic features.39 language planning: language standardization is known as language planning. This means that certain authorities, such as the government or government agency of a country, choose a particular speech variety and spread the use of it, including its pronunciation and spelling systems, across regional boundaries.40 standard language : The standard language is a superposed, socially prestigious dialect of language. It is the language employed by the government and the judiciary system, used by the mass media, and taught in educational institutions, in-cluding school settings where the language is taught as a foreign or second language.•。
心智图在高中国文教学的运用
心智圖在高中國文教學的運用王開府壹、參考論文王開府(2008)，心智圖與概念模組在語文閱讀與寫作思考教學之運用，國文學報，43期，頁263-296心智圖與概念模組在語文閱讀與寫作思考教學之運用國立臺灣師範大學國文學系教授王開府摘要本文的研究目的，在探討思考教學在國語文課程之運用，特以心智圖為例。
本文探討概念構圖、心智構圖；比較概念圖法與心智圖法的異同。
論述語文思考教學中概念模組(concept model) 的重要性，提出可用的多種概念模組。
並引用範文為例，說明概念模組在使用心智圖進行閱讀與寫作教學之實際運用。
關鍵詞：思考教學、語文教學、心智圖、概念圖、概念模組、閱讀、寫作AbstractApplying Mind Map and “Concept Model” tothe Teaching of Reading and Writing in Thinking Curriculum of LanguageWang, Kai-FuuDepartment of Chinese, National Taiwan Normal University, R.O.C.The purpose of this study is to probe into teaching thinking in Chinese language curriculum, and use mind map as an illustration for it. In the paper, concept mapping and mind mapping are discussed. It also compares mind mapping with concept mapping in details. It emphasizes the significance of “concept model” used in teaching thinking in language curriculum. Many useful concept models are offered here. By means of some text examples, it discourses the practical application of concept models in which we use mind map in teaching reading and writing.Keywords: teaching thinking, teaching language, assessment, mind map, concept map, concept model, reading, writing.一、研究目的87年9月教育部公布「國民教育九年一貫課程總綱」，其「基本理念」已指出教育之諸多目的中，包含了培養「思考、判斷與創造能力」，並且主張課程基本內涵應包括「獨立思考」。
CH7
1. Mental Representation of Knowledge
3. Dual-Code Theory: Analogical Images Versus Symbols • Dual-Code theory (Allan ivio, 1969)
– We use both images (in analogue codes) and words (in a symbolic code) for representing information
2. Mental Manipulations of Images
1. Mental Rotations • Functional-equivalence hypothesis does apply to image scaling
– Participants were asked to observe pairs of twodimensional (2-D) pictures showing three-dimensional (3-D) geometric forms – Participants then were asked to tell whether a given image was or was not a rotation of the original stimulus (p. 127) – The response times for answering the questions about the figures formed a linear function of the degree to which the figures were rotated; i.e. for each increase in the degree of rotation of the figures, there was a corresponding increase in the response times
人类脑科学研究计划的进展
人类脑科学研究计划的进展【摘要】理解大脑的工作机制是人类科学发展的终极命题，2013年欧盟和美国相继宣布投入大量资金开展新一轮的脑研究计划，我国也于2016年推出中国的脑研究计划。
脑科学研究不仅是当下神经科学的研究前沿，更是解决神经精神疾病带来的日益增加的社会负担的突破口。
本文总结了世界主要发达国家的脑研究计划进展，并重点介绍我国脑计划的布局、展开及优势，以期为广大科研工作者提供最新的脑科学研究国际动向和国内发展情况。
【关键词】脑计划; 脑科学; 类脑智能【Abstract】 Understanding the working mechanism of the brain is the ultimate proposition for the development of human science.In 2013，the European Union and the United States announced that they had invested large funds to carry out a new round of brain research programs，and China also launched a brain research program in 2016.Brain science research is not onlythe frontier of neuroscience research，but also the breakthrough to solve the increasing social burden caused by neuropsychiatric diseases.This paper summarizes the progress of brain research projects in major developedcountries in the world，and emphatically introduces the layout，developmentand advantages of brain projects in China，in order to provide the latest international and domestic development situation of brain science research for the majority of scientific researchers.【Key words】 Brain project; Brain science; Brain-inspired intelligenceFirst-author’s address：Department of Anatomy and K.K.Leung Brain Research Centre，the Fourth Military Medical University，Xi’an 710032，Chinadoi：10.3969/j.issn.1674-4985.2019.07.044腦是支配人的一切生命活动的最高中枢，也是一切思维活动的物质基础，对人类大脑的研究是人类认识自身的一项终极挑战。
产品经理工作流程英文版
产品经理工作流程英文版The role of a product manager is a multifaceted one, encompassing a wide range of responsibilities that are crucial to the success of any product or service. From ideation to launch and beyond, the product manager is the driving force behind the development and implementation of a product that meets the needs of the target market. In this essay, we will delve into the comprehensive work process of a product manager, highlighting the key steps and considerations involved.Ideation and Market ResearchThe product manager's journey begins with the identification of a market need or opportunity. Through extensive market research, they gather valuable insights into the target audience, their pain points, and their preferences. This research may involve conducting surveys, analyzing industry trends, and engaging with potential customers to understand their needs and expectations.With a deep understanding of the market, the product manager then collaborates with cross-functional teams, such as engineering, design,and marketing, to generate innovative product ideas. This ideation process often involves brainstorming sessions, user scenario mapping, and concept validation to ensure the proposed solutions align with the identified market needs.Product Definition and RoadmappingOnce the product idea has been solidified, the product manager takes on the crucial task of defining the product's features, functionality, and user experience. This involves creating detailed product specifications, user stories, and wireframes that serve as a blueprint for the development team.Alongside the product definition, the product manager develops a comprehensive product roadmap. This roadmap outlines the product's strategic vision, prioritizes feature development, and aligns the various teams involved in the product's lifecycle. The roadmap serves as a guiding document, ensuring that the product evolves in a cohesive and strategic manner.Agile Development and CollaborationIn the modern software development landscape, the product manager often works within an agile framework, collaborating closely with the engineering team throughout the development process. This collaboration involves regular check-ins, sprint planning, and the review of incremental product releases.The product manager acts as the bridge between the development team and the business, translating user requirements into technical specifications and providing feedback on the product's progress. They also work closely with the design team to ensure the product's user experience aligns with the overall vision and meets the needs of the target audience.Continuous Feedback and IterationAs the product moves through the development cycle, the product manager actively solicits feedback from various stakeholders, including end-users, sales teams, and customer support. This feedback is then incorporated into the product roadmap, driving the continuous improvement and iteration of the product.The product manager carefully analyzes user behavior, usage metrics, and market trends to identify areas for enhancement and optimization. They work with the development team to prioritize and implement these improvements, ensuring the product remains relevant and competitive in the market.Launch and Go-to-Market StrategyWhen the product is ready for launch, the product manager collaborates with the marketing and sales teams to develop a comprehensive go-to-market strategy. This strategy encompassesvarious elements, such as pricing, packaging, promotional campaigns, and distribution channels.The product manager plays a crucial role in aligning the go-to-market efforts with the product's value proposition and target audience. They work closely with the marketing team to craft compelling messaging, develop sales enablement materials, and ensure a seamless customer experience from the initial awareness stage to the final purchase.Post-Launch Monitoring and OptimizationThe product manager's responsibilities do not end with the product launch. They continue to monitor the product's performance, analyze customer feedback, and identify areas for ongoing improvement. This may involve adjusting pricing, refining features, or addressing customer pain points.The product manager also collaborates with the customer success and support teams to gather valuable insights from the field, ensuring that the product remains aligned with the evolving needs of the customer base. These insights are then fed back into the product roadmap, driving the continuous evolution and optimization of the product.ConclusionThe work process of a product manager is a dynamic and multifaceted endeavor that requires a unique blend of strategic thinking, technical understanding, and customer-centric focus. From the initial ideation and market research to the post-launch monitoring and optimization, the product manager plays a pivotal role in the success of any product or service.By navigating the various stages of the product lifecycle, the product manager ensures that the product not only meets the needs of the target market but also remains competitive and relevant in an ever-changing landscape. The product manager's ability to collaborate effectively with cross-functional teams, make data-driven decisions, and continuously adapt to market trends is essential in driving the success of any product or service.。
认知的具身化（Embodiment）
认知的具身化（Embodiment）摘要：随着认知的计算隐喻的局限和困境的加深，从上个世纪80年代以来，在认知科学中具身化（embodiment）的观念已经受到越来越多的强调。
具身化、情境性和生成的思想在认知科学中已经有了广泛的融合。
具身认知的思想认为，认知不是一个先验的逻辑能力，而是一个连续进化的发展的情境性过程；身体在认知中之所以是核心的，是因为身体活动本身体现了推动认知发展的生存意向性。
皮亚杰和维果斯基的内化理论、莱考夫和约翰逊的隐喻投射理论表明了身体活动如何向高级认知发展的。
目前借助动力系统理论，关于具身认知的神经建模研究也蓬勃发展起来了。
一个对认知更为全景的轮廓已经形成。
关键词：认知|情境性|生成|具身化|动力学。
随着认知的计算隐喻的局限和困境的加深，从上个世纪80年代以来，在认知科学中具身化（embodiment）的观念已经受到越来越多的强调：“在哲学、心理学、神经科学、机器人学、教育、认知人类学、语言学以及行为和思想的动力系统进路（approach）中，人们已经日益频繁地谈到具身化和情境性（situatedness）。
”[1]例如，在认知发展领域有西伦（E. Thelen）的工作；在语言学领域有莱考夫（G. Lakoff）和约翰逊（M. Johnson）的工作；在机器人学领域有鲍拉德（Ballard）、黑霍（Hayhoe）、普克（Pook）、和劳（Rao）的工作；在神经科学和动力学领域有西伦、盖拉德（T. van Gelder）、希尔（Chiel）、比尔（Beer）、埃德尔曼（G. M. Edelman）；在哲学领域有克拉克（A. Clark）、瓦雷拉（F. J. Varel）、汤普森（E. Thompson）和罗施（Rosch）的工作；等等。
1 具身认知1.1 关于“embodied” 和“embodiment”的译法和用法目前关于“embodiment”和“embodied”，国内还没有形成一个统一的译法。
英语数学词汇
Algebraic Equation代数方程Elementary Operations-Addition基础混算-加法Elementary Operations-Subtaction基础混算-减法Elementary Operations-Multiplication 基础混算-乘法Elementary Operations-Division基础混算-除法Elementary Operation基础四则混算Decimal Operations小数混算Fractional Operations分数混算Convert fractional no. into decimal no. 分数转小数Convert fractional no. into percentage. 分数转百分数Convert decimal no. into percentage. 小数转百分数Convert percentage into decimal no. 百分数转小数Percentage百分数Numerals数字符号Common factors and multiples公因子及公倍数Sorting数字排序Area图形面积Perimeter图形周界Change Units : Time单位转换-时间Change Units : Weight单位转换-重量Change Units :Length单位转换-长度Directed Numbers有向数Fractional Operations分数混算Decimal Operations小数混算Convert fractional no. into decimal no. 分数转小数Convert fractional no. into percentage.分数转百分数Convert decimal no. into percentage.小数转百分数Convert percentage into decimal no.百分数转小数Percentage百分数Indices指数Algebraic Substitution代数代入Polynomials多项式Co-Geometry坐标几何学Solving Linear Equation解一元线性方程Solving Simultaneous Equation解联立方程Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Geometry几何学Inequalities不等式Rate and Ratio比和比例Bearing方位角Trigonometry三角学Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of central tendency统计学-量度集中趋势Salary Tax薪俸税Bridging Game汉英对对碰Indices指数Function函数Rate and Ratio比和比例Trigonometry三角学Inequalities不等式Linear Programming线性规划Co-Geometry坐标几何学Slope直线斜率Equation of Straight Line直线方程x-intercept ( Equation of St. Line )直线x轴截距y-intercept ( Equation of St. Line )直线y轴截距Factorization因式分解Quadratic Equation二次方程x-intercept ( Quadratic Equation )二次曲线x轴截距Method of Bisection分半方法Polynomials多项式Probability概率Statistics-Graph统计学-统计图表Statistics-Measure of central tendency统计学-量度集中趋势Statistics-Measure of dispersion统计学-量度分布Statistics-Normal Distribution统计学-正态分布Surds根式Probability概率Statistics-Measure of dispersion 统计学-量度离差Statistics-Normal Distribution统计学-正态分布Statistics-Binomial Distribution 统计学Statistics-Poisson Distribution 统计学Statistics-Geometric Distribution 统计学Co-Geometry坐标几何学Sequence序列十万Hundred thousand三位数3-digit number千Thousand千万Ten million小数Decimal分子Numerator分母Denominator分数Fraction五位数5-digit number公因子Common factor公倍数Common multiple中国数字Chinese numeral平方Square平方根Square root古代计时工具Ancient timing device古代记时工具Ancient time-recording device 古代记数方法Ancient counting method古代数字Ancient numeral包含Grouping四位数4-digit number四则计算Mixed operations (The four operations)加Plus加法Addition加法交换性质Commutative property of addition未知数Unknown百分数Percentage百万Million合成数Composite number多位数Large number因子Factor折扣Discount近似值Approximation阿拉伯数字Hindu-Arabic numeral定价Marked price括号Bracket计算器Calculator差Difference真分数Proper fraction退位Decomposition除Divide除法Division除数Divisor乘Multiply乘法Multiplication乘法交换性质Commutative property of multiplication乘法表Multiplication table乘法结合性质Associative property of multiplication被除数Dividend珠算Computation using Chinese abacus倍数Multiple假分数Improper fraction带分数mixed number现代计算工具Modern calculating devices售价Selling price万Ten thousand最大公因子Highest Common Factor (H.C.F.)最小公倍数Lowest Common Multiple (L.C.M.)减Minus / Subtract减少Decrease减法Subtraction等分Sharing等于Equal进位Carrying短除法Short division单数Odd number循环小数Recurring decimal零Zero算盘Chinese abacus亿Hundred million增加Increase质数Prime number积Product整除性Divisibility双数Even number罗马数字Roman numeral数学 mathematics, maths(BrE), math(AmE) 公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和 sum减 minus(prep.), subtract(v.), subtraction(n.) 被减数 minuend减数 subtrahend差 remainder乘 times(prep.), multiply(v.), multiplication(n .)被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided by(prep.), divide(v.), division(n.) 被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n 次方根倒数（reciprocal） x的倒数为1/x有理数 rational number无理数 irrational number实数 real number虚数 imaginary number数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil十进制 decimal system二进制 binary system十六进制 hexadecimal system权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit无效数字 insignificant digit代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown, x-factor, y-factor, z-factor等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方 the power of four, the fourth powern次方 the power of n, the nth power开方 evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth rootsqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236常量 constant变量 variable坐标系 coordinates坐标轴 x-axis, y-axis, z-axis横坐标 x-coordinate纵坐标 y-coordinate原点 origin象限quadrant截距(有正负之分)intercede（方程的）解solution几何geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle等腰三角形 isosceles triangle等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width周长 perimeter面积 area相似 similar全等 congruent三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant补充：集合aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition 值域 range单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.)无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral复数 complex number矩阵 matrix行列式 determinant圆 circle 圆心 centre(BrE), center(AmE)半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference轨迹 locus, loca(pl.)平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron旋转 rotation轴 axis球 sphere半球 hemisphere底面 undersurface表面积 surface area体积 volume空间 space双曲线 hyperbola抛物线 parabola四面体 tetrahedron五面体 pentahedron六面体 hexahedron菱形 rhomb, rhombus, rhombi(pl.), diamond正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE), orthocenter(AmE)重心 barycentre(BrE), barycenter(AmE)内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph曲线统计图 curve diagram扇形统计图 pie diagramEnglish Chineseabbreviation 简写符号；简写abscissa 横坐标absolute complement 绝对补集absolute error 绝对误差absolute inequality 绝不等式absolute maximum 绝对极大值absolute minimum 绝对极小值absolute monotonic 绝对单调absolute value 绝对值accelerate 加速acceleration 加速度acceleration due to gravity 重力加速度; 地心加速度accumulation 累积accumulative 累积的accuracy 准确度act on 施于action 作用; 作用力acute angle 锐角acute-angled triangle 锐角三角形add 加addition 加法addition formula 加法公式addition law 加法定律addition law(of probability) （概率）加法定律additive inverse 加法逆元; 加法反元additive property 可加性adjacent angle 邻角adjacent side 邻边adjoint matrix 伴随矩阵algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式algebraic number 代数数algebraic operation 代数运算algebraically closed 代数封闭algorithm 算法系统; 规则系统alternate angle （交）错角alternate segment 内错弓形alternating series 交错级数alternative hypothesis 择一假设; 备择假设; 另一假设altitude 高；高度；顶垂线；高线ambiguous case 两义情况；二义情况amount 本利和；总数analysis 分析；解析analytic geometry 解析几何angle 角angle at the centre 圆心角angle at the circumference 圆周角angle between a line and a plane 直 与平面的交角angle between two planes 两平面的交角angle bisection 角平分angle bisector 角平分线 ；分角线 angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角angle of elevation 仰角angle of friction 静摩擦角; 极限角angle of greatest slope 最大斜率的角angle of inclination 倾斜角angle of intersection 相交角；交角angle of projection 投射角angle of rotation 旋转角angle of the sector 扇形角angle sum of a triangle 三角形内角和angles at a point 同顶角angular displacement 角移位angular momentum 角动量angular motion 角运动angular velocity 角速度annum(X% per annum) 年（年利率X%）anti-clockwise direction 逆时针方向；返时针方向anti-clockwise moment 逆时针力矩anti-derivative 反导数; 反微商anti-logarithm 逆对数；反对数anti-symmetric 反对称apex 顶点approach 接近；趋近approximate value 近似值approximation 近似；略计；逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc length 弧长arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积Argand diagram 阿根图, 阿氏图argument (1)论证; (2)辐角argument of a complex number 复数的辐角argument of a function 函数的自变量arithmetic 算术arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列arithmetic series 等差级数arm 边array 数组; 数组arrow 前号ascending order 递升序ascending powers of X X 的升幂assertion 断语; 断定associative law 结合律assumed mean 假定平均数assumption 假定；假设asymmetrical 非对称asymptote 渐近asymptotic error constant 渐近误差常数at rest 静止augmented matrix 增广矩阵auxiliary angle 辅助角auxiliary circle 辅助圆auxiliary equation 辅助方程average 平均；平均数；平均值average speed 平均速率axiom 公理axiom of existence 存在公理axiom of extension 延伸公理axiom of inclusion 包含公理axiom of pairing 配对公理axiom of power 幂集公理axiom of specification 分类公理axiomatic theory of probability 概率公理论axis 轴axis of parabola 拋物线的轴axis of revolution 旋转轴axis of rotation 旋转轴axis of symmetry 对称轴back substitution 回代bar chart 棒形图；条线图；条形图；线条图base （1）底；（2）基；基数base angle 底角base area 底面base line 底线base number 底数；基数base of logarithm 对数的底basis 基Bayes' theorem 贝叶斯定理bearing 方位（角）；角方向（角）bell-shaped curve 钟形图belong to 属于Bernoulli distribution 伯努利分布Bernoulli trials 伯努利试验bias 偏差；偏倚biconditional 双修件式; 双修件句bijection 对射; 双射; 单满射bijective function 对射函数; 只射函数billion 十亿bimodal distribution 双峰分布binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式binomial distribution 二项分布binomial expression 二项式binomial series 二项级数binomial theorem 二项式定理bisect 平分；等分bisection method 分半法；分半方法bisector 等分线 ；平分线Boolean algebra 布尔代数boundary condition 边界条件boundary line 界（线）；边界bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号breadth 阔度broken line graph 折线图calculation 计算calculator 计算器；计算器calculus (1) 微积分学; (2) 演算cancel 消法；相消canellation law 消去律canonical 典型; 标准capacity 容量cardioid 心脏Cartesian coordinates 笛卡儿坐标Cartesian equation 笛卡儿方程Cartesian plane 笛卡儿平面Cartesian product 笛卡儿积category 类型；范畴catenary 悬链Cauchy sequence 柯西序列Cauchy's principal value 柯西主值Cauchy-Schwarz inequality 柯西 - 许瓦尔兹不等式central limit theorem 中心极限定理central line 中线central tendency 集中趋centre 中心；心centre of a circle 圆心centre of gravity 重心centre of mass 质量中心centrifugal force 离心力centripedal acceleration 向心加速度centripedal force force 向心力centroid 形心；距心certain event 必然事件chain rule 链式法则chance 机会change of axes 坐标轴的变换change of base 基的变换change of coordinates 坐标轴的变换change of subject 主项变换change of variable 换元；变量的换characteristic equation 特征(征)方程characteristic function 特征(征)函数characteristic of logarithm 对数的首数; 对数的定位部characteristic root 特征(征)根chart 图；图表check digit 检验数位checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circular motion 圆周运动circular permutation 环形排列; 圆形排列; 循环排列circumcentre 外心；外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆cissoid 蔓叶class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classical theory of probability 古典概率论classification 分类clnometer 测斜仪clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coaxial 共轴coaxial circles 共轴圆coaxial system 共轴系coded data 编码数据coding method 编码法co-domain 上域coefficient 系数coefficient of friction 摩擦系数coefficient of restitution 碰撞系数; 恢复系数coefficient of variation 变差系数cofactor 余因子; 余因式cofactor matrix 列矩阵coincide 迭合；重合collection of terms 并项collinear 共线collinear planes 共线面collision 碰撞column (1)列；纵行；(2) 柱column matrix 列矩阵column vector 列向量combination 组合common chord 公弦common denominator 同分母；公分母common difference 公差common divisor 公约数；公约common factor 公因子；公因子common logarithm 常用对数common multiple 公位数；公倍common ratio 公比common tangent 公切commutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图compatible 可相容的complement 余；补余complement law 补余律complementary angle 余角complementary equation 补充方程complementary event 互补事件complementary function 余函数complementary probability 互补概率complete oscillation 全振动completing the square 配方complex conjugate 复共轭complex number 复数complex unmber plane 复数平面complex root 复数根component 分量component of force 分力composite function 复合函数; 合成函数composite number 复合数；合成数composition of mappings 映射构合composition of relations 复合关系compound angle 复角compound angle formula 复角公式compound bar chart 综合棒形图compound discount 复折扣compound interest 复利；复利息compound probability 合成概率compound statement 复合命题; 复合叙述computation 计算computer 计算机；电子计算器concave 凹concave downward 凹向下的concave polygon 凹多边形concave upward 凹向上的concentric circles 同心圆concept 概念conclusion 结论concurrent 共点concyclic 共圆concyclic points 共圆点condition 条件conditional 条件句；条件式conditional identity 条件恒等式conditional inequality 条件不等式conditional probability 条件概率cone 锥；圆锥（体）confidence coefficient 置信系数confidence interval 置信区间confidence level 置信水平confidence limit 置信极限confocal section 共焦圆锥曲 congruence (1)全等；(2)同余congruence class 同余类congruent 全等congruent figures 全等图形congruent triangles 全等三角形conic 二次曲 ;圆锥曲conic section 二次曲 ;圆锥曲conical pendulum 圆锥摆conjecture 猜想conjugate 共轭conjugate axis 共轭conjugate diameters 共轭轴conjugate hyperbola 共轭(直)径conjugate imaginary / complex number 共轭双曲conjugate radical 共轭虚/复数conjugate surd 共轭根式; 共轭不尽根conjunction 合取connective 连词connector box 捙接框consecutive integers 连续整数consecutive numbers 连续数；相邻数consequence 结论；推论consequent 条件；后项conservation of energy 能量守恒conservation of momentum 动量守恒conserved 守恒consistency condition 相容条件consistent 一贯的；相容的consistent estimator 相容估计量constant 常数constant acceleration 恒加速度constant force 恒力constant of integration 积分常数constant speed 恒速率constant term 常项constant velocity 怛速度constraint 约束；约束条件construct 作construction 作图construction of equation 方程的设立continued proportion 连比例continued ratio 连比continuity 连续性continuity correction 连续校正continuous 连续的continuous data 连续数据continuous function 连续函数continuous proportion 连续比例continuous random variable 连续随机变量contradiction 矛盾converge 收敛convergence 收敛性convergent 收敛的convergent iteration 收敛的迭代convergent sequence 收敛序列convergent series 收敛级数converse 逆(定理)converse of a relation 逆关系converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形convexity 凸性coordinate 坐标coordinate geometry 解析几何；坐标几何coordinate system 坐标系系定理；系；推论coplanar 共面coplanar forces 共面力coplanar lines 共面co-prime 互质; 互素corollary 系定理; 系; 推论correct to 准确至；取值至correlation 相关correlation coefficient 相关系数correspondence 对应corresponding angles (1)同位角；(2)对应角corresponding element 对应边corresponding sides 对应边cosecant 余割cosine 余弦cosine formula 余弦公式cost price 成本cotangent 余切countable 可数countable set 可数集countably infinite 可数无限counter clockwise direction 逆时针方向；返时针方向counter example 反例counting 数数；计数couple 力偶Carmer's rule 克莱玛法则criterion 准则critical point 临界点critical region 临界域cirtical value 临界值cross-multiplication 交叉相乘cross-section 横切面；横截面；截痕cube 正方体；立方；立方体cube root 立方根cubic 三次方；立方；三次(的)cubic equation 三次方程cubic roots of unity 单位的立方根cuboid 长方体；矩体cumulative 累积的cumulative distribution function 累积分布函数cumulative frequecy 累积频数；累积频率cumulative frequency curve 累积频数曲cumulative frequcncy distribution 累积频数分布cumulative frequency polygon 累积频数多边形；累积频率直方图curvature of a curve 曲线的曲率curve 曲线curve sketching 曲线描绘(法)curve tracing 曲线描迹(法)curved line 曲线curved surface 曲面curved surface area 曲面面积cyclic expression 输换式cyclic permutation 圆形排列cyclic quadrilateral 圆内接四边形cycloid 旋输线; 摆线cylinder 柱；圆柱体cylindrical 圆柱形的damped oscillation 阻尼振动data 数据De Moivre's theorem 棣美弗定理De Morgan's law 德摩根律decagon 十边形decay 衰变decay factor 衰变因子decelerate 减速decelaration 减速度decile 十分位数decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制decision box 判定框declarative sentence 说明语句declarative statement 说明命题decoding 译码decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列decreasing series 递减级数；下降级数decrement 减量deduce 演绎deduction 推论deductive reasoning 演绎推理definite 确定的；定的definite integral 定积分definition 定义degenerated conic section 降级锥曲线degree (1) 度; (2) 次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of confidence 置信度degree of freedom 自由度degree of ODE 常微分方程次数degree of precision 精确度delete 删除; 删去denary number 十进数denominator 分母dependence (1)相关; (2)应变dependent event(s) 相关事件; 相依事件; 从属事件dependent variable 应变量; 应变数depreciation 折旧derivable 可导derivative 导数derived curve 导函数曲线derived function 导函数derived statistics 推算统计资料; 派生统计资料descending order 递降序descending powers of x x的降序descriptive statistics 描述统计学detached coefficients 分离系数(法)determinant 行列式deviation 偏差; 变差deviation from the mean 离均差diagonal 对角线diagonal matrix 对角矩阵diagram 图; 图表diameter 直径diameter of a conic 二次曲线的直径difference 差difference equation 差分方程difference of sets 差集differentiable 可微differential 微分differential coefficient 微商; 微分系数differential equation 微分方程differential mean value theorem 微分中值定理differentiate 求...的导数differentiate from first principle 从基本原理求导数differentiation 微分法digit 数字dimension 量; 量网; 维(数)direct impact 直接碰撞direct image 直接像direct proportion 正比例direct tax, direct taxation 直接税direct variation 正变(分)directed angle 有向角directed line 有向直线directed line segment 有向线段directed number 有向数direction 方向; 方位direction angle 方向角direction cosine 方向余弦direction number 方向数direction ratio 方向比directrix 准线Dirichlet function 狄利克来函数discontinuity 不连续性discontinuous 间断(的);连续(的); 不连续(的)discontinuous point 不连续点discount 折扣discrete 分立; 离散discrete data 离散数据; 间断数据discrete random variable 间断随机变数discrete uniform distribution 离散均匀分布discriminant 判别式disjoint 不相交的disjoint sets 不相交的集disjunction 析取dispersion 离差displacement 位移disprove 反证distance 距离distance formula 距离公式distinct roots 相异根distincr solution 相异解distribution 公布distributive law 分配律diverge 发散divergence 发散(性)divergent 发散的divergent iteration 发散性迭代divergent sequence 发散序列divergent series 发散级数divide 除dividend (1)被除数；(2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor of zero 零因子dodecagon 十二边形domain 定义域dot 点dot product 点积double angle 二倍角double angle formula 二倍角公式double root 二重根dual 对偶duality (1)对偶性; (2) 双重性due east/ south/ west /north 向东/ 南/ 西/ 北dynamics 动力学eccentric angle 离心角eccentric circles 离心圆eccentricity 离心率echelon form 梯阵式echelon matrix 梯矩阵edge 棱；边efficient estimator 有效估计量effort 施力eigenvalue 本征值eigenvector 本征向量elastic body 弹性体elastic collision 弹性碰撞elastic constant 弹性常数elastic force 弹力elasticity 弹性element 元素elementary event 基本事件elementary function 初等函数elementary row operation 基本行运算elimination 消法elimination method 消去法；消元法ellipse 椭圆ellipsiod 椭球体elliptic function 椭圆函数elongation 伸张；展empirical data 实验数据empirical formula 实验公式empirical probability 实验概率；经验概率empty set 空集encoding 编码enclosure 界限end point 端点energy 能; 能量entire surd 整方根epicycloid 外摆线equal 相等equal ratios theorem 等比定理equal roots 等根equal sets 等集equality 等(式)equality sign 等号equation 方程equation in one unknown 一元方程equation in two unknowns (variables) 二元方程equation of a straight line 直线方程equation of locus 轨迹方程equiangular 等角(的)equidistant 等距(的)equilateral 等边(的)equilateral polygon 等边多边形equilateral triangle 等边三角形equilibrium 平衡equiprobable 等概率的equiprobable space 等概率空间equivalence 等价equivalence class 等价类equivalence relation 等价关系equivalent 等价(的)error 误差error allowance 误差宽容度error estimate 误差估计error term 误差项error tolerance 误差宽容度escribed circle 旁切圆estimate 估计；估计量estimator 估计量Euclidean algorithm 欧几里德算法Euclidean geometry 欧几里德几何Euler's formula 尤拉公式；欧拉公式evaluate 计值even function 偶函数even number 偶数evenly distributed 均匀分布的event 事件exact 真确exact differential form 恰当微分形式exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解example 例excentre 外心exception 例外excess 起exclusive 不包含exclusive disjunction 不包含性析取exclusive events 互斥事件exercise 练习exhaustive event(s) 彻底事件existential quantifier 存在量词expand 展开expand form 展开式expansion 展式expectation 期望expectation value, expected value 期望值；预期值experiment 实验；试验experimental 试验的experimental probability 实验概率explicit function 显函数exponent 指数exponential function 指数函数exponential order 指数阶; 指数级express…in terms of…以………表达expression 式；数式extension 外延；延长；扩张；扩充extension of a function 函数的扩张exterior angle 外角external angle bisector 外分角external point of division 外分点extreme point 极值点extreme value 极值extremum 极值face 面factor 因子；因式；商factor method 因式分解法factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式分解factorization of polynomial 多项式因式分解fallacy 谬误FALSE 假(的)falsehood 假值family 族family of circles 圆族family of concentric circles 同心圆族family of straight lines 直线族feasible solution 可行解；容许解Fermat's last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数figure (1)图(形)；(2)数字final velocity 末速度finite 有限finite dimensional vector space 有限维向量空间finite population 有限总体finite probability space 有限概率空间finite sequence 有限序列finite series 有限级数finite set 有限集first approximation 首近似值first derivative 一阶导数first order differential equation 一阶微分方程first projection 第一投影; 第一射影first quartile 第一四分位数first term 首项fixed deposit 定期存款fixed point 定点fixed point iteration method 定点迭代法fixed pulley 定滑轮flow chart 流程图focal axis 焦轴focal chord 焦弦focal length 焦距focus(foci) 焦点folium of Descartes 笛卡儿叶形线foot of perpendicular 垂足for all X 对所有Xfor each /every X 对每一Xforce 力forced oscillation 受迫振动form 形式；型formal proof 形式化的证明format 格式；规格formula(formulae) 公式four leaved rose curve 四瓣玫瑰线four rules 四则four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程fractional index 分数指数fractional inequality 分式不等式free fall 自由下坠free vector 自由向量; 自由矢量frequency 频数；频率frequency distribution 频数分布；频率分布frequency distribution table 频数分布表frequency polygon 频数多边形；频率多边形friction 摩擦; 摩擦力frictionless motion 无摩擦运动frustum 平截头体fulcrum 支点function 函数function of function 复合函数；迭函数functional notation 函数记号fundamental theorem of algebra 代数基本定理fundamental theorem of calculus 微积分基本定理gain 增益；赚；盈利gain perent 赚率；增益率；盈利百分率game （1）对策；（2）博奕Gaussian distribution 高斯分布Gaussian elimination 高斯消去法general form 一般式；通式general solution 通解；一般解general term 通项generating function 母函数; 生成函数generator (1)母线; (2)生成元geoborad 几何板geometric distribution 几何分布geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列geometric series 等比级数geometry 几何；几何学given 给定；已知global 全局; 整体global maximum 全局极大值; 整体极大值global minimum 全局极小值; 整体极小值golden section 黄金分割grade 等级gradient (1)斜率；倾斜率；(2)梯度grand total 总计graph 图像；图形；图表graph paper 图表纸graphical method 图解法graphical representation 图示；以图样表达graphical solution 图解gravitational acceleration 重力加速度gravity 重力greatest term 最大项greatest value 最大值grid lines 网网格线group 组；grouped data 分组数据；分类数据grouping terms 并项；集项growth 增长growth factor 增长因子half angle 半角half angle formula 半角公式half closed interval 半闭区间half open interval 半开区间harmonic mean (1) 调和平均数; (2) 调和中项harmonic progression 调和级数head 正面（钱币）height 高（度）helix 螺旋线hemisphere 半球体；半球heptagon 七边形Heron's formula 希罗公式heterogeneous (1)参差的; (2)不纯一的hexagon 六边形higher order derivative 高阶导数highest common factor(H.C.F) 最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图Holder's Inequality 赫耳德不等式homogeneous 齐次的homogeneous equation 齐次方程Hooke's law 虎克定律horizontal 水平的；水平horizontal asymptote 水平渐近线horizontal component 水平分量horizontal line 横线 ；水平线horizontal range 水平射程hyperbola 双曲线hyperbolic function 双曲函数hypergeometric distribution 超几何分布hypocycloid 内摆线hypotenuse 斜边hypothesis 假设hypothesis testing 假设检验hypothetical syllogism 假设三段论hypotrochoid 次内摆线idempotent 全幂等的identical 全等；恒等identity 等（式）identity element 单位元identity law 同一律identity mapping 恒等映射identity matrix 恒等矩阵identity relation 恒等关系式if and only if/iff 当且仅当；若且仅若if…, then 若….则；如果…..则illustration 例证；说明image 像点；像image axis 虚轴imaginary circle 虚圆imaginary number 虚数imaginary part 虚部imaginary root 虚根imaginary unit 虚数单位impact 碰撞implication 蕴涵式；蕴含式implicit definition 隐定义implicit function 隐函数imply 蕴涵；蕴含impossible event 不可能事件improper fraction 假分数improper integral 广义积分; 非正常积分impulse 冲量impulsive force 冲力incentre 内力incircle 内切圆inclination 倾角；斜角inclined plane 斜面included angle 夹角included side 夹边inclusion mapping 包含映射。
英语数学词汇M-N
数学专业词汇对照以字母M--N 开头mach angle 马赫角mach cone 马赫锥mach number 马赫数machine computation 机破算machine computing 机破算machine equation 机平程machine language 机骑言machine word 计算机语mackey topology 麦基拓扑maclaurin expansion 马克劳林展开maclaurin formula 马克劳林公式macro instruction 广义指令macrooperation 大运算macroparameter 宏观参数macrostatistics 宏观统计学magic circle 幻圆magic cube 幻立方magic figure 幻图magic square 纵横图magnetic head 磁头magnetic store 磁存储器magnetic tape 磁带magnetohydrodynamics 磁铃力学magnitude 量main diagonal 衷角线main program 痔序major axis 长轴major cycle 大循环major premise 大前提major term 大词majorant 强级数majorant criterion 比较检验majorant series 强级数majority 多数majority decision function 多数判定函数majority function 强函数majority game 强对策majorized sequence 优化序列majorized series 优化级数mal posed problem 不适定问题malfunction 错误动作maltiple classification 廖分类manifold 廖manifold classification 廖分类manifold of flags 旗廖manifold without boundary 无边廖manipulation 操作mannheim curve 曼海姆曲线mantissa 尾数many body problem 多体问题many dimentional sepce 多维空间many valued composition law 多值合成律many valued function 多值函数many valued logic 多值逻辑many valued mapping 多值映射map 映射map coloring problem 地图着色问题map projection 地图投影mapping 映射mapping cone 映射锥mapping cylinder 映射柱mapping function 映射函数mapping norm 映射范数mapping of sets 集映射mapping of the boundary 边缘映射mapping space 映射空间mapping theorem 映射定理mapping transformation 映射变换marginal density 边缘密度marginal distribution 边缘分布marginal distribution density function 边缘分布密度函数marginal distribution function 边缘分布函数mark 记号market model 市场模型marking function 标记函数markoff chain 马尔可夫链markov chain 马尔可夫链markov decision process 马尔可夫决策过程markov matrix 马尔可夫矩阵markov process 马尔可夫过程markov transform 马尔可夫变换marriage problem 配对问题mass 质量master program 痔序master sample 标准样本matching 匹配matching theorems 匹配定理material implication 实质蕴涵mathematical 数学的mathematical analysis 数学分析mathematical approximation 数学近似法mathematical constant 数学常数mathematical expectation 期望值mathematical formula 数学公式mathematical induction 数学归纳法mathematical logic 数理逻辑mathematical model 数学模型mathematical pendulum 数学摆mathematical physics 数学物理mathematical programming 数学规划mathematical random sample 数学随机样本mathematical statistics 数理统计mathematics 数学mathieu equation 马提厄方程mathieu function 马提厄函数mathieu group 马提厄群matricial rank 矩阵的秩matrix 矩阵matrix algebra 矩阵代数matrix analysis 矩阵分析matrix calculation 矩阵计算matrix element 矩阵元matrix equation 矩阵方程matrix factorization method 矩阵因子分解方法matrix form 矩阵形式matrix function 矩阵函数matrix game 矩阵对策matrix group 矩阵群matrix inversion 矩阵求逆matrix norm 矩阵范数matrix of coefficients 系数矩阵matrix of the transformation 变换矩阵matrix operator 矩阵算子matrix power series 矩阵幂级数matrix product 矩阵积matrix representation 阵表示matrix ring 矩阵环matrix semigroup 矩阵半群matrix series 矩阵级数matrix solution 矩阵解matrix transformation 矩阵变换matrix tree theorem 矩阵狮理matrix unit 矩阵单位matroid 矩阵胚maximal abelian extension 最大阿贝耳扩张maximal chain 连通链maximal element 极大元maximal equivalent orber 极大整环maximal hermitian operator 最大埃尔米特算子maximal ideal 极大理想maximal ideal space 极大理想空间maximal operator 最大算子maximal order 极大整环maximal principle 最大值原理maximal separable extension 极大可分扩张maximal strip 极大带maximal tree 最大树生成树maximality 极大性maximin 极大极小maximization 极大化maximizing sequence 极大化序列maximum 最大maximum condition 极大条件maximum deviation 最大偏差maximum ergodic theorem 极大遍历定理maximum likelihood equations 极大似然方程maximum likelihood estimating function 极大似然估计量maximum likelihood estimator 极大似然估计量maximum likelihood method 极大似然法maximum likelihood principle 极大似然法maximum matching 极大匹配maximum modulus principle 最大模原理maximum number 最大数maximum of a function 函数最大maximum or minimum condition 极大或极小条件maximum point 最大点maximum principle 最大值原理maximum problem 极大值问题maximum solution 最大解maximum term 极大项maximum value 绝对极大值maxwell boltzmann distribution law 麦克斯韦玻耳兹曼分布律maxwell's distributlon law 麦克斯事分布律maxwell's equations 麦克斯事方程meager set 贫集mean 平均mean continuity 中数连续性mean convergence 平均收敛mean convergence of p th order p 阶平均收敛mean curvature 平均曲率mean curvature of surface 曲面的平均曲率mean density 平均密度mean derivative 平均微商mean deviation 平均偏差mean difference 平均差mean error 平均误差mean life 平均寿命mean number 平均数mean ordinate 平均纵坐标mean pay off 平均支付mean proportional 比例中项mean square 均方mean square contingency 均方列联mean square deviation 方差mean square of error 误差的均方mean square value 均方值mean term 内项mean type 平均型mean value 平均值mean value method 平均值法mean value theorem 平均值定理mean vector 均值向量measurability 可测性measurable 可测的measurable function 可测函数measurable mapping 可测映射measurable set 可测集measure 测度measure of dispersion 离差的度量measure of skewness 偏度measure preserving transformation 保测变换measure space 测度空间measure theory 测度论measure zero 零测度measurement 测量measuring error 测量误差measuring rule 量尺mechanics 力学mechanism 机构median 中位数median line 中线median point 中点mediant 中间数medium 媒体meet 交meet homomorphic image 保交同态像meet irreducible element 交不可约元素mega 兆member 项member of an equation 方程的端边memory 存储器memory capacity 存储容量memory cell 存储单元memory register 存储寄存器mental arithmetic 心算meridian 子午线meromorphic differential 亚纯微分meromorphic function 亚纯函数meromorphic function element 亚纯函数元素meromorphic mapping 亚纯映射meromorphism 亚纯映射meromorphy 亚纯mesh point 网格点mesh size 网格大小mesokurtic distribution 常峰态分布meta axiom of choice 亚选择公理metabelian group 亚交换群metacompact space 亚紧空间metaharmonic function 亚低函数metalanguage 元语言metalogic of predicates 谓词元逻辑metatheorem 元定理meter 米method of approximation 近似法method of artificial variables 人工变量法method of balayage 扫除法method of characteristic curves 特者法method of comparison 比较法method of conjugate gradients 共轭梯度法method of difference 差分法method of elimination 消元法method of estimation 估计法method of exhaustion 穷竭法method of false position 试位法method of finite elements 有限元法method of fractional steps 分步法method of integration of partial differential equations 偏微分方程的积分法method of iteration 迭代法method of partial fractions 部分分数法method of perturbation 扰动法method of potentials 起脚石法method of power series 幂级数法method of principal axes 轴法method of principal components 种量法method of regularization 正则化法method of residues 剩余法method of runge kutta type 朗格库塔型的方法method of steepest ascent 最速上升法method of steepest descent 最速下降法method of successive approximation 逐次近似法method of undetermined coefficients 比较法metre 米metric 度量metric coefficient 度量系数metric connection 度量联络metric form 度量形式metric normal form of quadratic form 二次形式的度量标准形式metric space 度量空间metric subspace 度量子空间metric tensor 基本张量metric topology 度量拓扑metrically convex subset 度量凸子集metrically dense 度量的稠密metrizability 可度量性metrizable 可度量化的metrizable group 可度量化群metrizable uniform space 可度量化一致空间metrization 度量化metrization theorem of urysohn 乌里申度量化定理microlocal analysis 微局部分析mid square method 平方取中法middle term 中项midperpendicular 中垂线midpoint 中点midrange 中列数millimeter 毫米million 百万minimal automaton 极小自动机minimal basis 极小基minimal disjunctive normal form 极小析取范式minimal element 极小元素minimal generating set 不可约生成集minimal graph 极小图形minimal manifold 极小簇minimal model 极小模型minimal polynomial 极小多项式minimal propositional calculus 极小命题演算minimal solution 极小解minimal submanifold 极小子廖minimal sufficient estimator 最小充分估计量minimal sufficient statistic 最小充分统计量minimal surface 极小曲面minimal type 极小类型minimal variety 极小簇minimality 极小性minimax 极小极大minimax decision function 极小极大判决函数minimax inequality 极小极大不等式minimax principle 极小极大原理minimax solution 极小极大解minimax strategy 极小极大策略minimax theorem 极小极大定理minimization 极小化minimizing method 极小化法minimizing sequence 极小化序列minimum 最小minimum condition 极小条件minimum covering 极小覆盖minimum density 极小密度minimum integral 极小解minimum modulus 最小模minimum modulus principle 最小模原理minimum number 最小数minimum of a function 函数的最小minimum point 极小点minimum principle 极小原理minimum problem 极小问题minimum solution 极小解minimum value 最小值minimum with a condition 条件极小minimum with a constraint 条件极小minkowski approximation theorem 闵可夫斯基逼近定理minkowski inequalities 闵可夫斯基不等式minkowskian addition 闵可夫斯基加法minkowskian linear combination 闵可夫斯基线性组合minkowskian space 闵可夫斯基空间minor 子式minor arc 劣弧minor axis 短轴minor cycle 小循环minor determinant 子行列式minor premise 小前提minor term 小词minorant 弱函数minorant function 弱函数minuend 被减数minus infinity 负无穷大minus mark 负号minute 分miscalculation 计算误差;计算误差missing plot technique 缺区补救技术missing value 缺少值mistake 错误mix 混合mixed area 混合面积mixed concomitant 混合相伴式mixed differential parameter 混合微分参数mixed distribution 混合分布mixed graph 混合图形mixed group 混合群mixed ideal 混合理想mixed number 带分数mixed partial derivative 混合偏导数mixed problem 混合问题mixed side condition 混合边条件mixed strategy 混合策略mixed tensor 混合张量mixed type 混合型mixed vertex 混合顶点mixing problem 混合问题mixing ratio 混合比mixture 混合mnemonic 助记的mnemonic device 助记装置mnemonics 助记mobility 可动性modal class 众数组modal proposition 模态命题modal system 模态系统modal value 最常见的值modality logics 模态逻辑mode 众数mode of vibration 振动模式model 模型model of moving means 移动平均模型model test 模型试验model theory 模型理论modern geometry 近世几何学modification 变形modified bessel function 修正贝塞耳函数modified newton method 修正牛顿法modular 模的modular category 模范畴modular character 模特征modular equation 模方程modular figure 模图modular form 模形式modular function 模函数modular group 模群modular lattice 模格modular matrix 模矩阵modular substitution 模置换modular variety 模簇module 模module of boundaries 边界模module of homomorphisms 同态模module of program 程序的模module of quotients 商模moduli space 参模空间modulo 模modulus 绝对值;模modulus of a congruence 同余模modulus of elasticity 弹性模数modulus of periodicity 周期的模modulus of rigidity 刚性模量modus tollens 否定式moment 矩moment generating function 矩量母函数moment matrix 矩量矩阵moment of distribution 分布矩moment of force 力矩moment of inertia 惯性矩moment of momentum 动量矩moments method 矩量法momentum 动量monad 单子monge cone 蒙日锥monic 首一的monic polynomial 首一多项式monitor 监督程序monocyclic system 单循环系monodromy 单值monodromy group 单值群monodromy theorem 单值定理monogenic 单演的monogenic function 单演函数monogenic module 循环模monogyre 一次对称轴monoid 单式半群monoidal representation 单项表示monoidal transformation 单项变换monomial 单项式monomial equation 单项方程monomial factor 单项因子monomial form 单项形式monomial group 单项群monomial representation 单项表示monomorphism 单一同态monotone approximation 单灯近monotone class 单掂monotone decreasing 单递减的monotone decreasing function 单递减函数monotone function 单弹数monotone increasing function 单递增函数monotone numbering 单掂号monotone sequence 单凋列monotonic function 单弹数monotonic system of sets 单掂monotonic transformation 单典换monotonically decreasing sequence 单递减序列monotonically increasing sequence 单递增序列monotonicity 单翟monotony interval 单跌间monte carlo method 蒙特卡罗法monte carlo simulation 蒙特卡罗模拟montel space 空间moore smith convergence 穆尔史密斯收敛morphism 射morse inequalities 莫尔斯不等式morse theory 莫尔斯理论mortality rate 死亡率mortality table 死亡率表most powerful test 最大功效检定most probable duration 最可能持续时间most probable value 最常见的值most stringent test 最紧迫检验motion 运动motion equation 运动方程movable singularity 可移奇点move 步着movement 运动moving arm 移动臂moving average 移动平均moving average method 移动平均法moving frame 活动标架moving trihedral 怜三面形moving trihedron 怜三面形mrkoff process 马尔可夫过程mu continuity 连续性mu continuous function 连续函数mu integrable 可积分mu measurable 可测的mu singular 奇异multi dimensional integral 多维积分multi modal distribution 多重模态分布multi person game 多人对策multi phase sampling 多相抽样法multi purpose computer 万能计算机multi stage game 多阶段对策multi stage sampling 多级抽样法multi valued mapping 多值映射multi valuedness 多值性multiaddress 多地址multicollinearity 多重共线性multidimensional space 多维空间multigraph 多重图multigroup 超群multilinear form 多重线性形式multilinear function 多重线性函数multinomial 多项式multinomial coefficient 多项式系数multinomial distribution 多项分布multinomial expansion 多项展开式multinomial series 多项级数multinomial theorem 多项式定理multiple 倍数multiple arc 多重弧multiple correlation coefficient 多重相关系数multiple decision problem 多重判定问题multiple edge 多重棱multiple fourier series 多重傅里叶级数multiple hypergraph 多重超图multiple markov process 多重马尔可夫过程multiple point 多重点multiple regression 多重回归multiple root 多重根multiple sequence 多重序列multiple series 多重级数multiple stratification 多层化multiple tangent 多重切线multiple test 多重检验multiple valued 多值的multiple valued function 多值函数multiplicand 被乘数multiplicand register 被乘数寄存器multiplication 乘multiplication operator 乘法算子multiplication ring 乘环multiplication sign 乘号multiplication table 九九表multiplication theorem 乘法定理multiplicative 乘法的multiplicative axiom 乘法公理multiplicative character 乘法特贞multiplicative group 乘法群multiplicative lattice 乘格multiplicative process 繁殖过程multiplicatively closed set 积闭集multiplicator 乘数multiplicity 重数multiplicity of a root 根的重数multiplier 乘数;乘群multiplier register 乘数寄存器multiply 乘multiply connected domain 多连通区域multiply connected region 多连通区域multiply connected sequence 多连通序列multiply connected space 多连通空间multiply monotone sequence 多重单凋列multiply periodic function 多重周期函数multiply transitive group 多重可迁群multipolar 多极的multiprogram processing 多级程序处理multistage programming 多阶段规划multistep method 多步方法multitude 多数multivalent 多叶的multivalent function 多叶函数multivalued decision 多值判断multivariate analysis 多元分析multivariate analysis of variance 多元方差分析multivariate distribution 多元分布multivariate distribution function 多元分布函数multivariate statistics 多元统计multivector 多重矢量mutual information 交互信息mutually disjoint 互不相交的mutually disjoint events 互不相交事件mutually disjoint subsets 互不相交子集mutually independent events 互相独立事件myria 万myriad 无数的myriads 无数n ary relation n 元关系n ball n 维球n cell n 维胞腔n chromatic graph n 色图n coboundary n 上边缘n cocycle n 上循环n connected space n 连通空间n dimensional column vector n 维列向量n dimensional euclidean space n 维欧几里得空间n dimensional rectangular parallelepiped n 维长方体n dimensional row vector n 维行向量n dimensional simplex n 单形n dimensional skeleton n 维骨架n disk n 维圆盘n element set n 元集n fold extension n 重扩张n gon n 角n graph n 图n homogeneous variety n 齐次簇n person game n 人对策n simplex n 单形n sphere bundle n 球丛n th member 第n 项n th partial quotient 第n 偏商n th power operation n 次幂运算n th root n 次根n th term 第n 项n times continuously differentiable n 次连续可微的n times continuously differentiable function n 次连续可微函数n tuple n 组n tuply connected domain n 重连通域n universal bundle n 通用丛nabla 倒三角算子nabla calculation 倒三角算子计算nabla operator 倒三角算子napier's logarithm 讷代对数natural boundary 自然边界natural boundary condition 自然边界条件natural coordinates 自然坐标natural equation 自然方程natural equivalence 自然等价natural exponential function 自然指数函数natural frequency 固有频率natural geometry 自然几何natural injection 自然单射natural isomorphism 自然等价natural language 自然语言natural logarithm 自然对数natural mapping 自然映射natural number 自然数natural oscillation 固有振荡natural sine 正弦真数natural transformation 自然变换naught 零necessary and sufficient conditions 必要充分的条件necessary and sufficient statistic 必要充分统计量necessary condition 必要条件necessity 必然性negation 否定negation sign 否定符号negation symbol 否定符号negative 负数negative angle 负角negative binomial distribution 负二项分布negative complex 负复形negative correlation 负相关negative definite form 负定型negative definite hermitian form 负定埃尔米特形式negative definite quadratic form 负定二次形式negative function 负函数negative number 负数negative operator 负算子negative parity 负电阻negative part 负部分negative particular proposition 否定特称命题negative proposition 否定命题negative rotation 反时针方向旋转negative semidefinite 半负定的negative semidefinite eigenvalue problem 半负定特盏问题negative semidefinite form 半负定型negative semidefinite quadratic form 半负定二次形式negative sign 负号negative skewness 负偏斜性negative variation 负变差negligible quantity 可除量neighborhood 邻域neighborhood base 邻域基neighborhood basis 邻域基neighborhood filter 邻域滤子neighborhood retract 邻域收缩核neighborhood space 邻域空间neighborhood system 邻域系neighborhood topology 邻域拓扑neighboring vertex 邻近项点nephroid 肾脏线nerve 神经nested intervals 区间套net 网net function 网格函数net of curves 曲线网net of lines 直线网network 网络network analysis 网络分析network flow problem 网络潦题network matrix 网络矩阵neumann boundary condition 诺伊曼边界条件neumann function 诺伊曼函数neumann problem 诺伊曼问题neumann series 诺伊曼级数neutral element 零元素neutral line 中线neutral plane 中性平面neutral point 中性点newton diagram 牛顿多边形newton formula 牛顿公式newton identities 牛顿恒等式newton interpolation polynomial 牛顿插值多项式newton method 牛顿法newton potential 牛顿位势newtonian mechanics 牛顿力学nice function 佳函数nil ideal 零理想nil radical 幂零根基nilalgebra 幂零代数nilpotency 幂零nilpotent 幂零nilpotent algebra 幂零代数nilpotent element 幂零元素nilpotent group 幂零群nilpotent ideal 幂零理想nilpotent matrix 幂零矩阵nilpotent radical 幂零根基nine point circle 九点圆nine point finite difference scheme 九点有限差分格式niveau line 等位线niveau surface 等位面nodal curve 结点曲线nodal line 交点线nodal point 节点node 节点node locus 结点轨迹node of a curve 曲线的结点noetherian category 诺特范畴noetherian object 诺特对象nomogram 算图nomographic 列线图的nomographic chart 算图nomography 图算法non additivity 非加性non archimedean geometry 非阿基米德几何non archimedean valuation 非阿基米德赋值non countable set 不可数集non critical point 非奇点non denumerable 不可数的non denumerable set 不可数集non developable ruled surface 非可展直纹曲面non enumerable set 不可数集non euclidean geometry 非欧几里得几何学non euclidean motion 非欧几里得运动non euclidean space 非欧几里得空间non euclidean translation 非欧几里得平移non euclidean trigonometry 非欧几里得三角学non homogeneity 非齐non homogeneous chain 非齐次马尔可夫链non homogeneous markov chain 非齐次马尔可夫链non isotropic plane 非迷向平面non linear 非线性的non negative semidefinite matrix 非负半正定阵non oriented graph 无向图non parametric test 无分布检验non pascalian geometry 非拍斯卡几何non ramified extension 非分歧扩张non rational function 无理分数non relativistic approximation 非相对性近似non reversibility 不可逆性non singular 非奇的non stationary random process 不平稳随机过程non steady state 不稳定状态non symmetric 非对称的non symmetry 非对称non zero sum game 非零和对策nonabsolutely convergent series 非绝对收敛级数nonagon 九边形nonassociate 非结合的nonassociative ring 非结合环nonbasic variable 非基本变量noncentral chi squre distribution 非中心分布noncentral f distribution 非中心f 分布noncentral t distribution 非中心t 分布noncentrality parameter 非中心参数nonclosed group 非闭群noncommutative group 非交换群noncommutative ring 非交换环noncommutative valuation 非交换赋值noncommuting operators 非交换算子noncomparable elements 非可比元素nondegeneracy 非退化nondegenerate collineation 非退化直射变换nondegenerate conic 非退化二次曲线nondegenerate critical point 非退化临界点nondegenerate distribution 非退化分布nondegenerate set 非退化集nondense set 疏集nondenumerability 不可数性nondeterministic automaton 不确定性自动机nondiagonal element 非对角元nondiscrete space 非离散空间nonexistence 不存在性nonfinite set 非有限集nonholonomic constraint 不完全约束nonhomogeneity 非齐性nonhomogeneous 非齐次的nonhomogeneous linear boundary value problem 非齐次线性边值问题nonhomogeneous linear differential equation 非齐次线性微分方程nonhomogeneous linear system of differential equations 非齐次线性微分方程组nonisotropic line 非迷向线nonlimiting ordinal 非极限序数nonlinear equation 非线性方程nonlinear functional analysis 非线性泛函分析nonlinear lattice dynamics 非线性点阵力学nonlinear operator 非线性算子nonlinear optimization 非线性最优化nonlinear oscillations 非线性振动nonlinear problem 非线性问题nonlinear programming 非线性最优化nonlinear restriction 非线性限制nonlinear system 非线性系统nonlinear trend 非线性瞧nonlinear vibration 非线性振动nonlinearity 非线性nonlogical axiom 非逻辑公理nonlogical constant 非逻辑常数nonmeager set 非贫集nonmeasurable set 不可测集nonnegative divisor 非负除数nonnegative number 非负数nonnumeric algorithm 非数值的算法nonorientable contour 不可定向周线nonorientable surface 不可定向的曲面nonorthogonal factor 非正交因子nonparametric confidence region 非参数置信区域nonparametric estimation 非参数估计nonparametric method 非参数法nonparametric test 非参数检定nonperfect set 非完备集nonperiodic 非周期的nonperiodical function 非周期函数nonplanar graph 非平面图形nonprincipal character 非重贞nonrandom sample 非随机样本nonrandomized test 非随机化检验nonrational function 非有理函数nonremovable discontinuity 非可去不连续点nonrepresentative sampling 非代表抽样nonresidue 非剩余nonsense correlation 产生错觉相关nonsingular bilinear form 非奇双线性型nonsingular curve 非奇曲线nonsingular linear transformation 非退化线性变换nonsingular matrix 非退化阵nonspecial group 非特殊群nonstable 不稳定的nonstable homotopy group 非稳定的同伦群nonstandard analysis 非标准分析nonstandard model 非标准模型nonstandard numbers 非标准数nonsymmetric relation 非对称关系nonsymmetry 非对称nontangential 不相切的nontrivial element 非平凡元素nontrivial solution 非平凡解nonuniform convergence 非一致收敛nonvoid proper subset 非空真子集nonvoid set 非空集nonzero vector 非零向量norm 范数norm axioms 范数公理norm form 范形式norm of a matrix 阵的范数norm of vector 向量的模norm preserving mapping 保范映射norm residue 范数剩余norm residue symbol 范数剩余符号norm topology 范拓朴normability 可模性normal 法线normal algorithm 正规算法normal basis theorem 正规基定理normal bundle 法丛normal chain 正规链normal cone 法锥面normal congruence 法汇normal coordinates 正规坐标normal correlation 正态相关normal curvature 法曲率normal curvature vector 法曲率向量normal curve 正规曲线normal density 正规密度normal derivative 法向导数normal dispersion 正常色散normal distribution 正态分布normal distribution function 正态分布函数normal equations 正规方程normal error model 正规误差模型normal extension 正规开拓normal family 正规族normal force 法向力normal form 标准型normal form problem 标准形问题normal form theorem 正规形式定理normal function 正规函数normal homomorphism 正规同态normal integral 正规积分normal linear operator 正规线性算子normal mapping 正规映射normal matrix 正规矩阵normal number 正规数normal operator 正规算子normal order 良序normal plane 法面normal polygon 正规多角形normal polynomial 正规多项式normal population 正态总体normal probability paper 正态概率纸normal process 高斯过程normal sequence 正规序列normal series 正规列normal set 良序集normal simplicial mapping 正规单形映射normal solvable operator 正规可解算子normal space 正规空间normal surface 法曲面normal tensor 正规张量normal to the surface 曲面的法线normal valuation 正规赋值normal variate 正常变量normal variety 正规簇normal vector 法向量normality 正规性normalization 标准化normalization theorem 正规化定理normalize 正规化normalized basis 正规化基normalized function 规范化函数normalized variate 正规化变量normalized vector 正规化向量normalizer 正规化子normalizing factor 正则化因数normed algebra 赋范代数normed linear space 赋范线性空间normed space 赋范线性空间northwest corner rule 北午角规则notation 记法notation free from bracket 无括号记号notation of backus 巴科斯记号notion 概念nought 零nowhere convergent sequence 无处收敛序列nowhere convergent series 无处收敛级数nowhere dense 无处稠密的nowhere dense set 无处稠密点集nowhere dense subset 无处稠密子集nuclear operator 核算子nuclear space 核空间nucleus of an integral equation 积分方程的核null 零null class 零类null divisor 零因子null ellipse 零椭圆null function 零函数null hypothesis 虚假设null line 零线null matrix 零矩阵null method 衡消法null plane 零面null point 零点null ray 零射线null relation 零关系null representation 零表示null sequence 零序列null set 空集null solution 零解null system 零系null transformation 零变换null vector 零向量nullity 退化阶数nullring 零环nullspace 零空间number 数number defined by cut 切断数number defined by the dedekind cut 切断数number field 数域number interval 数区间number line 数值轴number notation 数记法number of partitions 划分数number of repetitions 重复数number of replications 重复数number of sheets 叶数number sequence 数列number set 数集number system 数系number theory 数论number variable 数变量numeration 计算numerator 分子numeric representation of information 信息的数值表示numerical 数值的numerical algorithm 数值算法numerical axis 数值轴numerical calculation 数值计算numerical coding 数值编码numerical coefficient 数字系数numerical computation 数值计算numerical constant 数值常数numerical data 数值数据numerical determinant 数字行列式numerical differentiation 数值微分numerical equality 数值等式numerical equation 数字方程numerical error 数值误差numerical example 数值例numerical function 数值函数numerical inequality 数值不等式numerical integration 数值积分法numerical invariant 不变数numerical mathematics 数值数学numerical method 数值法numerical model 数值模型numerical operator 数字算子numerical quadrature 数值积分法numerical series 数值级数numerical solution 数值解numerical solution of linear equations 线性方程组的数值解法numerical stability 数值稳定性numerical table 数表numerical value 数值numerical value equation 数值方程nutation 章动。
不动点定理,一般均衡及纳什均衡笔记
2 Brouwer’s Fixed Point Theorem
Brouwer’s fixed point theorem is proved by Brouwer’s fixed point theorem for unit ball. Through following two facts, we can reach Brouwer’s fixed point theorem. √ n • A unit ball B n and a ball with any ”radius”( α) Bα are homeomorphic.
d(Φ(x∗ ), x∗ )
Since ε > 0 is arbitrary here, we must then have d(Φ(x∗ ), x∗ ) = 0, which is possible only if Φ(x∗ ) = x∗ . To prove the uniqueness assertion, observe that if x ∈ X was another fixed point of Φ, we would then have d(x, x∗ ) = d(Φ(x), Φ(x∗ )) possible only if x = x∗ (since K < 1). Kd(x, x∗ ),which is
ε 2
for all m = M, M + 1, · · · , and hence d(Φ(x∗ ), xm+1 ) + d(xm+1 , x∗ ) = d(Φ(x∗ ), Φ(xm ) + d(xm+1 , x∗ ) Kd(x∗ , xm ) + d(xm+1 , x∗ ) ε ε < + 2 2
运营方案的英文
运营方案的英文IntroductionOperational planning is a vital aspect of any business or organization. It involves creating a strategic plan that outlines the objectives and goals of the organization, as well as the necessary resources and actions to achieve them. Effective operational planning is essential for ensuring the smooth and efficient functioning of the organization, as well as for driving growth and success.In this operational plan, we will outline the key components of our operational strategy, including our objectives, resources, actions, and timelines. We will also identify potential challenges and risks, and propose actionable solutions to mitigate them.ObjectiveThe primary objective of our operational plan is to streamline our business processes, improve efficiency, and drive growth. We aim to achieve this by:Increasing productivity and minimizing wasteEnhancing customer satisfaction and loyaltyOptimizing resource allocation and utilizationMaximizing revenue and profitabilityDeveloping a competitive advantage in the marketTo achieve these objectives, we will focus on the following key areas:Strategic resource managementProcess optimization and automationCustomer service and experienceFinancial management and planningMarket analysis and competitivenessResource ManagementEffective resource management is crucial for the success of any business. This includes managing human resources, financial resources, and physical resources. We will focus on the following strategies to optimize our resource management:1. Human Resources: We will invest in training and development programs to enhance the skills and capabilities of our employees. This will not only improve productivity and job satisfaction but also reduce employee turnover and associated costs.2. Financial Resources: We will conduct a comprehensive financial analysis to identify areas of inefficiency and waste. By implementing cost-saving measures and improving financial planning, we aim to optimize our financial resources and maximize profitability.3. Physical Resources: We will assess our physical infrastructure and equipment to ensure optimal utilization. This may involve upgrading or replacing outdated equipment, as well as implementing maintenance and repair programs to prevent downtime and inefficiency.Process Optimization and AutomationStreamlining our business processes is essential for improving efficiency and reducing operational costs. We will focus on the following strategies to optimize and automate our processes:1. Process Analysis: We will conduct a thorough analysis of our existing business processes to identify bottlenecks, redundancies, and inefficiencies. This will involve mapping out each process and identifying opportunities for improvement.2. Automation: Where possible, we will implement automation technologies to streamline repetitive andtime-consuming tasks. This may include the use of software solutions, robotics, and artificial intelligence to automate data entry, inventory management, and customer service processes.3. Continuous Improvement: We will establish a culture of continuous improvement, encouraging employees to suggest and implement process improvements. This may involve regular brainstorming sessions, feedback mechanisms, and performance metrics to track and measure improvements.Customer Service and ExperienceProviding exceptional customer service and experience is a key differentiator in today's competitive market. We will focus on the following strategies to enhance our customer service and experience:1. Customer Feedback: We will actively seek feedback from our customers to identify areas for improvement and address any issues or concerns. This may involve implementing customer surveys, feedback forms, and complaint resolution processes.2. Training and Development: We will invest in training and development programs to enhance the customer service skills of our employees. This may involve customer service training, communication skills development, and conflict resolution training.3. Personalization: We will focus on personalizing the customer experience through targeted marketing, customized products and services, and personalized communications. This may involve the use of customer data and analytics to tailor our offerings to individual customer needs and preferences.Financial Management and PlanningEffective financial management is essential for the long-term sustainability of our business. We will focus on the following strategies to optimize our financial management and planning:1. Budgeting and Forecasting: We will develop comprehensive budgets and financial forecasts to guideour financial planning and decision-making. This will involve setting clear financial targets, monitoringactual performance, and making adjustments as necessary.2. Cost Control: We will implement cost-saving measuresto reduce operational expenses and improve profitability. This may involve negotiating better terms with suppliers, outsourcing non-core functions, and implementing energy-saving initiatives.3. Investment and Growth: We will identify opportunities for investment and growth, both within our existing business and through strategic partnerships and acquisitions. This may involve conducting market research, feasibility studies, and risk assessments to evaluate potential opportunities.Market Analysis and CompetitivenessUnderstanding our market and staying competitive is essential for driving growth and success. We will focuson the following strategies to analyze our market and improve our competitiveness:1. Market Research: We will conduct comprehensive market research to understand our target customers, their needs and preferences, and the competitive landscape. This may involve surveys, focus groups, and data analysis to gain insights into market trends and customer behavior.2. Competitive Analysis: We will analyze our competitors to identify their strengths and weaknesses, and to identify potential opportunities and threats. This may involve benchmarking, SWOT analysis, and market positioning exercises to differentiate our offerings and value proposition.3. Innovation and Differentiation: We will focus on innovation and differentiation to stay ahead of the competition. This may involve product and service innovation, market differentiation, and the development of unique selling propositions to attract and retain customers.Challenges and RisksWhile we are confident in our operational plan, we recognize that there are potential challenges and risks that may impact our ability to achieve our objectives. We will focus on the following strategies to mitigate these challenges and risks:1. Risk Management: We will conduct a comprehensive risk assessment to identify potential threats to our business operations. This may involve analyzing internal and external risks, developing risk mitigation strategies, and implementing contingency plans.2. Change Management: We will focus on change management to ensure smooth implementation of our operational plan. This may involve communication and engagement strategies,training and development programs, and performance monitoring and feedback mechanisms.3. Crisis Management: We will develop crisis management plans to address potential crises or emergencies that may impact our business operations. This may involve developing response protocols, establishing communication channels, and training our employees on crisis management procedures.ConclusionIn conclusion, our operational plan is designed to drive growth and success by focusing on strategic resource management, process optimization and automation, customer service and experience, financial management and planning, and market analysis and competitiveness. By implementing the strategies outlined in this plan, we are confidentthat we will achieve our objectives and position our business for long-term sustainability and success. Wewill continue to monitor our progress and makeadjustments as necessary to ensure the successful implementation of our operational plan.。
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Mapping mental states into propositional planningFelipe R.Meneguzzi CPSE,PUCRS,Brazil felipe@cpts.pucrs.br Avelino F.Zorzo and Michael C.M´o ra Computer Science Dept.,PUCRS,Brazil{zorzo,michael}@inf.pucrs.brAbstractMost BDI agent architectures rely on plan libraries in or-der to ensure bounded time for means-ends reasoning.Nev-ertheless,the usage of fast planning algorithms to provide the agent with runtime planning capabilities is an alternate approach to augment agent autonomy andflexibility.This paper proposes an autonomous agent architecture based on the integration of a logic-based BDI model with proposi-tional planning algorithms through a mapping process. 1.IntroductionAmong the main requirements of an autonomous agent is the ability to perform means-end reasoning,i.e.the abil-ity to select a course of actions that ultimately achieves the goals of the agent[2].Thus,methods to accomplish such a requirement have long been a major research issue in Arti-ficial Intelligence,the most recognized result of these pur-suits lying in thefield of planning algorithms.Planning problems are very complex in the general case[3].This shortcoming in solving planning problems limits the usage of planning when it comes to long-term goals,resulting in the development of many approaches to practical reason-ing,the most notorious of which is the agent model known as Beliefs,Desires and Intentions or BDI[2].Such an ap-proach allows an agent to break down its goals so that the agent can commit itself to achieving only a subset of its entire goal universe.Yet,the agent still have to perform means-end reasoning to determine how he is to accomplish this subset of his goals,i.e.the agent must determine a plan to fulfill his selected goals.Most implementations of BDI agent architectures tend to avoid the inherent complexity of creating complete plans at run-time[5],exceptions to that rule,to the best of our knowledge,are very few[6,7].On the other hand,ad-vances on propositional planning have resulted in a series of planning algorithms capable of very efficient planning for a large class of problems[9,5].Therefore,it is an im-portant implementation advantage for BDI agents to be al-lowed to use such algorithms in order to perform their pro-cess of means-end reasoning[5].Agent languages such as 3APL[4]and Dribble[8]demonstrate a particular inter-est in using run-time planning strategies in order to pro-vide an agent with greater autonomy than it would other-wise be possible should plan libraries be used in the de-liberation process.Nevertheless,these languages do not yet address planning efficiency so that an agent can deal with complex problems in a timely manner.2.The X2BDI Agent ModelConsidering the goals set forth in the introduction,an extension of X-BDI was defined.Such an extension maps the agent’s mental state into propositional planning prob-lems during its deliberation process in order to use a plan-ning function to perform means-end reasoning.This agent model is called Extended X-BDI or X2BDI.The cognitive structure of X2BDI has the traditional components of a BDI agent,i.e.a set of Beliefs,Desires and Intentions.It also has a set of time axioms inherited from X-BDI.An X2BDI is composed of the same compo-nents as an X-BDI agent plus a propositional planning func-tion conforming to the formalism described in[5].The set of beliefs is a formalization of facts in ELP[1], whose consistency is maintained by means of the program revision process performed in ELP by the SLX procedure. From the agent’s point of view,it is assumed that its beliefs are always consistent.Every desire in an X2BDI agent is conditioned by a conjunction of literals called Body,which specifies the pre-conditions that must be satisfied in order for an agent to desire a property.Desires may be speci-fied to be valid only in a specific moment,or whenever its pre-conditions are valid.Desires also have a priority value used in the formation of an order relation among desire sets. There are two possible types of intentions:Primary Inten-tions,which refer to the intended properties,and Relative Intentions,which refer to actions able to bring about these properties.An agent may not intend something in the past, that is already true,or is impossible,i.e.there must be at least one plan available to the agent whose result is a world state where the intended property is true.In X-BDI the possibility of a property was veri-fied through the abduction of an Event Calculus theorythat would make the property true.In X2BDI the plan-ning process is abstracted from the operational definition of the agent,allowing any planning process that con-forms to the propositional planning formalism of[5]to be used.Thus,the notion of possibility of a desire is associ-ated with the existence of a plan to satisfy it.The reasoning process performed by X-BDI initiates with the selection of Eligible Desires,which represent the unsatisfied desires whose pre-conditions have been satis-fied.The elements of this set are not necessarily consis-tent among themselves.Candidate Desires are then gen-erated,which represent a set of Eligible Desires that are both consistent and possible and will be later adopted as Primary Intentions.In order to satisfy the properties repre-sented by Primary Intentions,the planning process gener-ates a sequence of temporally ordered actions that consti-tute the Relative Intentions.The process of selecting Candidate Desires seeks to choose a subset of Eligible Desires that contains only those that are internally consistent and possible,i.e.desires of properties P that can be simultaneously satisfied through a sequence of actions.Candidate Desires represent the most significant modification regarding the abductive planning in the original X-BDI[6].In X2BDI we use an external plan-ning function,thus separating the planning process previ-ously hard-coded within X-BDI.We define that a set of Candidate Desires is the subset of Eligible Desires with the greater priority value,and whose properties can be satisfied. Satisfiability is verified through the execution of a proposi-tional planner that processes a planning problem where the initial state contains the properties that the agent believes at the time of planning.The P properties present in the Can-didate Desires are used to generate the set Primary Inten-tions.Primary Intentions represent the agent’s commitment to achieving a set of objectives for which a course of ac-tion has been found.Relative Intentions correspond to the temporally ordered steps of the concrete plans generated to satisfy the agent’s Primary Intentions.The notion of agent commitment results from the fact that Relative Intentions must be non-contradictory regarding Primary Intentions. The computational effort and the time required to reconsider the whole set of intentions of a resource-bounded agent is generally significant regarding the environment change ra-tio.Therefore,intention reconsideration should not occur constantly,but only when the world changes in such a way as to threaten the plans an agent is executing or when an opportunity to satisfy more important goals is detected.As a consequence,X-BDI uses a set of reconsideration“trig-gers”generated when intentions are selected,and causes the agent to reconsider its course of action when activated. Such modifications should alter X-BDI functioning so that it uses propositional planning algorithms as the underpin-ning of the means-end reasoning and as possibility verifiers in the practical reasoning process.3.ConclusionsIn this paper we described the relationship be-tween propositional planning algorithms and the process of means-end reasoning in BDI agents.Such a relation-ship is defined in terms of a mapping between the BDI men-tal states of an X-BDI agent and planning problems.In order to verify the viability of such an approach we modi-fied the X-BDI agent model to cope with the usage of an external planning module that uses a Graphplan implemen-tation.Through the merger of BDI agents and fast planning algorithms,we expect the class of problems whose run-time resolution speed is feasible to be expanded towards that of planning algorithms used.Considering that the ma-jority of known BDI agent implementations use a plan library in the process of means-end reasoning in or-der to avoid the inherent complexity of planning at runtime, X2BDI provides an innovative way of implementing au-tonomous agents.Moreover,even though the original X-BDI did possess runtime planning capabilities,its plan-ning algorithm was very inefficient,therefore,the mapping defined in this paper allows X-BDI to use any proposi-tional planning algorithm,thus the agent model is able to use future planning algorithms[5].Acknowledgments The authors would like to thank Prof. L´u cia Giraffa,HP Brazil and CNPq for their collaboration. 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