The general two dimensional shifted Jacobi matrix method for solving the second order linear partial
2024届上海市嘉定区高三上学期一模英语试题
2024届上海市嘉定区高三上学期一模英语试题学校:___________姓名：___________班级：___________考号：___________一、语法填空Directions: After reading the passage below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word;for the other blanks, use one word that best fits each blankSeeing Math on the PageMath and literature are probably two of the subjects that bring students headaches. However, scientists wonder 1 the beauty of math can be found in literary works. Once Upon a Prime: The Wondrous Connections between Mathematics and Literature, a book published recently by UK mathematician Sarah Hart, 2 (present) some interesting thoughts about "three". She argues that the beauty of this number is indeed evident in many works of western literature and languages in general.‘Three’ is the minimum number 3 a two-dimensional shape can be defined. For example, three sticks can create a triangle, a stable structure. Many common phrases are in three words, such as “ready, set, go”. Being the first things kids may learn, some nursery rhymes have a word 4 (repeat) three times, such as “row, row, row your boat”. In stories, there are usually three main characters, such as Harry, Ron and Hermione in the Harry Potter series. For a series of novels, there are usually three books 5 four, according to Hart.Why is it always the third son who behaves differently from his two older brothers, thus 6 (win) the princess? “The reason for this,” Hart explains, “ is obvious. We require two repetitions to get to know the pattern, 7 the breaking of the pattern in the third character can surprise or amuse us.”Similarly, another study by researchers at the University of Vermont also connected math and storytelling. They analyzed more than 1, 300 fiction books and arranged for 10, 000 words from the books 8 (rate) by 50 participants on a happiness scale of 1 to 9. Then the ratings 9 (categorize) into different graphs, which showed how the readers' emotions changed while reading. It turned out that each story fit perfectly into one of six basic graphs, a mathematical pattern.“The idea that one would 10 choose between mathematics and literatureis something of a tragedy, ”Hart says, “The two fields are fundamentally linked”.二、选词填空Directions: After reading the passage below, fill in each blank with a proper word given in theFarm of the Future in the Sky Five storeys off the ground at Colorado State University, a highly unlikely garden grows under a long row of rooftop solar panels. It's late November at 9 am, when the temperature is-2℃ and the wind is cutting. Not long before my arrival,cool-season foods like leafy greens still grow, 12 from the intense sunlight up there. This is no ordinary green roof, but an expansive and 13 outdoor laboratory. The idea behind it is explained by Jennifer Bousselot, the director of the rooftop farm. Solar panels tend to get too hot on conventional roof tops, and that heat reduces their efficiency while plants help cool them off. “If you have plants under there, ” Bousselot said, “they create ideal 14 for solar panels to operate. Also, the shade of the panels encourages the growth of plants. A win-win solution. ”Therefore, the overall goal of the rooftop farm is to grow more food for 15 urban populations while generating clean energy and making buildings more energy efficient. Without the sun beating down 16 on a bare roof, green roofs boost a building's energy efficiency by about 10 percent. That is, you don't need to run as much air-conditioning to 17 cool the place during a heat wave. This innovative approach can also maximize land use, making urban spaces not just consumers of resources, but also active18 to both energy and agricultural production.However, being 19 on a rooftop comes with more challenges than a typical farming site. The wind loads on a roof make it challenging to install a tracking system and irrigation (灌溉) is also trickier. The expenses are substantially increased due to higher20 costs and the difficulties of moving and installing all the sensors and materials high in the air.It is obviously early days for rooftop farms, but some effects were already evident. Instead of being big, dead spaces, roofs may act as booming ecosystems.三、完形填空“So …tell me about yourself. ”The toughest job interview question may seem like a softball from the interviewer’s perspective: It seems 21 because it feels like a free pass: no request for real-life examples, no technical challenge, not even the feared “What’s your biggest fault? ”Just…tell me anything.Receiving such an open invitation invites more 22 than opportunities, because you’re given no framework for your response —just a blank, clue-free paper. I often see this 23 situation in my point-making workshops: communicating without a point.What your prospective employer most needs from you is a point (“I am an important asset (资产) to the company”), not a 24 (“All about me”). But how do you get from the interviewer’s broad question to a specific and 25 point?Start with realizing that your interviewer already knows your job history thanks to your resume (简历). So you should be more than your 26 . Remember that interviews are more about making strong 27 than proving qualifications. This is a two-step process that will require some homework. First, identify what the organization specifically needs from this role. Second, 28 your response to position yourself as the best person to fill that need.Identifying the organization’s need means examining the job description like a treasure map. Phrases like “required, ”“must have, ”and “highly desired” mean what they say, so29 those in your planning. Items further down the list or labeled “preferred” may be less important, even if you meet those standards. The 30 of a job description can be telling as well. Descriptions that sound personal, or come right out and say “sense of humor preferred” indicate a workplace where people like to have fun. 31 , a very formal job posting might indicate a conservative workplace where people are expected to be serious about the work.Pulling from these soures, write down the three personal qualities they’re most looking for like “self-starter, ” “team player, ”or “interest in healthcare”. Now change the 32slightly to “I’m a self-starter” or “At work, my approach is ... ” Then pick a story from your professional life that 33 you filling that particular need of the job. Feel free to add details, but don’t 34 the primary elements. Assume they can smell a lie from a mile away, whether they can or can’t.In this way, you should do more than just widen eyes in the room. Why? Because you’ve matched who you are and your personal story with the company’s brand and primary need. You didn’t just tell them about you;you pointed out why you 35 to them. 21．A．hard B．easy C．huge D．small 22．A．missions B．joys C．comments D．risks 23．A．unlikely B．favourable.C．problematic D．competent 24．A．book report B．phone call C．desk lamp D．lunch break 25．A．declared B．tailored.C．rejected D．assessed 26．A．profile B．criterion C．dimension D．nickname 27．A．transitions B．judgments C．matches D．distributions 28．A．stabilize B．customize C．memorize D．authorize 29．A．diversify B．approve C．delete D．highlight 30．A．tone B．format C．picture D．length 31．A．For instance B．By contrast C．After all D．In addition 32．A．blogging B．networking C．messaging D．wording 33．A．illustrates B．suspends C．dismisses D．circulates 34．A．make up B．put off C．break down D．get through 35．A．submitted B．extended C．mattered D．shifted四、阅读选择To us, the kitchen was a mysterious place. Our kitchen at home was so simple: an old Sparks oven, a refrigerator, a sink, and a table. At the New Eastern, it was a busy factory. Almost an entire wall was taken up by a line of huge black woks (锅). This was my father’s stage. He strode (大步走) the length of the four woks, each one fired up by gas flames underneath. Beneath him, blocks of wood, raised off the ground an inch or two, served to give his legs and feet some spring.The sink was the size of a bathtub (浴); the refrigerator had glass doors and stretched threetimes as wide as the one at home. Every appliance was bigger, and there were things we never saw anywhere else, like the big metal oven in which my father hung long poles holding large pieces of pork. We could hear the fire roaring from the bottom of it. My dad would go about his business, and then, always at exactly the right time, he’d wander over, lift off the top, and take out several poles of barbecued pork—bright red, with black at the tips. If I happened by at that magical moment, I’d stop. “Yeet-gow!” I’d say. And he’d skillfully chop off a piece of the juicy, sweet meat. “One dollar!” he’d shout, and then hand it over.My father made the best food in town. There was nothing he wouldn’t try. He was once proud of a rock candy he invented and determined to sell at the front counter of the New Eastern. We, of course, served as his guinea pigs—we couldn’t bring ourselves to tell him the sad truth: The candy was so hard that it was uneatable. I rolled a piece around my mouth. “Tastes good, Ba-Ba, ”I said. Then, when he looked away, I spat it out.Sometimes, he liked to invent stories to us. Watching my little sister Shirley biting on an apple, he’d lean over. “Don’t eat the seed,” he said, “or an apple tree will grow inside you.” “What?” “Yes. Right inside your stomach, an apple tree!”36．It can be learned from paragraph 1 and 2 that____________.A．the author’s father can repair springs B．the author enjoys observing in thekitchenC．the author helps to cook difficult dishes D．the author’s family lives in a busyfactory37．How does the author develop the idea that “the kitchen is a mysterious place”?A．By describing how his father manages various tasks in the kitchen.B．By classifying the kitchen appliances into different categories.C．By contrasting the restaurant kitchen with the kitchen at home.D．By explaining why large pieces of pork were placed in the oven.38．The author mentions the incident of a rock candy in paragraph 3_____________.A．to highlight how he disliked the food his father madeB．to illustrate why they often kept secrets from his fatherC．to emphasize the troubled relationship with his fatherD．to show the family’s support for his father’s experiments39．Which of the following words can best describe the author’s father?A．dynamic and playful B．strict and innovativeC．talented and greedy D．hardworking and outdatedSocial engineering refers to the practice of using non-technical methods to trick people into doing something that gives away sensitive information. Here, watch this case ...40．It can be learned from “THE ATTACK” that_______.A．Sandra asks Marcus for his password.B．Marcus steals the key corporate data.C．The attacker gains Marcus's trust first.D．Sandra is a senior director of the bank. 41．Which of the following best fits the “?” in step ℃of “THE DEFENSE"?A．LESSON B．HEALTH C．PROGRAM D．FINANCE 42．Which of the following is covered in the case?A．What loss the company has suffered B．How Marcus regretted receiving the call C．What Natalie has found about the domain D．How effectively Ray responded to the attackNew research confirms that human footprints found in New Mexico are probably thescientists knew about human habitation and migration(迁徙).The footprints were discovered at the edge of an ancient lakebed in White Sands national park. According to the new paper published in the journal Science, they date back to between 21, 000 and 23, 000 years ago. Actually, the estimated age of the footprints was first reported in Science in 2021, but some researchers raised concerns about the dates. Questions focused on whether seeds of water plants used for the original dating may have absorbed ancient carbon from the lake—which could, in theory, throw off radiocarbon dating by thousands of years. But the new study presents two additional lines of evidence for the older date range. It uses two entirely different materials found at the site, ancient pollen(花粉)and stone grains.The reported age of the footprints challenges the once conventional wisdom that humans did not reach the Americas until a few thousand years before rising sea levels covered the Bering land bridge between Russia and Alaska, perhaps about 15, 000 years ago. “This is a subject that's always been controversial because it's so significant. It's about how we understand the last chapter of the peopling of the world, ”said Thomas Urban, an archaeologist (考古学家)at Comell University, who was involved in the 2021 study but not the new one.Thomas Stafford, an independent archaeological geologist in New Mexico, who was not involved in the study, said he“was a bit suspicious before”but now is convinced. The new study isolated about75, 000 grams of pure pollen from the same stone layer that contained the footprints. "Dating pollen is laborious but worthwhile, "said Kathleen Springer, a research geologist at the US Geological Survey and a co-author of the new paper.Ancient footprints of any kind can provide archaeologists with a quick look of a moment in time. While some archeological sites in the Americas point to similar date ranges—including necklaces carved from giant animal remains in Brazil—scientists still question whether such objects really indicate human presence. “White Sands is unique because there's no question these footprints were left by people, "said Jennifer Raff, a scientist at the University of Kansas, who was not involved in the study.43．The underlined word"upends”(paragraph 1)is closest in meaning to“_______".A．comprises B．connects C．challenges D．compares44．According to the passage, what is special about the new research?A．It shows the footprints were made by the Russians.B．It offers more convincing lines of evidence for dating.C．It confirms that the ancient humans enjoyed living by the lake.D．It reveals the footprints are much younger than previously thought.45．It can be inferred from the last paragraph that_____________.A．necklaces are valuable objects for archaeologists to date animalsB．human footprints are often sure signs of human presenceC．ancient objects in Brazil are excluded from the studyD．White Sands is one important archaeological site46．Which of the following might be the best title of the passage?A．Scientists Discovers New Species of Humans in AmericasB．Humans Reached Americas 15, 000 Years Earlier Than BelievedC．American Archaeologists Unearthed Valuable Manmade ObjectsD．New Research Confirms Early Human Presence in AmericasWhat to Know If Buying a Flipped HouseHouse flipping is hardly new. For someone who is working in the real estate market, a flipped or recently renovated (翻新的)home can be very appealing. But how about you, the home-hunter? 47You certainly don’t need to avoid flipped properties. A flipped property does have some strong selling points. A lot of its features and fixtures have been replaced or improved. Certainly, you’ll save on the time and trouble of doing the renovation yourself. But there are some things to watch out for if you’re considering buying one.48 For example, Alice recently toured a flipped house whose kitchen drawer was blocked by the refrigerator and the dishwasher wasn’t installed correctly -things that would prevent people from being able to function in there. Addressing issues like these can become costly, especially if you haven’t factored them into your budget.Don’t neglect your right to a professional inspection. 49 So getting an expert to go take a thorough look at the property is crucial, to make sure everything is up to code. It’s going to be really important to do your sewer(下水道)and separate roof inspections. Flipped houses may seem up-to-date on the surface, but shiny new finishes can sometimes masksubstandard work.Finally, flipped properties are rarely advertised as such. Therefore, it is crucial to work with aknowledgeable real estate agent. 50 When he tours a house that he suspects is being flipped, he’ll check who owned the home previously, and will reach out to other agents in his network to see if anyone has experience buying from them.A．The key is to look for places where improvements were done poorly.B．An experienced agent is probably going to have a better eye than the buyer.C．Is buying one of these quick-turnaround properties a good idea?D．Set aside money for any problems that may crop up or ask the seller to cover them. E．How do you know if the previous owner has moved out of the house?F．Flippers sometimes skip getting permits for the work they do.五、书面表达51．Directions: Read the following passage. Summarize the main idea and the main point(s)of the passage in no more than 60 words. Use your own words as far as possible.Dealing with One Missed WorkoutIt’s a common dilemma (图局)for anyone on a training plan: You miss one workout and become awashed with guilt. To make up for it, you add those extra miles to your next workout. But according to the professionals, this isn’t the right way to go about it. “A single workout is not going to make or break a training plan. The key to training is consistency over time,” says John Raglin, PhD, professor in the Department of Kinesiology at Indiana University Bloomington.When you miss a workout, the temptation is to think, “Oh, I’ve got to do more tomorrow”. But when you try to catch up on your workouts, you run a couple of risks: “Certainly an injury, but also becoming over-tired, which could ruin your training after that, ” says Raglin. This is a phenomenon called ‘non-functional overreaching’, “he says. Eventually, this could lead to overtraining syndrome (综合症), which is characterized by a decrease in performance later due to a long-term increase in training load without adequate recovery.So how do you move forward if you skipped a run or five?Well first, people download generalized training plans without understanding that they are meant to be adapted to life. There is a whole host of life stressors—job, kids, friendships, travel—and exercise is justanother type of stress. Actually, when things get chaotic in your life, it may be necessary to just let go. Next, if you missed a workout, you have to ask yourself why: “Was it just because your schedule got out of hand or because you were feeling overly exhausted? ” Understanding why you missed the workout can offer some insights into how to tailor your program to suit your lifestyle.___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ____________________六、翻译52．门后挂着毛巾和睡衣，方便客人使用。
Unit 1 Period 1 Reading课件-高中英语(人教版2019选择性必修第三册)
Read the passage and make a flow chart to show the changes in Western painting styles.
Put the statements in the right order.
A. This changed with the emotional paintings of Giotto di Bondone. B. At this time ideas on perspective by Masaccio were adopted by Leonardo da Vinci,
The School of Athens is a description of philosophy. The scene takes place in classical times, as both the architecture and the garments (服饰) indicate. Figures representing each subject that must be mastered in order to hold a true philosophic debate – astronomy, geometry (几何), and arithmetic (算数) - are described in concrete form. The arbiters (仲裁) of this rule, the main figures, Plato and Aristotle, are shown in the center, engaged in such a dialogue.
“What is art?” E. So, named after a painting by Claude Monet, Impressionism focused on light and
leadership第四单元翻译
描述了发展的双因素理论在俄亥俄州立大学
讨论了管理方格识别和地方五个锚方式对网格
INTRODUCTION
When traits theory was not productive the focus shifted toward behavior of leaders
“What do leaders actually do and how do they do it?”
组织工作
考虑初始结构是独立的规模
TWO-FACTOR APPROACHES, cont.
Blake and Mouton managerial grid:
Explored the concern for task and concern for relationship
Built upon the work of the Michigan and Ohio State studies
其他研究人员把重点放在分歧的专制（任务）与民主（社会）风格
生产导向与员工导向
工作中心和员工为中心
专制与参与
任务导向与社会情感面向
McGREGOR THEORY X AND THEORY Y
McGregor created two alternative sets of assumptions of human motivation
早期行为的方法
勒温，利比特，和白色（爱荷华大学）发现三个不同的领导风格
专制作风–正式规则，法规，控制
民主作风–合作，参与和参与，互动
–自由放任风格“让”，不干涉，不参与
连续的
EARLY BEHAVIORAL APPROACHES, cont.
General findings:
Singularity of the density of states in the two-dimensional Hubbard model from finite size
a r X i v :c o n d -m a t /9503139v 1 27 M a r 1995Singularity of the density of states in the two-dimensional Hubbard model from finitesize scaling of Yang-Lee zerosE.Abraham 1,I.M.Barbour 2,P.H.Cullen 1,E.G.Klepfish 3,E.R.Pike 3and Sarben Sarkar 31Department of Physics,Heriot-Watt University,Edinburgh EH144AS,UK 2Department of Physics,University of Glasgow,Glasgow G128QQ,UK 3Department of Physics,King’s College London,London WC2R 2LS,UK(February 6,2008)A finite size scaling is applied to the Yang-Lee zeros of the grand canonical partition function for the 2-D Hubbard model in the complex chemical potential plane.The logarithmic scaling of the imaginary part of the zeros with the system size indicates a singular dependence of the carrier density on the chemical potential.Our analysis points to a second-order phase transition with critical exponent 12±1transition controlled by the chemical potential.As in order-disorder transitions,one would expect a symmetry breaking signalled by an order parameter.In this model,the particle-hole symmetry is broken by introducing an “external field”which causes the particle density to be-come non-zero.Furthermore,the possibility of the free energy having a singularity at some finite value of the chemical potential is not excluded:in fact it can be a transition indicated by a divergence of the correlation length.A singularity of the free energy at finite “exter-nal field”was found in finite-temperature lattice QCD by using theYang-Leeanalysisforthechiral phase tran-sition [14].A possible scenario for such a transition at finite chemical potential,is one in which the particle den-sity consists of two components derived from the regular and singular parts of the free energy.Since we are dealing with a grand canonical ensemble,the particle number can be calculated for a given chem-ical potential as opposed to constraining the chemical potential by a fixed particle number.Hence the chem-ical potential can be thought of as an external field for exploring the behaviour of the free energy.From the mi-croscopic point of view,the critical values of the chemical potential are associated with singularities of the density of states.Transitions related to the singularity of the density of states are known as Lifshitz transitions [15].In metals these transitions only take place at zero tem-perature,while at finite temperatures the singularities are rounded.However,for a small ratio of temperature to the deviation from the critical values of the chemical potential,the singularity can be traced even at finite tem-perature.Lifshitz transitions may result from topological changes of the Fermi surface,and may occur inside the Brillouin zone as well as on its boundaries [16].In the case of strongly correlated electron systems the shape of the Fermi surface is indeed affected,which in turn may lead to an extension of the Lifshitz-type singularities into the finite-temperature regime.In relating the macroscopic quantity of the carrier den-sity to the density of quasiparticle states,we assumed the validity of a single particle excitation picture.Whether strong correlations completely distort this description is beyond the scope of the current study.However,the iden-tification of the criticality using the Yang-Lee analysis,remains valid even if collective excitations prevail.The paper is organised as follows.In Section 2we out-line the essentials of the computational technique used to simulate the grand canonical partition function and present its expansion as a polynomial in the fugacity vari-able.In Section 3we present the Yang-Lee zeros of the partition function calculated on 62–102lattices and high-light their qualitative differences from the 42lattice.In Section 4we analyse the finite size scaling of the Yang-Lee zeros and compare it to the real-space renormaliza-tion group prediction for a second-order phase transition.Finally,in Section 5we present a summary of our resultsand an outlook for future work.II.SIMULATION ALGORITHM AND FUGACITY EXPANSION OF THE GRAND CANONICALPARTITION FUNCTIONThe model we are studying in this work is a two-dimensional single-band Hubbard HamiltonianˆH=−t <i,j>,σc †i,σc j,σ+U i n i +−12 −µi(n i ++n i −)(1)where the i,j denote the nearest neighbour spatial lat-tice sites,σis the spin degree of freedom and n iσis theelectron number operator c †iσc iσ.The constants t and U correspond to the hopping parameter and the on-site Coulomb repulsion respectively.The chemical potential µis introduced such that µ=0corresponds to half-filling,i.e.the actual chemical potential is shifted from µto µ−U412.(5)This transformation enables one to integrate out the fermionic degrees of freedom and the resulting partition function is written as an ensemble average of a product of two determinantsZ ={s i,l =±1}˜z = {s i,l =±1}det(M +)det(M −)(6)such thatM ±=I +P ± =I +n τ l =1B ±l(7)where the matrices B ±l are defined asB ±l =e −(±dtV )e −dtK e dtµ(8)with V ij =δij s i,l and K ij =1if i,j are nearestneigh-boursand Kij=0otherwise.The matrices in (7)and (8)are of size (n x n y )×(n x n y ),corresponding to the spatial size of the lattice.The expectation value of a physical observable at chemical potential µ,<O >µ,is given by<O >µ=O ˜z (µ){s i,l =±1}˜z (µ,{s i,l })(9)where the sum over the configurations of Ising fields isdenoted by an integral.Since ˜z (µ)is not positive definite for Re(µ)=0we weight the ensemble of configurations by the absolute value of ˜z (µ)at some µ=µ0.Thus<O >µ= O ˜z (µ)˜z (µ)|˜z (µ0)|µ0|˜z (µ0)|µ0(10)The partition function Z (µ)is given byZ (µ)∝˜z (µ)N c˜z (µ0)|˜z (µ0)|×e µβ+e −µβ−e µ0β−e −µ0βn (16)When the average sign is near unity,it is safe to as-sume that the lattice configurations reflect accurately thequantum degrees of freedom.Following Blankenbecler et al.[1]the diagonal matrix elements of the equal-time Green’s operator G ±=(I +P ±)−1accurately describe the fermion density on a given configuration.In this regime the adiabatic approximation,which is the basis of the finite-temperature algorithm,is valid.The situa-tion differs strongly when the average sign becomes small.We are in this case sampling positive and negative ˜z (µ0)configurations with almost equal probability since the ac-ceptance criterion depends only on the absolute value of ˜z (µ0).In the simulations of the HSfields the situation is dif-ferent from the case of fermions interacting with dynam-ical bosonfields presented in Ref.[1].The auxilary HS fields do not have a kinetic energy term in the bosonic action which would suppress their rapidfluctuations and hence recover the adiabaticity.From the previous sim-ulations on a42lattice[3]we know that avoiding the sign problem,by updating at half-filling,results in high uncontrolledfluctuations of the expansion coefficients for the statistical weight,thus severely limiting the range of validity of the expansion.It is therefore important to obtain the partition function for the widest range ofµ0 and observe the persistence of the hierarchy of the ex-pansion coefficients of Z.An error analysis is required to establish the Gaussian distribution of the simulated observables.We present in the following section results of the bootstrap analysis[17]performed on our data for several values ofµ0.III.TEMPERATURE AND LATTICE-SIZEDEPENDENCE OF THE YANG-LEE ZEROS The simulations were performed in the intermediate on-site repulsion regime U=4t forβ=5,6,7.5on lat-tices42,62,82and forβ=5,6on a102lattice.The ex-pansion coefficients given by eqn.(14)are obtained with relatively small errors and exhibit clear Gaussian distri-bution over the ensemble.This behaviour was recorded for a wide range ofµ0which makes our simulations reli-able in spite of the sign problem.In Fig.1(a-c)we present typical distributions of thefirst coefficients correspond-ing to n=1−7in eqn.(14)(normalized with respect to the zeroth power coefficient)forβ=5−7.5for differ-entµ0.The coefficients are obtained using the bootstrap method on over10000configurations forβ=5increasing to over30000forβ=7.5.In spite of different values of the average sign in these simulations,the coefficients of the expansion(16)indicate good correspondence between coefficients obtained with different values of the update chemical potentialµ0:the normalized coefficients taken from differentµ0values and equal power of the expansion variable correspond within the statistical error estimated using the bootstrap analysis.(To compare these coeffi-cients we had to shift the expansion by2coshµ0β.)We also performed a bootstrap analysis of the zeros in theµplane which shows clear Gaussian distribution of their real and imaginary parts(see Fig.2).In addition, we observe overlapping results(i.e.same zeros)obtained with different values ofµ0.The distribution of Yang-Lee zeros in the complexµ-plane is presented in Fig.3(a-c)for the zeros nearest to the real axis.We observe a gradual decrease of the imaginary part as the lattice size increases.The quantitative analysis of this behaviour is discussed in the next section.The critical domain can be identified by the behaviour of the density of Yang-Lee zeros’in the positive half-plane of the fugacity.We expect tofind that this density is tem-perature and volume dependent as the system approaches the phase transition.If the temperature is much higher than the critical temperature,the zeros stay far from the positive real axis as it happens in the high-temperature limit of the one-dimensional Ising model(T c=0)in which,forβ=0,the points of singularity of the free energy lie at fugacity value−1.As the temperature de-creases we expect the zeros to migrate to the positive half-plane with their density,in this region,increasing with the system’s volume.Figures4(a-c)show the number N(θ)of zeros in the sector(0,θ)as a function of the angleθ.The zeros shown in thesefigures are those presented in Fig.3(a-c)in the chemical potential plane with other zeros lying further from the positive real half-axis added in.We included only the zeros having absolute value less than one which we are able to do because if y i is a zero in the fugacity plane,so is1/y i.The errors are shown where they were estimated using the bootstrap analysis(see Fig.2).Forβ=5,even for the largest simulated lattice102, all the zeros are in the negative half-plane.We notice a gradual movement of the pattern of the zeros towards the smallerθvalues with an increasing density of the zeros nearθ=πIV.FINITE SIZE SCALING AND THESINGULARITY OF THE DENSITY OF STATESAs a starting point for thefinite size analysis of theYang-Lee singularities we recall the scaling hypothesis forthe partition function singularities in the critical domain[11].Following this hypothesis,for a change of scale ofthe linear dimension LLL→−1),˜µ=(1−µT cδ(23)Following the real-space renormalization group treatmentof Ref.[11]and assuming that the change of scaleλisa continuous parameter,the exponentαθis related tothe critical exponentνof the correlation length asαθ=1ξ(θλ)=ξ(θ)αθwe obtain ξ∼|θ|−1|θ|ναµ)(26)where θλhas been scaled to ±1and ˜µλexpressed in terms of ˜µand θ.Differentiating this equation with respect to ˜µyields:<n >sing =(−θ)ν(d −αµ)∂F sing (X,Y )ν(d −αµ)singinto the ar-gument Y =˜µαµ(28)which defines the critical exponent 1αµin terms of the scaling exponent αµof the Yang-Lee zeros.Fig.5presents the scaling of the imaginary part of the µzeros for different values of the temperature.The linear regression slope of the logarithm of the imaginary part of the zeros plotted against the logarithm of the inverse lin-ear dimension of the simulation volume,increases when the temperature decreases from β=5to β=6.The re-sults of β=7.5correspond to αµ=1.3within the errors of the zeros as the simulation volume increases from 62to 82.As it is seen from Fig.3,we can trace zeros with similar real part (Re (µ1)≈0.7which is also consistentwith the critical value of the chemical potential given in Ref.[22])as the lattice size increases,which allows us to examine only the scaling of the imaginary part.Table 1presents the values of αµand 1αµδ0.5±0.0560.5±0.21.3±0.3∂µ,as a function ofthe chemical potential on an 82lattice.The location of the peaks of the susceptibility,rounded by the finite size effects,is in good agreement with the distribution of the real part of the Yang-Lee zeros in the complex µ-plane (see Fig.3)which is particularly evident in the β=7.5simulations (Fig.4(c)).The contribution of each zero to the susceptibility can be singled out by expressing the free energy as:F =2n x n yi =1(y −y i )(29)where y is the fugacity variable and y i is the correspond-ing zero of the partition function.The dotted lines on these plots correspond to the contribution of the nearby zeros while the full polynomial contribution is given by the solid lines.We see that the developing singularities are indeed governed by the zeros closest to the real axis.The sharpening of the singularity as the temperature de-creases is also in accordance with the dependence of the distribution of the zeros on the temperature.The singularities of the free energy and its derivative with respect to the chemical potential,can be related to the quasiparticle density of states.To do this we assume that single particle excitations accurately represent the spectrum of the system.The relationship between the average particle density and the density of states ρ(ω)is given by<n >=∞dω1dµ=ρsing (µ)∝1δ−1(32)and hence the rate of divergence of the density of states.As in the case of Lifshitz transitions the singularity of the particle number is rounded at finite temperature.However,for sufficiently low temperatures,the singular-ity of the density of states remains manifest in the free energy,the average particle density,and particle suscep-tibility [15].The regular part of the density of states does not contribute to the criticality,so we can concentrate on the singular part only.Consider a behaviour of the typedensity of states diverging as the−1ρsing(ω)∝(ω−µc)1δ.(33)with the valueδfor the particle number governed by thedivergence of the density of states(at low temperatures)in spite of thefinite-temperature rounding of the singu-larity itself.This rounding of the singularity is indeedreflected in the difference between the values ofαµatβ=5andβ=6.V.DISCUSSION AND OUTLOOKWe note that in ourfinite size scaling analysis we donot include logarithmic corrections.In particular,thesecorrections may prove significant when taking into ac-count the fact that we are dealing with a two-dimensionalsystem in which the pattern of the phase transition islikely to be of Kosterlitz-Thouless type[23].The loga-rithmic corrections to the scaling laws have been provenessential in a recent work of Kenna and Irving[24].In-clusion of these corrections would allow us to obtain thecritical exponents with higher accuracy.However,suchanalysis would require simulations on even larger lattices.The linearfits for the logarithmic scaling and the criti-cal exponents obtained,are to be viewed as approximatevalues reflecting the general behaviour of the Yang-Leezeros as the temperature and lattice size are varied.Al-though the bootstrap analysis provided us with accurateestimates of the statistical error on the values of the ex-pansion coefficients and the Yang-Lee zeros,the smallnumber of zeros obtained with sufficient accuracy doesnot allow us to claim higher precision for the critical ex-ponents on the basis of more elaboratefittings of the scal-ing behaviour.Thefinite-size effects may still be signifi-cant,especially as the simulation temperature decreases,thus affecting the scaling of the Yang-Lee zeros with thesystem rger lattice simulations will therefore berequired for an accurate evaluation of the critical expo-nent for the particle density and the density of states.Nevertheless,the onset of a singularity atfinite temper-ature,and its persistence as the lattice size increases,areevident.The estimate of the critical exponent for the diver-gence rate of the density of states of the quasiparticleexcitation spectrum is particularly relevant to the highT c superconductivity scenario based on the van Hove sin-gularities[25],[26],[27].It is emphasized in Ref.[25]thatthe logarithmic singularity of a two-dimensional electrongas can,due to electronic correlations,turn into a power-law divergence resulting in an extended saddle point atthe lattice momenta(π,0)and(0,π).In the case of the14.I.M.Barbour,A.J.Bell and E.G.Klepfish,Nucl.Phys.B389,285(1993).15.I.M.Lifshitz,JETP38,1569(1960).16.A.A.Abrikosov,Fundamentals of the Theory ofMetals North-Holland(1988).17.P.Hall,The Bootstrap and Edgeworth expansion,Springer(1992).18.S.R.White et al.,Phys.Rev.B40,506(1989).19.J.E.Hirsch,Phys.Rev.B28,4059(1983).20.M.Suzuki,Prog.Theor.Phys.56,1454(1976).21.A.Moreo, D.Scalapino and E.Dagotto,Phys.Rev.B43,11442(1991).22.N.Furukawa and M.Imada,J.Phys.Soc.Japan61,3331(1992).23.J.Kosterlitz and D.Thouless,J.Phys.C6,1181(1973);J.Kosterlitz,J.Phys.C7,1046(1974).24.R.Kenna and A.C.Irving,unpublished.25.K.Gofron et al.,Phys.Rev.Lett.73,3302(1994).26.D.M.Newns,P.C.Pattnaik and C.C.Tsuei,Phys.Rev.B43,3075(1991);D.M.Newns et al.,Phys.Rev.Lett.24,1264(1992);D.M.Newns et al.,Phys.Rev.Lett.73,1264(1994).27.E.Dagotto,A.Nazarenko and A.Moreo,Phys.Rev.Lett.74,310(1995).28.A.A.Abrikosov,J.C.Campuzano and K.Gofron,Physica(Amsterdam)214C,73(1993).29.D.S.Dessau et al.,Phys.Rev.Lett.71,2781(1993);D.M.King et al.,Phys.Rev.Lett.73,3298(1994);P.Aebi et al.,Phys.Rev.Lett.72,2757(1994).30.E.Dagotto, A.Nazarenko and M.Boninsegni,Phys.Rev.Lett.73,728(1994).31.N.Bulut,D.J.Scalapino and S.R.White,Phys.Rev.Lett.73,748(1994).32.S.R.White,Phys.Rev.B44,4670(1991);M.Veki´c and S.R.White,Phys.Rev.B47,1160 (1993).33.C.E.Creffield,E.G.Klepfish,E.R.Pike and SarbenSarkar,unpublished.Figure CaptionsFigure1Bootstrap distribution of normalized coefficients for ex-pansion(14)at different update chemical potentialµ0for an82lattice.The corresponding power of expansion is indicated in the topfigure.(a)β=5,(b)β=6,(c)β=7.5.Figure2Bootstrap distributions for the Yang-Lee zeros in the complexµplane closest to the real axis.(a)102lat-tice atβ=5,(b)102lattice atβ=6,(c)82lattice at β=7.5.Figure3Yang-Lee zeros in the complexµplane closest to the real axis.(a)β=5,(b)β=6,(c)β=7.5.The correspond-ing lattice size is shown in the top right-hand corner. Figure4Angular distribution of the Yang-Lee zeros in the com-plex fugacity plane Error bars are drawn where esti-mated.(a)β=5,(b)β=6,(c)β=7.5.Figure5Scaling of the imaginary part ofµ1(Re(µ1)≈=0.7)as a function of lattice size.αm u indicates the thefit of the logarithmic scaling.Figure6Electronic susceptibility as a function of chemical poten-tial for an82lattice.The solid line represents the con-tribution of all the2n x n y zeros and the dotted line the contribution of the six zeros nearest to the real-µaxis.(a)β=5,(b)β=6,(c)β=7.5.。
单体和低聚物的含量对聚酰胺6切片性能的影响
浙江理工大学学报,第51卷,第2期,2024年3月J o u r n a l o f Z h e j i a n g S c i -T e c h U n i v e r s i t yD O I :10.3969/j.i s s n .1673-3851(n ).2024.02.004收稿日期:2023-04-06 网络出版日期:2023-07-07基金项目:浙江省自然科学基金项目(L D Q 23E 030001)作者简介:郭银涛(1997- ),男,安徽阜阳人,硕士研究生,主要从事再生P A 6性能分析方面的研究㊂通信作者:吕汪洋,E -m a i l :l u w y@z s t u .e d u .c n 单体和低聚物的含量对聚酰胺6切片性能的影响郭银涛,王勇军,吕汪洋(浙江理工大学纺织纤维材料与加工技术国家工程实验室,杭州310018) 摘 要:采用溶解/沉淀法对聚酰胺6(P A 6)中的单体及低聚物进行提取,利用液相色谱/飞行时间质谱/二极管阵列检测器(L C -T O F -M S -P D A )和聚合物色谱/多角度激光散射/示差折光检测器(A P C -M A L L S -R I D )联用方法测定P A 6中单体和低聚物含量㊁低聚物组成及P A 6的分子量和分布;通过热重分析仪㊁差示扫描量热仪和二维广角X 射线衍射仪分析P A 6切片中单体低聚物含量对切片热性能和结晶性能的影响㊂结果表明:物理再生P A 6(pr -P A 6)和化学再生P A 6(c r -P A 6)中单体及环状低聚物含量分别为2.079%和1.578%,比原生P A 6(P A 6)分别高0.683%和0.182%,其中再生P A 6切片中单体㊁环状二聚体和环状三聚体含量高于原生P A 6切片㊂P A 6㊁pr -P A 6和c r -P A 6的分子量分别为19620㊁20840g /m o l 和22210g /m o l ,分子量分布系数分别为1.47㊁1.56和1.49;三种P A 6切片的最大分解温度无明显变化㊂与原生P A 6切片相比,再生P A 6切片的结晶峰温度向高温区偏移,结晶温度从P A 6的176ħ增加至p r -P A 6的185ħ,且pr -P A 6和c r -P A 6切片中α晶型的相对含量增加㊂该研究可为提高P A 6材料的热性能及结晶性能提供理论基础㊂关键词:P A 6切片;单体;低聚物;液相色谱/飞行时间质谱/二极管阵列检测器;结晶中图分类号:T Q 317.2文献标志码:A文章编号:1673-3851(2024)03-0174-06引文格式:郭银涛,王勇军,吕汪洋.单体和低聚物的含量对聚酰胺6切片性能的影响[J ].浙江理工大学学报(自然科学),2024,51(2):174-179.R e f e r e n c e F o r m a t :G U O Y i n t a o ,W A N G Y o n g j u n ,L ÜW a n g y a n g .E f f e c t s o f m o n o m e r a n d o l i go m e r c o n t e n t i n p o l y a m i d e 6p e l l e t s o n t h e i r p r o p e r t i e s [J ].J o u r n a l o f Z h e j i a n g S c i -T e c h U n i v e r s i t y,2024,51(2):174-179.E f f e c t s o f m o n o m e r a n d o l i g o m e r c o n t e n t i n p o l y a m i d e 6p e l l e t s o n t h e i r p r o pe r t i e s G U O Y i n t a o ,W A N G Y o n g j u n ,L ÜW a n g y a n g(N a t i o n a l E n g i n e e r i n g L a b o r a t o r y f o r T e x t i l e F i b e r M a t e r i a l s a n d P r o c e s s i n g T e c h n o l o g y,Z h e j i a n g S c i -T e c h U n i v e r s i t y ,H a n gz h o u 310018,C h i n a ) A b s t r a c t :M o n o m e r s a n d o l i g o m e r s f r o m p o l y a m i d e 6(P A 6)w e r e e x t r a c t e d b y d i s s o l u t i o n /p r e c i p i t a t i o n m e t h o d ,a c o m b i n a t i o n o f l i q u i d c h r o m a t o g r a p h y /t i m e f l i g h t m a s s s p e c t r o m e t r y /ph o t o d i o d e a r r a y d e t e c t o r (L C -T O F -M S -P D A )a n d a p o l y m e r c h r o m a t o g r a p h y /m u l t i -a n g l e l a s e r -l i g h t -s c a t t e r i n g/r e f r a c t i v e i n d e x d e t e c t o r (A P C -M A L L S -R I D )w a s u s e d t o m e a s u r e t h e m o n o m e r a n d o l i go m e r c o n t e n t a n d o l i g o m e r c o m p o s i t i o n o f P A 6,P A 6m o l e c u l a r w e i gh t a n d i t s d i s t r i b u t i o n i n P A 6.T h e e f f e c t s o f t h e m o n o m e r a n d o l i g o m e r c o n t e n t o n t h e t h e r m a l a n d c r y s t a l l i z a t i o n p r o p e r t i e s o f P A 6p e l l e t s w e r e a n a l yz e d b y t h e r m o g r a v i m e t r i c a n a l y z e r ,d i f f e r e n t i a l s c a n n i n g c a l o r i m e t e r a n d t w o -d i m e n s i o n a l w i d e -a n g l e X -r a yd i f f r a c t o me t e r .T h e r e s u l t s i n d i c a t e t h a t t h e m o n o m e r a n d c y c l i c o l i g o m e r c o n t e n t s i n p h y s i c a l l y r e c yc l ed P A 6(p r -P A 6)a n d c he m i c a l l y r e c y c l e d P A 6(c r -P A 6)p e l l e t s w e r e 2.079%a n d 1.578%,r e s p e c t i v e l y,0.683%a n d 0.182%h i g h e r t h a n t h o s e i n t h e o r i g i n a l P A 6(P A 6)p e l l e t s ,w h i l e t h e m o n o m e r ,c yc l i cd i me r a n d c y c l i c t r i m e r c o n t e n t s i n t h e r e c y c l e d P A 6p e l l e t s w e r e h i g h e r t h a n t h o s e of t h e o r i gi n a l P A 6p e l l e t s .T h e m o l e c u l a r w e i gh t s o f P A 6,p r -P A 6a n d c r -P A 6w e r e 19620g /m o l ,20840g /m o l a n d22210g/m o l,r e s p e c t i v e l y,w i t h t h e m o l e c u l a r w e i g h t d i s t r i b u t i o n c o e f f i c i e n t s o f P A6,p r-P A6a n d c r-P A6 b e i n g1.47,1.56a n d1.49,r e s p e c t i v e l y.T h e m a x i m u m d e c o m p o s i t i o n t e m p e r a t u r e s o f t h e t h r e e P A6 p e l l e t s d i d n o t c h a n g e s i g n i f i c a n t l y.C o m p a r e d w i t h t h e o r i g i n a l P A6p e l l e t s,t h e c r y s t a l l i z a t i o n p e a k t e m p e r a t u r e o f r e g e n e r a t e d P A6p e l l e t s s h i f t e d t o t h e h i g h t e m p e r a t u r e r e g i o n,a n d t h e c r y s t a l l i z a t i o n t e m p e r a t u r e i n c r e a s e d f r o m176ħf o r P A6t o185ħf o r p r-P A6,a n d t h e r e l a t i v e c o n t e n t o fαc r y s t a l l i n e f o r m s i n p r-P A6a n d c r-P A6p e l l e t s i n c r e a s e d.T h i s s t u d y c a n p r o v i d e a t h e o r e t i c a l b a s i s f o r i m p r o v i n g t h e t h e r m a l a n d c r y s t a l l i z a t i o n p r o p e r t i e s o f P A6m a t e r i a l s.K e y w o r d s:P A6p e l l e t s;m o n o m e r s;o l i g o m e r s;l i q u i d c h r o m a t o g r a p h y/t i m e f l i g h t m a s s s p e c t r o m e t r y/p h o t o d i o d e a r r a y d e t e c t o r(L C-T O F-M S-P D A);c r y s t a l l i z a t i o n0引言聚酰胺6(P A6)材料广泛应用于日常生活和工业工程,如纺织品㊁轮胎帘子布和渔网等[1-2]㊂因具有优异的耐化学性和耐磨性,导致P A6材料在自然环境中难以分解[3-5]㊂为了缓解环境压力及减少P A6材料的浪费,对其进行回收再利用处理是重要途径[6]㊂P A6材料回收再利用的方法主要有物理法和化学法[7-10]㊂物理法指将废旧P A6材料进行清洗㊁干燥和添加各种助剂进行重新熔融造粒的方法;化学法指将废旧P A6材料降解成相应的小单体,然后重新聚合成P A6的方法㊂然而,无论是物理法还是化学法,均会对P A6的性能产生一定的影响㊂对P A6材料结构性能变化进行相关分析的研究近年来受到广泛关注㊂目前,聚合物材料的结构性能的表征方法有傅里叶变换红外光谱法㊁差示扫描量热法和热重分析法等方法[11-14]㊂然而,这些技术却不能高效准确地表征聚合物中低聚物的含量及组成㊂目前,液相色谱技术在对低聚物含量测试方面具有很大的优势,具有相对较高的速度㊁效率和灵敏度㊂通过将液相色谱与合适的检测仪器联用,例如液相色谱和质谱(L C-M S)联用以及液相色谱和化学发光氮检测耦合联用(H P L C-C L N D)能够显著提高检测能力[15-16]㊂本文拟采用更高效㊁快捷的液相色谱/飞行时间质谱/二极管阵列检测器(L C-T O F-M S-P D A)方法对P A6材料中单体及低聚物的含量进行表征㊂目前,常用提取P A6中低聚物的方法为热水萃取法,该方法需要消耗大量时间,且对单体及低聚物提取不完全,急需发展有效的提取方法㊂本文建立了一种对P A6中单体及低聚物提取较完全的溶剂/沉淀法㊂该方法选择合适的良性溶剂和不良溶剂对P A6材料中的单体及低聚物进行提取㊂在此基础上,进一步分析P A6切片中单体和低聚物含量对其性能的影响㊂综上所述,本文采用溶解/沉淀法对P A6材料中单体及低聚物进行提取,利用L C-T O F-M S-P D A 方法对P A6材料中单体及低聚物含量进行表征,采用先进聚合物色谱/多角度激光光散射/示差折光检测器(A P C-M A L L S-R I D)对样品的分子量及其分布进行分析,并通过热分析仪(T G A)㊁差示扫描量热仪(D S C)和二维广角X射线衍射仪(W A X D)分析再生P A6切片中单体及低聚物对其热性能和结晶性能的影响㊂研究结果可为提高P A6材料的热性能及结晶性能提供一定的理论基础㊂1实验部分1.1实验材料P A6切片来自上海纺织工业技术监督局,包括原生P A6(P A6,相对黏度2.8)㊁物理法再生P A6 (p r-P A6,相对黏度2.8)和化学法再生P A6(c r-P A6,相对黏度3.1)㊂乙腈(M e C N,ȡ99.9%)购自默克试剂公司三氟乙酸钠(色谱纯,ȡ99.7%),六氟异丙醇(H F I P,ȡ99.9%),甲醇(A R,ȡ95%)均购自阿拉丁试剂公司㊂1.2P A6样品中单体及低聚物的提取及P A6粉末样品制备将P A6样品(0.5g)在25ħ下溶解于H F I P (7m L)中,随后边搅拌边缓慢滴加沉淀剂甲醇,待大量沉淀析出后,将剩余液体转移至25m L容量瓶中定容,静置待用㊂将P A6样品先液氮冷冻2m i n,再放入粉碎机中粉碎10m i n,得到P A6粉末样品㊂1.3测试与表征采用液相色谱/飞行时间质谱/二极管阵列检测器(美国W a t e r s公司,型号U P L C S y n a p t G2-S H D M S)分析P A6切片中单体和低聚物的含量,流动相由水(A相)和色谱级乙腈(B相)组成,其中流动相采用梯度洗脱,流动相流速为0.3m L/m i n㊂采用先进聚合物色谱(美国W a t e r s公司,型号571第2期郭银涛等:单体和低聚物的含量对聚酰胺6切片性能的影响W a t e r s1525/2414)结合多角度激光光散射仪和示差折光检测器对P A6切片的分子量及分布进行测定,流动相和溶剂为含5m m o l/L三氟乙酸钠的六氟异丙醇溶液,流动相流速为0.4m L/m i n㊂采用热重分析仪(瑞士M e t t l e r公司,型号T G A1/D S C1)考察P A6切片的热稳定性,N2流速为45m L/m i n,测试温度范围25~550ħ,升温速率为10ħ/m i n㊂采用差示扫描量热仪(瑞士M e t t l e r公司,型号A v a n c eⅡ400)测试P A6样品的结晶性能,N2流速为45m L/m i n,升温测试温度范围25~300ħ,并保温3m i n,降温测试温度范围300~25ħ,升温和降温速率均为10ħ/m i n㊂采用二维广角X射线衍射仪(德国B r u k e r公司,型号D8D i s c o v e r)分析P A6切片的晶体结构,采用C u Kα辐射源,电压和电流分别为40k V和40m A,扫描范围为2ʎ~76ʎ㊂2结果与讨论2.1液相色谱/飞行时间质谱/二极管阵列检测器分析液相色谱/飞行时间质谱/二极管阵列检测器(L C-T O F-M S-P D A)不仅能获得聚合物材料中单体及低聚物的分子量,还可以根据其形状及大小对单体和低聚物进行分离㊂P A6中单体及低聚物L C图如图1所示,从中可以看出,单体和低聚物能被有效地分离㊂溶解/沉淀法能有效提取单体㊁环状二聚体至环状九聚体(C1~C9)等低聚物,且C2㊁C1㊁C3㊁C4㊁C5㊁C6㊁C7㊁C8和C9依次被洗脱出来㊂可以清晰地看出C2保留时间短于C1,这可能是因为C2与色谱柱填料之间存在弱相互作用[17]㊂单体及低聚物相对应的分子质量如表1所示,其中测试相对分子量由飞行时间质谱测得,理论相对分子量由计算机计算得到;C1相对分子量为加H+后的相对分子量,C2~ C9相对分子量为加N a+后的相对分子量㊂P A6分子链中的酰胺键为吸水性基团,故在单体及低聚物含量测试前需进行烘干处理㊂P A6切片样品中单体和低聚物含量(质量含量)见表2㊂从中可以看出单体和低聚物含量随聚合度的增加呈现先下降随后上升再下降的趋势,其中p r-P A6比P A6中单体及低聚物比P A6高约0.683%㊂p r-P A6和c r-P A6切片中C1~C5的低聚物含量均显著增加,p r-P A6比P A6高约0.69%,而c r-P A6比P A6高约0.198%㊂相比P A6切片,p r-P A6和图1单体和环状低聚物对应的L C图表1单体及低聚物的分子量[C n+H/N a]+(n=1,2, ,9)测试相对分子量(m/z)P A6p r-P A6c r-P A6理论相对分子量(m/z) [C1+H]+114.0925114.0925114.0921114.0919 [C2+N a]+249.1583249.1582249.1583249.1579 [C3+N a]+362.2419362.2430362.2430362.2420 [C4+N a]+475.3273475.3278475.3270475.3260 [C5+N a]+588.4115588.4120588.4125588.4101 [C6+N a]+701.4951701.4952701.4955701.4942 [C7+N a]+814.5803814.5789814.5787814.5782 [C8+N a]+927.6641927.6642927.6653927.6623 [C9+N a]+1040.75671040.74781040.75391040.7463 c r-P A6切片中C6~C9的含量变化不明显,三种样品都仅在0.643%左右㊂这是因为在再生过程中,高温熔融会导致P A6材料大分子的分子链断裂,生成分子量较低的低聚物所致㊂c r-P A6中的单体及低聚物总含量高于P A6且低于p r-P A6,这主要是因为在c r-P A6的制备是将材料中分子链解聚成单体或低聚物,然后解聚获得单体及低聚物重新聚合制备c r-P A6材料㊂2.2先进聚合物色谱分析聚合物的分子量过大或过小会影响聚合物的加工性能,故对聚合物分子量测试具有重要意义㊂表3展示了不同切片的平均分子量及多分散指数㊂从中可以看出,P A6切片具有较小的分子量分布系数(重均分子量/数均分子量,M w/M n),对应的M n为19620g/m o l;p r-P A6切片的分子量分布系数最大,对应的M n为20840g/m o l,这与多分散指数会随着低聚物含量的增加而增加的结论吻合㊂P A6中低聚物含量低,因其链长均匀,故而导致分子量分布变窄, M n值也较低㊂图2是示差折光(R I)和光散射(L S)信号图㊂从中可以发现,当样品分子量越大,到达峰值所需的时间越短㊂由于c r-P A6在重聚的过程中加671浙江理工大学学报(自然科学)2024年第51卷入扩链剂,使得分子链长度增加并生成凝胶结构[18],因而c r -P A 6切片的M n 最大,达到22210g /m o l㊂总之,再生过程会使P A 6材料的M n 增加,低聚物的增多会使分子链分布变宽,分子量分布系数增加㊂表2 P A 6切片单体及低聚物含量%样品名称C 1C 2C 3C 4C 5C 6C 7C 8C 9总含量P A 60.1080.0480.1310.1960.2630.2780.2370.1020.0331.396pr -P A 60.6450.0750.1830.2450.2880.2820.2330.1050.0212.079c r -P A 60.1380.0820.1800.2480.2960.2810.2380.0910.0261.578表3 不同切片的平均分子量及多分散指数切片名称M n /(g ㊃m o l -1)M w /M n P A 6196201.47pr -P A 6208401.56c r -P A 6222101.49图2 不同P A 6切片的L S 信号和R I 信号图2.3 P A 6切片热性能分析2.3.1 热重分析仪分析P A 6材料的热稳定性在循环再利用过程也会受到一定的影响㊂P A 6切片热重图如图3所示㊂从中可以看出,P A 6切片的初始分解温度为350ħ,P A 6㊁pr -P A 6及c r -P A 6样品质量损失5%对应的温度分别为407.5㊁402.6ħ和407.2ħ㊂此外,从图3中可以看出,P A 6切片的残留量比c r -P A 6的残留量高约2%,比p r -P A 6的残留量高约5%㊂这是由于P A 6材料中低聚物含量高会使分子量的分布变宽,降低了分子量的均匀性,从而导致该部分在降解过程中更容易发生化学键断裂[19],使pr -P A 6切片在初始阶段的热分解速度加快㊂P A 6切片的热重微分曲线如图4所示㊂从中可以看出P A 6的分解速率最快,但三者的分解温度基本相同,并没有发生较大改变㊂图3 不同P A 6切片的T G 曲线图4 不同P A 6切片D T G 曲线2.3.2 差示扫描量热仪分析采用D S C 对P A 6切片的熔融结晶过程进行研究,结果如图5所示㊂从中可以看出,再生P A 6切片和原生P A 6切片的升温和降温曲线相似[2],表明再生过程对P A 6切片的熔融结晶过程影响很小㊂降温结晶过程曲线如图5(a ),与原生P A 6切片相比,再生P A 6切片的结晶峰温度向高温区偏移,结晶温度从原生P A 6的176ħ增加至p r -P A 6的185ħ㊂造成这种现象的原因是,一方面,p r -P A 6和c r -P A 6中低聚物含量较高使分子量分布变宽,从而低分子化合物含量较高;另一方面,P A 6再加工过程中分子链的断裂导致不完整晶体产生[21]㊂这两个方面都会使再生P A 6切片的结晶速率加快及结晶峰向高温偏移㊂结晶温度升高不利于纺丝过程,主要表现为切片在纺丝过程中的拉伸性能变差,更容易771第2期郭银涛等:单体和低聚物的含量对聚酰胺6切片性能的影响发生断丝和毛丝㊂升温过程曲线如图5(b),再生P A6和原生P A6切片的熔点为222ħ左右,表明再生过程对P A6切片的熔融温度没有明显的影响㊂图5不同P A6切片的D S C图2.4P A6切片二维广角X射线衍射仪分析P A6材料在熔融加工㊁冷却后可形成两种主要晶型,即热力学稳定的α晶型和亚稳态的γ晶型[22]㊂从图6所示样品的二维广角X射线衍射图能够看到明显的衍射环㊂对二维衍射图进行软件处理,可以得到如图7所示的一维衍射强度曲线㊂P A6再生前后出现3个突出的衍射环,衍射环的位置没有改变,分别对应19.8ʎ㊁21.2ʎ和23.1ʎ㊂其中19.8ʎ和23.1ʎ对应于α晶型,而21.2ʎ对应γ晶型[23]㊂这说明3种P A6材料的晶型结构未发生改变㊂对于再生P A6材料, 23.1ʎ处的信号强度相比21.2ʎ更强,这说明该样品中23.1ʎ对应的α晶型的相对含量增加㊂3结论为研究P A6切片中单体及低聚物含量对其性能的影响,采用溶解/沉淀法对P A6材料中单体及低聚物进行提取,利用L C-T O F-M S-P D A联用法分析单体及低聚物含量,通过A P C-M A L L S-R I D测试样品分子量及其分布,结合热性能和结晶性能测试分析单体及低聚物含量对P A6材料性能的影响㊂所得主要结论如下:a)再生P A6中所含单体和低聚物的总量高于图6P A6样品X R D 二维衍射图图7P A6样品X R D一维衍射图原生P A6㊂这主要是再生P A6切片中单体㊁环状二聚体和环状三聚体的含量较高㊂物理再生P A6(p r-P A6)和化学再生P A6(c r-P A6)中单体及环状低聚物含量分别为2.079%和1.578%,比原生P A6 (P A6)分别高0.683%和0.182%㊂b)P A6切片的分子量分布随低聚物含量的增加而变宽,且再生过程能够增加P A6材料分子量㊂P A6㊁p r-P A6和c r-P A6的分子量分别为19620㊁20840g/m o l和22210g/m o l,分子量分布分别为1.47㊁1.56和1.49㊂c)较高含量的低聚物能够提高P A6材料的结晶温度㊁结晶速率以及初始热分解速率㊂结晶温度从原生P A6的176ħ增加至p r-P A6的185ħ,但三种P A6切片的最大分解温度无明显变化㊂871浙江理工大学学报(自然科学)2024年第51卷d)再生前后P A6材料的晶型结构未发生改变㊂当结晶温度从P A6的176ħ增加至p r-P A6的185ħ, p r-P A6和c r-P A6切片中α晶型的相对含量增加㊂参考文献:[1]P e n g C,T a n g X J,G o n g X Y,e t a l.D e v e l o p m e n t a n da p p l i c a t i o n o f a m a s s s p e c t r o m e t r y m e t h o d f o r q u a n t i f y i n g n y l o n m i c r o p l a s t i c s i n e n v i r o n m e n t[J].A n a l y t i c a l C h e m i s t r y,2020,92(20):13930-13935.[2]M o n d r a g o n G,K o r t a b e r r i a G,M e n d i b u r u E,e t a l. T h e r m o m e c h a n i c a l r e c y c l i n g o f p o l y a m i d e6f r o m f i s h i n g n e t s w a s t e[J].J o u r n a l o f A p p l i e d P o l y m e r S c i e n c e, 2020,137(10):48442.[3]B a n e r j e e S S,B h o w m i c k A K.N o v e l n a n o s t r u c t u r e d p o l y a m i d e6/f l u o r o e l a s t o m e r t h e r m o p l a s t i c e l a s t o m e r i c b l e n d s:I n f l u e n c e o f i n t e r a c t i o n a n d m o r p h o l o g y o n p h y s i c a l p r o p e r t i e s[J].P o l y m e r,2013,54(24):6561-6571. [4]E s m i z a d e h E,V a h i d i f a r A,S h o j a i e S,e t a l.T a i l o r i n g t h e p r o p e r t i e s o f P A6i n t o h i g h-p e r f o r m a n c e t h e r m o p l a s t i c e l a s t o m e r:S i m u l t a n e o u s r e i n f o r c e m e n t a n d i m p a c t p r o p e r t y m o d i f i c a t i o n[J].M a t e r i a l s T o d a yC o m m u n i c a t i o n s,2021,26:102027.[5]Še h i'c A,V a s i l j e v i'c J,J o r d a n o v I,e t a l.I n f l u e n c e o f N-,P-a n d S i-b a s e d f l a m e r e t a r d a n t m i x t u r e s o n f l a m m a b i l i t y,t h e r m a l b e h a v i o r a n d m e c h a n i c a l p r o p e r t i e s o f P A6c o m p o s i t e f i b e r s[J].F i b e r s a n d P o l y m e r s,2018,19(6):1194-1206.[6]李文武.基于热裂解色谱的P A6和P A66纤维鉴别及定量分析研究[D].杭州:浙江理工大学,2017:1-3.[7]C h e n J Y,L i Z,J i n L J,e t a l.C a t a l y t i c h y d r o t h e r m a ld e p o l y m e r i z a t i o n o f n y l o n6[J].J o u r n a l o f M a t e r i a lC y c l e s a n d W a s t e M a n a g e m e n t,2010,12(4):321-325.[8]A l b e r t i C,F i g u e i r a R,H o f m a n n M,e t a l.C h e m i c a l r e c y c l i n g o f e n d-o f-l i f e p o l y a m i d e6v i a r i n g c l o s i n g d e p o l y m e r i z a t i o n[J].C h e m i s t r y S e l e c t,2019,4(43): 12638-12642.[9]黄梅.聚酰胺类材料化学解聚反应研究[D].青岛:青岛科技大学,2018:6-10.[10]Z a g a r E,C e s a r e k U,D r i n c i c A,e t a l.Q u a n t i t a t i v ed e t e r m i n a t i o n o f P A6a n d/o r P A66c o n t e n t i n p o l y a m i d e-c o n t a i n i n g w a s t e s[J].A C S S u s t a i n a b l eC h e m i s t r y&E n g i n e e r i n g,2020,8(31):11818-11826.[11]张书敏,江龙发,周丽萍,等.再生塑料颗粒固体废物的典型特征及其识别技术[J].中国口岸科学技术, 2021,3(9):70-76.[12]王成云,邹慧萍,林君峰,等.D S C法快速鉴别塑料新料和再生料[J].上海塑料,2021,49(2):32-38. [13]孔维恒,王琳丽,郝欣,等.便携式拉曼光谱仪快速识别塑料新料与再生料[J].分析仪器,2019(5):109-111.[14]刘能盛.再生塑料检验鉴别技术的研究[D].广州:广东工业大学,2016:20-52.[15]S c h w e i g h u b e r A,G a l l M,F i s c h e r J,e t a l.D e v e l o p m e n t o f a n L C-M S m e t h o d f o r t h e s e m i q u a n t i t a t i v e d e t e r m i n a t i o n o f p o l y a m i d e6c o n t a m i n a t i o n s i n p o l y o l e f i n r e c y c l a t e s[J].A n a l y t i c a l a n d B i o a n a l y t i c a l C h e m i s t r y, 2021,413(4):1091-1098.[16]H e i m r i c h M,Bön s c h M,N i c k l H,e t a l.C y c l i c o l i g o m e r s i n p o l y a m i d e f o r f o o d c o n t a c t m a t e r i a l: Q u a n t i f i c a t i o n b y H P L C-C L N D a n d s i n g l e-s u b s t a n c e c a l i b r a t i o n[J].F o o d A d d i t i v e s&C o n t a m i n a n t s:P a r t A:C h e m i s t r y,A n a l y s i s,C o n t r o l,E x p o s u r e&R i s kA s s e s s m e n,2012,29(5):846-860.[17]M e n g e r i n k Y,P e t e r s R,K e r k h o f f M,e t a l.A n a l y s i s o f l i n e a r a n d c y c l i c o l i g o m e r s i n p o l y a m i d e-6w i t h o u t s a m p l e p r e p a r a t i o n b y l i q u i d c h r o m a t o g r a p h y u s i n g t h e s a n d w i c h i n j e c t i o n m e t h o d[J].J o u r n a l o fC h r o m a t o g r a p h y A,2000,876(1/2):37-50.[18]C a i Q Q,B a i T W,Z h a n g H J,e t a l.C a t a l y s t-f r e e s y n t h e s i s o f p o l y e s t e r s v i a c o n v e n t i o n a l m e l t p o l y c o n d e n s a t i o n[J].M a t e r i a l s T o d a y,2021,51:155-164.[19]L i R G,S h i K H,Y e L,e t a l.I n t e r c a l a t i o n s t r u c t u r ea n d e n h a n c e d t h e r m a l o x i d a t i v e s t ab i l i t y o f p o l y a m i d e 6/g r a p h e n e n a n oc o m p o s i t e s p r e p a r ed t h r o u g h i n s i t u p o l y me r i z a t i o n[J].I n d u s t r i a l&E n g i n e e r i n gC h e m i s t r y R e s e a r c h,2017,56(46):13715-13724.[20]T u n a B,B e n k r e i r a H.C h a i n e x t e n s i o n o f r e c y c l e d P A6 [J].P o l y m e r E n g i n e e r i n g&S c i e n c e,2018,58(7): 1037-1042.[21]S u K H,L i n J H,L i n C C.I n f l u e n c e o f r e p r o c e s s i n g o n t h e m e c h a n i c a l p r o p e r t i e s a n d s t r u c t u r e o f p o l y a m i d e 6[J].J o u r n a l o f M a t e r i a l s P r o c e s s i n g T e c h n o l o g y, 2007,192/193:532-538.[22]L i M Q,Z h a n g Y D,Z h u F,e t a l.I n f l u e n c e o f P A6 p a r t i c l e f i l l e r o n m o r p h o l o g y,c r y s t a l l i z a t i o n b e h a v i o r a n d d y n a m i c m e c h a n i c a l p r o p e r t i e s o f p o l y(ε-c a p r o l a c t o n e)a s a n e f f i c i e n t n u c l e a t i n g a g e n t[J]. J o u r n a l o f P o l y m e r R e s e a r c h,2021,28(12):461.[23]L i X R,H a n P,S o n g G J,e t a l.A s s e m b l y o f p o l y a m i d e6n a n o t u b e a r r a y s w i t h o r d e r e d p a t t e r n s a n d t h e c r y s t a l l i z a t i o n b e h a v i o r[J].M a t e r i a l s L e t t e r s, 2015,141:157-160.(责任编辑:刘国金)971第2期郭银涛等:单体和低聚物的含量对聚酰胺6切片性能的影响。
2019新人教版高中英语选择性必修三unit1课文及翻译(英汉对照)
新人教版高中英语选择性必修三课文及翻译Unit1 Reading and ThinkingA SHORT HISTORY OF WESTERN PAINTING西方绘画艺术简史What is Western art? It is hard to give a precise definition. As there have been so many different styles of Western art, it is impossible to describe them all in a short text. Perhaps the best way to understand Western art is to look at the development of Western painting over the centuries.什么是西方艺术?很难给出一个精确的定义。
由于西方的艺术风格多种多样，在短短的一篇课文里不可能进行全面的描述。
也许了解西方艺术的最好方法就是看看几个世纪以来西方绘画的发展。
The Middle Ages (from the 5th to the 15th century)中世纪(5世纪到15世纪)During the Middle Ages, the purpose of Western art was to teach people about Christianity. Thus, artists were not interested in painting realistic scenes. Their works were often primitive and two-dimensional, and the main characters were often made much larger than everyone else to show their importance. This began to change in the 13th century with Giotto di Bondone (1267-1337). While his paintings still had religious themes, they showed real people in a real environment. In particular, his paintings are set apart from other paintings by their realistic human faces and deep emotional impact.在中世纪，西方艺术的目的是向人们传授基督教因此，艺术家对写实场景不感兴趣。
电影分类英文版
Science Fiction Film
• Science fiction as the name
implies that "science fantasy", is "to science fiction feature film, the content of its basic characteristics from today's known scientific principles and scientific achievements, the world or for the future of the distant past the pattern of the fantasy of the description.
• The movie, which is also called film. It combines photograph by the activity with slide-show art develop a kind of continuous images. And it is a art that can accommodate tragicomedy and literature, sculpture, architecture, and other comprehensive art. But it also has the artistic characteristics alone. Film on artistic expression not only has the characteristics of other form of art, and they can use the strong artistic film montage set skills, with above all other artistic means of performance, and can replicate a lot of film.
The Two-Dimensional Analogue of General Relativity
a rXiv:g r-qc/93141v 129Oct1993THE TWO-DIMENSIONAL ANALOGUE OF GENERAL RELATIVITY Jos´e P.S.Lemos Departamento de Astrof´ısica,Observat´o rio Nacional-CNPq,Rua General Jos´e Cristino 77,20921Rio de Janeiro,Brazil,&Departamento de F ´ısica,Instituto Superior T´e cnico,Av.Rovisco Pais 1,1096Lisboa,Portugal.Paulo M.S´a Centro de F ´ısica da Mat´e ria Condensada,Av.Prof.Gama Pinto 2,1699Lisboa Codex,Portugal.Abstract General Relativity in three or more dimensions can be obtained by taking the limit ω→∞in the Brans-Dicke theory.In two dimensions General Relativity is an unacceptable theory.We show that the two-dimensional closest analogue of General Relativity is a theory that also arises in the limit ω→∞of the two-dimensional Brans-Dicke theory.11.IntroductionIt is known that in two-dimensional(2D)spacetimes the Einstein-Hilbert action,S= d2x√2g ab R,which is identically zero for any2D metric.The energy-momentum tensor is definedasT ab≡2−gδ(√δg ab,(1)where L matter is the Lagrangean for the matterfields.Then,assuming Ein-stein’s equations,G ab−Λg ab=T ab,the vanishing of G ab implies that T ab should be proportional toΛg ab,giving an unacceptable theory.Thus,one has to consider alternative2D theories of gravitation.Teitelboim and Jackiw[1]have proposed the simplest model for a2D theory of gravitation,given by the constant curvature equation R−Λ= 0.Introducing an auxiliary scalarfield,Φ(x),one can derive this equation through an action given byS= d2x√−g ψR+1−ge−2φ R−4ω(∂φ)2+4λ2 ,(4)whereωis a parameter,λis a constant usually related toΛasΛ=−4λ2, andΦandφare related throughΦ=e−2φ.This action includes several important cases:forω=0one recovers the Teitelboim-Jackiw theory given2in eq.(2),ω=−1−gR,since it gives G ab=R ab−1−ge−2φR,whereφis a scalarfield.Variation with respect toφ,δSterm proportional to(∂φ)2have to be introduced in the action.If the action is to be homogeneous inφsuch that S[constant+φ]=constant×S[φ],then the proportionality term in(∂φ)2is a constant which we callω.The action can then be written asS= d2x√−g e−2φ R−4ω(∂φ)2+4λ2 +4L matter ,(6)where g is the determinant of the2D metric,R is the curvature scalar,φis a scalarfield,λandωare constants.Variation of this action with respect to g ab andφgives,respectively,e2φT ab=−2(ω+1)D aφD bφ+D a D bφ−g ab D c D cφ+(ω+2)g ab D cφD cφ−g abλ2,(7) R−4ωD c D cφ+4ωD cφD cφ+4λ2=0,(8) where D represents the covariant derivative.The limitω→∞in eq.(8) makes sense if one makesφ=φ0+ϕω2 ,(9)where the numerical factor1The trace of eq.(7)together with(9)gives4ωe2φ0eϕ2ω(∂ϕ)2−8ωλ2.(11) Then,comparing(10)and(11)we obtainR+4ωe2φ0eϕ2ω(∂ϕ)2.(12) Finally,redefiningΛ=−8ωλ2,(13)¯T=−4ωe2φ0T,(14) and taking the limitω→∞one hasR=2ϕ,(15)R−Λ=T,(16) where we have dropped the bar over T.Note that the limitω→−∞gives the same theory.Substituting(9)into action(6)one obtainsS=−1−g −2ωR+ϕR+(∂ϕ)2−g ϕR+1limitω→∞(the R=T theory)as the2D analogue of General Relativity. Thus,equation(16)is the2D equivalent of Einstein equations;equation(15) determines the auxiliaryfieldϕ.5.ConclusionsThe theory we have shown to be2D natural analogue of General Relativity has been explored by Mann and colaborators.It admits gravitational collapse [12,13],gravitational waves[12],particle solutions with horizons and their causal structure[3,14],cosmological solutions[12,15],and semiclassical approximations[5].We have found in another work[9]that this theory also admits a vacuum black hole with two rather surprising properties:(i)it is a black hole of constant curvature,and(ii)it has no spacetime singularities.Black holes of constant curvature have also been found in three dimensions by identifying certain points of the anti-de Sitter spacetime[17].The two dimensional constant curvature black hole version arises through a similar procedure and is analogous to theω=0(see eq.(4))black hole[16].On the other hand non-singular black holes have also appeared in the framework of an exact solution of2D string theory[18].Thus,it seems that the non-singular character of these black holes is a property of the2D world.As afinal remark we would like to point out,that whereas we have discussed here the2D analogue of General Relativity,the theory given by ω=−11984)p.327;R.Jackiw,in:Quantum Theory of Gravity,essays in honour of the60th birthday of B.DeWitt,ed.S.Christensen(Adam Hilger-Bristol,1984)p.403.[2]J.D.Brown,M.Henneaux and C.Teitelboim,Phys.Rev.D33(1986)319.[3]R.B.Mann,A.Shiekh and L.Tarasov,Nucl.Phys.B341(1990)134.[4]C.G.Torre,Phys.Rev.D40(1989)2588.[5]R.B.Mann,S.M.Morsink,A.S.Sikkema and T.G.Steele,Phys.Rev.D43(1991)3948.[6]J.P.S.Lemos,“Two-Dimensional Black Holes and General Relati-vity”,preprint DF/IST-13.93,1993.[7]G.Mandal,A.M.Sengupta and S.R.Wadia,Mod.Phys.Lett.A6(1991)1685.[8]E.Witten,Phys.Rev.D44(1991)314.[9]J.P.S.Lemos and P.M.S´a,“The Black Holes of a General Two-Diemsional Dilaton Gravity Theory”,preprint DF/IST-9.93,1993.[10]R.B.Mann and S.F.Ross,Phys.Rev.D47(1993)3312.[11]T.Banks and M.O’Loughlin,Nucl.Phys.B362(1991)649.[12]A.E.Sikkema and R.B.Mann,Class.Quant.Grav.8(1991)219.[13]R.B.Mann and S.F.Ross,Class.Quant.Grav.9(1992)2335.[14]D.Christensen and R.B.Mann,Class.Quant.Grav.9(1992)1769.[15]K.C.K.Chan and R.B.Mann,Class.Quant.Grav.10(1993)913.[16]J.P.S.Lemos and P.M.S´a,“Non-Singular Constant CurvatureTwo-Dimensional Black Hole”,preprint DF/IST-8.93(revised version), 1993.7[17]M.Ba˜n ados,M.Henneaux,C.Teitelboim and J.Zanneli,Phys.Rev.D48(1993)1506.[18]M.J.Perry and E.Teo,Phys.Rev.Lett.70(1993)2669.8。
On the concept of normal shift in non-metric geometry
1. What is normal shift ? Brief historical overview. Phenomenon of normal shift is very simple by its nature. Let’s consider it in three-dimensional Euclidean space R3 . Suppose that σ is some smooth orientable surface in R3 . At each point p ∈ σ one can draw unit normal vector n such that n = n(p) would be a smooth vector-valued function on σ . Let’s move each point p of σ in the direction of vector n(p) to the distance t which is the same for all points p ∈ σ . Then moved points pt would form another surface σt as shown on Fig. 1.1. Changing parameter t we would obtain one-parametric family of surfaces. This construction is known as Bonnet transformation. In Bonnet construction initial surface σ is transformed by moving each point of σ . Trajectories of motion in this case are straight lines directed along normal vectors and points of σ move along them with a constant speed |v| = 1. Therefore parameter t, which is the distance of displacement, can also be interpreted as time variable. Bonnet noted that all surfaces σt in his construction are perpendicular to the trajectories of moving points. For this reason his construction is also known as normal displacement or normal shift. Basic observation by Bonnet, i. e. orthogonality of surfaces σt and shift trajectories, gave an impetus for generalization of his construction. This was done by me
利用聚类算法区分小尺度电离层行扰事件与赤道等离子体泡事件
0254-6124/2020/40(6)-1014-10 Chin. J. Space Sci. 空间科学学报WANG Ling, YIN Fan. Distinguish small-scale traveling ionospheric disturbances and equatorial plasma bubbles by clustering algorithm (in Chinese). Chin. J. Space Sci., 2020, 40(6): 1014-1023. DOI:10.11728/cjss2020.06.1014利用聚类算法区分小尺度电离层行扰事件与赤道等离子体泡事件**国家重点研发计划项目(2018YFC1503501, 2018YFC1503501-01),国家自然科学基金重点项目(41431073)和国家自然科学基金面上项目(41474157)共同资助2020-01-13收到原稿，2020-04-17收到修定稿E-mail: ****************.cn.通信作者尹凡，E-mail: **************.cn汪领尹凡(武汉大学电子信息学院武汉430072)摘 要 利用Swarm 卫星2015年1月1日至2019年12月31日的50Hz 高频磁场数据，根据阈值判断垂直于主磁场方向的扰动，对磁纬45°N-45°S 之间的小尺度电离层行扰事件进行探测.为避免混淆而产生的干扰，可以根据阈值判断平行于主磁场方向是否发生扰动，从而排除典型的赤道等离子体泡事件.但对于较弱的赤道等 离子体泡事件，扰动阈值判断无效.为避免弱赤道等离子体泡事件的污染，根据小尺度电离层行扰事件和赤道等离 子体泡事件在不同参数空间中的密度分布差异，利用基于密度的聚类算法将赤道等离子体泡事件进一步甄别提取.结果表明，聚类算法能够有效地将赤道等离子体泡事件从小尺度电离层行扰事件中甄选出来，并使小尺度电离层行 扰事件聚类与赤道等离子体泡事件聚类形成清晰的边界.由聚类算法导出的弱赤道等离子体泡爭件主要分布在磁纬15°N —15°S,地理经度20°-60°W,月份10至3月之间，并且在20:00MLT-24:00MLT 存在高发生率，同 时依赖于太阳活动，这也验证了前人的相关研究结果.关键词 聚类算法，电离层,小尺度电离层行扰，赤道等离子体泡中图分类号P352Distinguish Small-scale Traveling IonosphericDisturbances and Equatorial PlasmaBubbles by Clustering AlgorithmWANG Ling YIN Fan(School of Electronic Information, Wuhan University, Wuhan 430072)Abstract By analyzing the 50 Hz high-frequency magnetic field data by Swarm from January 2015to December 2019, according to the magnetic disturbances above the threshold in the perpendiculardirection to the main field, Small-Scale Traveling Ionospheric Disturbances (SSTID) within ±45°Nmagnetic 1st itude have been detected. When detecting SSTID, Equatorial Plasma Bubbles (EPB) can be excluded by determining whether there is magnetic disturbance above the threshold in the汪领等：利用聚类算法区分小尺度电离层行扰事件和赤道等离子体泡事件1015direction which is parallel to the mean ambient field.However,when the disturbance is weak,the algorithm can n ot completely exclude it.According to the different density distribu t ion of SSTID and EPB in parameter space,the EPB can be distinguished by a density-based clustering algorithin.The results demonstrate that the clustering algorithm is very effective on separating EPB and SSTID in different two-dimensional parameteT spaces and brings out a clear boundary between the high density region and low density region.The EPB identified by the clustering algorithm shows the strong dependence on solar activity and their statistical features are consistent with the previous study.Key words Clustering algorithm,Ionosphere,Small-Scale Traveling Ionospheric Disturbance(SSTID), Equatorial Plasma Bubble(EPB)0引言由于等离子体的不稳定性,各种从上和从下的能量输入会导致电离层发生扰动现象，而并不总是保持稳态和均匀分层结构.波长小于10km的小尺度电离层行扰(Small-Scale Traveling Ionospheric Disturbance,SSTID)是一种经常发生在中低纬地区的电离层扰动现象，被认为是夜间波长几百km左右的中尺度电离层行扰(Medium-Scale Traveling Ionospheric Disturbance,MSTID)的一种演化，二者的统计特征基本一致太阳活动平静期的夜间中纬度电离层经常发生MSTIDd这是由电离层F层的Perkins不稳定和与其相连的偶发E层不稳定之间的耦合作用产生的【3-7】.与MSTID事件导致的中纬度中尺度磁场波动(Mid-latitude Magnetic Field fluctuation,MMF)类似，中低纬度SSTID事件也会导致与场向电流相关的小尺度磁场波动(Small-Scale Mid-Latitude Magnetic Fluctuation,SSMMF).通常MMF以及SSMMF在电离层顶部都不伴随电子密度的扰动，而且磁扰动只存在于主磁场的垂直方向［1'81-Yin等⑴研究发现SSMMF的统计特征与夜间MMF【&9］的统计特征存在一致性：SSMMF与MMF均主要分布在南北半球磁纬25°N-45°S之间，磁赤道低纬度附近(磁纬1(TN—10°S之间)和南大西洋异常(South Atlantic Anomaly,SAA)区域分布极其稀疏；在季节依赖性上均表现岀在夏至季节分布最密集，冬至其次，春秋分是事件发生的低谷期.在磁地方时上.SSMMF主要分别分布在0&00MLT-12:00MLT以及17:00MLT -23:00MLT.SSMMF整体对太阳活动没有依赖性.另一种电离层扰动现象是发生在低纬赤道地区的由瑞利泰勒不稳定性导致的等离子体密度不规则结构，通常被称为赤道扩展F(Equatorial Spread F, ESF)或赤道等离子体泡(Equatorial Plasma Bubble,EPB)【iot2］epb泡内电子密度远低于背景电离层电子密度，其电子密度耗尽可以达到90%以上. Liihr等(13-17\Park等网、Xiong等［叭Stolle 等【"I、Yokoyama等购研究使用CHAMP卫星观测结果，发现EPB产生的压强梯度驱动的电流和场向电流分别导致平行于主磁场和垂直于主磁场方向的磁场强度发生扰动.EPB主要出现在地理经度20°-60°W(SAA区域范围)，月份10至3月之间分布最密集，夏至季节分布非常稀疏，主要出现在20:00MLT-24:00MLT,并且依赖于太阳活动强度［14-18］.中低纬度的SSTID事件和EPB事件都会导致磁场扰动.利用星载高精度磁力计捕捉到的扰动信号对两种现象已进行了充分研究.但在研究这两种不同机制的事件时，必须对二者加以区分，否则会产生混淆•其区分的关键在于：SSTID事件导致的磁扰动存在于主磁场的垂直方向，在主磁场的平行方向上则表现平静;赤道等离子体泡产生的磁场扰动也明显存在于主磁场平行方向.Park等〔"I、Xiong等【叭Stolle等Ml、Liihr等【切通过分析CHAMP卫星磁场数据中平行于主磁场方向上的扰动来确定EPB 事件.Yin等⑴和Park等［&切分析CHAMP以及Swarm卫星磁场数据时，通过垂直于主磁场方向上的扰动来确定MSTID和SSTID事件，并且通过排除平行于主磁场方向的磁扰来避免EPB事件的1016Chin.J.Space Sci.空间科学学报2020,40(6)污染.一般地，事件性质可以通过不同方向上的时序信号是否存在超过设定阈值的扰动来确定.但是，由于EPB事件磁扰动的复杂，性,Stolle等网利用人工判读的方法来验证EPB事件但对于事件数量巨大的SSTID事件，人工判读显然不合适.Yin等【1】在探测SSTID事件时，虽然通过阈值判定的方法排除了EPB事件，但观察最终得到的SSTID事件集合在地理经度、地方时与磁纬等二维参数空间中分布，仍然可以发现明显的EPB事件的分布特征，即SSTID 事件集是不纯净的，受到了未被完全排除的EPB事件的污染.通过分析发现，SSTID探测算法中仅通过判定平行于主磁场方向上的磁扰来排除EPB事件的污染是存在缺陷的.一个非典型EPB事件，当其平行于主磁场方向上的磁扰持续时间比较短且扰动幅度相对较小(低于阈值但又不是噪声)时，会导致其不被判定为EPB事件，而被误判为SSTID事件.如果降低SSTID探测算法中排除EPB事件的判断阈值，又会因为噪声信号产生事件漏报，而排除了本该探测到的SSTID事件;而升高判断阈值则会将更多的EPB污染事件误报为SSTID事件,从而导致SSTID数据集污染更严重.另外,由于使用的等离子体密度数据的采样频率为2 Hz,远低于50Hz磁场数据，并且非典型EPB事件磁扰动及电子密度扰动均较弱，因此通过观测等离子体密度数据的扰动来排除非典型EPB事件也不合适.但非典型EPB事件和典型EPB事件的统计属，性是一致的.在Yin等〔1】的统计结果中，污染性的EPB事件地理上明显分布在磁赤道附近的SAA区域,在地方时上则集中分布在22:00MLT附近，这与已有观测一致.无论EPB污染事件是典型的还是非典型的,其在参数空间中的统计特征明显与SSTID事件不同.值得研究的是，是否存在一种能利用这两种事件在不同参数空间中的密度分布差异来对SSTID事件集合中未排除的EPB 事件进行进一步提取、剔除的方法，利用该方法进行数据处理,不仅能保证SSTID事件集的纯净性，而且能对未排除的EPB事件特征进行深入研究.基于密度的DBSCAN(Density-Based Spatial Clustering of Applications with Noise)I19)聚类算法能够弥补时序信号阈值判定事件算法存在的缺陷，对SSTID事件集合中存在的非典型EPB污染事件进行甄别.本文利用三颗Swarm卫星2015年1月1日至2019年12月31日的高精度磁场数据，探测磁纬45°N-45°S之间的SSTID事件.使用了通过判定平行主磁场方向上是否存在超过设定阈值的磁扰动来排除EPB事件的算法，针对使用这种算法的处理结果，使用基于密度的DBSCAN聚类算法对非典型EPB污染事件进行进一步甄选.最后分析验证由聚类算法导出的EPB事件的地理经度、磁地方时、季节和对太阳活动依赖性特征.1数据来源及处理方法1.1数据来源2013年11月22日欧空局(ESA)启动了Swarm 地球探测任务，将三颗卫星(Swarm-Alpha,Swarm-Bravo和Swarm-Char l ie)成功发射到近地极轨轨道. Swarm卫星的主要目标是测量迄今为止最完整、最高精度的地球磁场数据.经过卫星发射和轨道调试，2014年4月17日三颗卫星的飞行轨道最终配置完成.其中，相对较低的两颗卫星(Swarm-Alpha 和Swarm-Charlie)以462km的初始高度和87.35°的倾角轨道并行飞行.二者南北方向的距离大约只有75km,东西方向地理经度相差约为1.5°.Swarm-Bravo卫星单独飞行在520km的高度上，其轨道倾角为87.75°.本文使用了三颗Swarm卫星搭载的矢量场磁强计测量的50Hz高采样率磁场数据和朗缪尔探针测量的2Hz等离子体密度数据*.1.2SSTID事件探测方法Swarm卫星测量的50Hz磁场数据是基于North-East-Center(NEC)地理学坐标系，而SSTID 事件导致的磁扰动更容易出现在强背景磁场的垂直方向上.因此，需要将磁场数据从NEC坐标系转换到平均场(Mean-Field Aligned,MFA)坐标系.在MFA 坐标系中，磁场分量B x,B Z1B y构成MFA中的三个磁场正交分量，B z沿着平均磁场的方向，B y垂直于磁子午线并且指向东向I?。
不同足部姿势受试者使用外侧楔形鞋垫后股四头肌肌电和膝关节力学特征改变的研究
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Effects of lateral wedged insoles on knee kinematics and quadriceps femoris EMG activity of different foot postures subjects/QIU Rongmei, ZHU Jiahui, LIU Xia, et al.//Chinese Journal of Rehabilitation Medicine, 2021,36(6)：692—697 Abstract Objective: T o study the c h a n g e s o f myoelectricity o f quadriceps a n d b i o m e c h a n i c s characteristics o f k n e e joint
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JACS副编辑的主成分分析方法的应用
Differential Receptors Create Patterns Diagnostic for ATP and GTPShawn C.McCleskey,Michael J.Griffin,Stephen E.Schneider,John T.McDevitt,*andEric V.Anslyn*Uni V ersity of Texas at Austin,Department of Chemistry and Biochemistry,Austin,Texas 78712Received September 30,2002;E-mail:anslyn@Historically,chemical sensing has required the creation of a highly selective receptor for each component to be detected within a complex mixture.A more recent approach has been to use devices that rely on a series of chemo-or biosensors where analysis of complex mixtures arises from patterns produced by the combined response of all the sensors in the array.1This approach has been particularly successful for vapor-phase analysis.2Patterns can also be created that are diagnostic for single analytes.3We previously postulated that a series of random combinatorial receptors biased toward a class of analytes would be effective in an array setting.4To this end,we describe a sensing method utilizing a combinatorial library of receptors that can differentiate between highly structurally similar analytes,such as nucleotide phosphates,in water.The receptors consist of a rationally designed core with a binding cleft possessing guanidinium groups (Figure 1A).These guani-dinium groups impart an affinity for nucleotide triphosphates and are appended with tripeptides to incur differential binding properties.A previously reported screening of this same 4913-member library led to the identification a sensor (tripeptide Ser-Try-Ser)that was highly selective for adenosine 5′-triphosphate (ATP)over guanosine 5′-triphosphate (GTP).5The objective of this work is to determine whether the patterns generated by an unscreened library of receptors in an array can discriminate between structurally similar compounds,using ATP and GTP as test cases.Thirty beads from the library were randomly chosen,given an index number,and placed in a micromachined chip-based array platform that has been previously reported.6An electron micrograph of a representative 3×4array platform is shown in Figure 1C.Sample delivery to the chemosensors occurs using a previously described flow cell.6A schematic of the flow cell is shown in Figure 1D.The sample is introduced over the array and passes around and through the beads to exit the bottom of the wells.Red,green,and blue (RGB)transmitted light intensity values were recorded for each bead in the array over the period of the assay via a charge-coupled device (CCD).The signaling protocol used with the array platform was an indicator-displacement assay similar to those exploited in many of our single-analyte sensing schemes.7A schematic of the indicator-displacement scheme for this system is shown in Figure 1B.To impart color to the library members,an anionic chromophore,fluorescein (2),was introduced into the array containing different members from the combinatorial library of receptors.The cationic receptors (1)associate with the indicator,bringing about a distinct orange color to each bead.Blank beads show no orange color,indicating little indicator uptake.Upon exposure to solutions of nucleotide phosphates,the analyte displaces the indicator,fluores-cein,at different rates (Figure 2A and 2B)and each bead loses color.The RGB intensity values for the 30library beads in the array are recorded over time after a 2-mL injection of a 20mM sampleof ATP,GTP,or adenosine 5′-monophosphate (AMP)in 25mM HEPES buffer (pH 7.5).Three trials were performed for ATP,GTP,and AMP for a total of nine trials,and absorbance values were calculated by taking the negative log of the ratio of the blue channel intensity over the red channel intensity for each bead.6In Figure 2,A and B show a representative normalized absorbance trace for two of the beads in the array after an injection of GTP and AMP,respectively.These traces reveal that each chemosensor responds differently to various nucleotide phosphate samples.The slope of the absorbance values from 210to 435s was calculated for each bead in each sample,and these values were used for analysis because the indicator displacement rates were found to be most reproducible in this region.The slope of bead 28differs by 40%between the AMP and GTP trials,whereas the slope value for bead 23in each plot differs by only 26%.Although these slopes are easily differentiated by qualitative visual inspection,the rates of displacement for several trials can be compared more quantitatively by using pattern recognition algorithms.Figure 1.A microscopic to macroscopic representation of the sensing protocol.(A)General molecular structure of resin bound library of receptors (1)and fluorescein (2).(B)Signal transduction scheme used to detect nucleotide phosphates within the resin bound sensor.AA n )amino acid.(C)Scanning electron micrograph of a representative 3×4micro-array containing glass beads.(D)Design of flow cell used inexperiments.Published on Web 01/07/200311149J.AM.CHEM.SOC.2003,125,1114-111510.1021/ja021230b CCC:$25.00©2003American ChemicalSocietyPrincipal component analysis 8(PCA)was utilized to reduce the dimensionality of the data set.For each of the nine trials,a slope value was recorded for each of the 30beads.To identify patterns in the data,a principal component (PC)axis is calculated to lie along the line of maximum variance in the original data.Subsequent PC axes lie along lines describing diminishing levels of variance.The coordinates of the sample relative to the PC axes are termed scores and can be used as an indicator of correlation between analytes.Proximity in space on a score plot directly correlates to similarities in indicator displacement rates.Figure 2C shows a two-dimensional score plot for the first two principal components (PC1and PC2)with clustering of the AMP,GTP and ATP samples with one possible ATP outlier.PCA demonstrates that the array of library sensors can differentiate between structurally similar molecules such as AMP,GTP,and ATP.Factor loading values can be used to evaluate the individual sensors in the array.The values correspond to the cosine of the angle between a principal component axis and the original vari-able axis.Therefore,similar loading values correspond to similar sensor responses.Furthermore,loading values approaching 1or -1indicate that the individual sensor played a significant role in the formation of a particular component axis.Eight beads werechosen to be sequenced on the basis of their large and nearly overlapping factor loading values (Table 1).Bead 14,which possessed the lowest values,was sequenced to elucidate which receptors elicit minimal discrimination.It is interesting to note that the beads with high loading values possess serine (or the structurally similar amino acid threonine)and other aromatic amino acids,as found in our earlier screening of this library.5The role of these amino acids in differentiating nucleotide phosphates is still under investigation.In conclusion,the use of a combinatorial library of sensors and indicator-displacement assays in the context of a chip-based array allows for the differentiation of structurally similar analytes in aqueous solutions.The coupling of supramolecular chemistry principles with pattern recognition leads to this protocol for sensing.We are currently analyzing mixtures of analytes and other phosphate derivatives as a means to explore cross-reactivity between individual library members.Acknowledgment.We thank Dr.Klaus Linse and Michelle Gadush for their assistance in sequencing the library beads studied in this assay and Dwight Romanovicz and Myles Cavell for their contributions to Figure 1C and 1D,respectively.We also acknowl-edge funding from the National Institutes of Health (GM57306),ARO-MURI,the Welch Foundation,and the Beckman Center for Array Sensors.Supporting Information Available:Experimental details (PDF).This material is available free of charge via the Internet at .References(1)(a)Hayashi,K.;Yamanaka,M.;Toko,K.;Yamafuji,K.Sens.ActuatorsB 1990,2,205-213.(b)Albert,K..;Lewis,N.;Schauer,C.;Sotzing,G.;Stitzel,S.;Vaid,T.;Walt,D.Chem.Re V .2000,100,2595-2626.(2)(a)Lonergan,M.;Severin,E.;Dolemand,B.;Beaber,S.;Grubbs,R.;Lewis,N.Chem.Mater .1996,8,2298-2312.(b)Pearce,T.;Gardner,J.;Friel,S.;Barlett,P.;Blair,N.Analyst 1993,118,371-377.(3)(a)Drew,S.;Janzen,D.;Mann,K.Anal.Chem .2002,74,2547-2555.(b)Rakow,N.;Suslick,K.Nature 2000,406,710-712.(4)Lavigne,J.;Anslyn,E.Angew.Chem.,Int.Ed .2001,40,3118-3130.(5)Schneider,S.;O’Neil,S.;Anslyn,E.J.Am.Chem.Soc.2000,122,542-543.(6)Goodey,A.;Lavigne,J.;Savoy,S.;Rodriguez,M.;Curey,T.;Tsao,A.;Simmons,G.;Yoo,S.;Sohn,Y.;Anslyn,E.;Shear,J.;Niekirk,D.;McDevitt,J.J.Am.Chem.Soc 2001,123,2559-2570.(7)(a)Wiskur,S.;Anslyn,E.J.Am.Chem.Soc .2001,123,10109-10110.(b)Lavigne,J.;Anslyn,E.Angew.Chem .1999,111,3903-3906.(c)Niikura,K.;Metzger,A.;Anslyn,E.J.Am.Chem.Soc .1998,120,8533-8534.(8)(a)Jurs,P.;Bakken,G.;McClelland,H.Chem.Re V .2000,100,2649-2678.(b)Carey,W.;Beebe,K.;Kowalski,B.Anal.Chem.1986,58,149-153.JA021230BFigure 2.Absorbance values over time and principal component plot.To aid slope comparison,the plots were shifted so that the average of the initial 30data points prior to sample injection (not shown)had an absorbance of 1.00.(A)20mM GTP sample in 25mM HEPES buffered aqueous solution (pH 7.5)while eluting with 25mM HEPES buffer (pH 7.5)b Bead 23and O Bead 28.(B)20mM AMP sample in 25mM HEPES buffered aqueous solution (pH 7.5)while eluting with 25mM HEPES buffer (pH 7.5)b Bead 23and O Bead 28.(C)PCA score plot of the three trials for each nucleotide phosphate samples (2ATP,9AMP,and b GTP).Table 1.Sequencing Results and Factor Loading Values for the First Two Principal Components (PC1and PC2)tripeptide sequencefactor loading (PC1)factor loading (PC2)bead index numberAsp-Asn-Ser -0.980.1428Phe-Trp-Phe -0.88-0.1623Thr-Thr-Ser -0.880.3933Val-Asn-Tyr -0.84-0.2024Val-Pro-Ala 0.010.2114Ala-Met-Thr 0.17-0.9134Val-Gly-Ile 0.74-0.466Ser-His-Tyr 0.75-0.4725Thr-Thr-Ile 0.89-0.362C O M M U N I C A T I O N SJ.AM.CHEM.SOC.9VOL.125,NO.5,20031115。
X射线衍射仪(XRD)
X 射线衍射仪（XRD ）1、X 射线衍射仪（XRD ）原理当一束单色 X 射线照射到晶体上时，晶体中原子周围的电子受X 射线周期变化的电场作用而振动，从而使每个电子都变为发射球面电磁波的次生波源。
所发射球面波的频率与入射的X 射线相一致。
基于晶体结构的周期性，晶体中各个原子（原子上的电子）的散射波可相互干涉而叠加，称之为相干散射或衍射。
X 射线在晶体中的衍射现象，实质上是大量原子散射波相互干涉的结果。
每种晶体所产生的衍射花样都反映出晶体内部的原子分布规律。
根据上述原理，某晶体的衍射花样的特征最主要的是两个：（1）衍射线在空间的分布规律；（2）衍射线束的强度。
其中，衍射线的分布规律由晶胞大小，形状和位向决定，衍射线强度则取决于原子的品种和它们在晶胞的位置，因此，不同晶体具备不同的衍射图谱。
在混合物中，一种物质成分的衍射图谱与其他物质成分的存在与否无关，这就是利用X 射线衍射做物相分析的基础。
X 射线衍射是晶体的“指纹”，不同的物质具有不同的X 射线衍射特征峰值(点阵类型、晶胞大小、晶胞中原子或分子的数目、位置等)，结构参数不同则X 射线衍射线位置与强度也就各不相同，所以通过比较X射线衍射线位置与强度可区分出不同的物质成分。
布拉格方程，其中n 为衍射级数图1.1 布拉格衍射示意图布拉格方程反映的是衍射线方向和晶体结构之间的关系。
对于某一特定的晶体而言，只有满足布拉格方程的入射线角度才能够产生干涉增强，才会出现衍射条纹，这就是XRD 谱图的根本意义所在。
对于晶体材料，当待测晶体与入射束呈不同角度时，那些满足布拉格衍射的晶面就会被检测出来，体现在X 射线衍射（XRD ）图谱上就是具有不同的衍射强度的衍射峰。
对于非晶体材料，由于其结构不存在晶体结构中原子排列的长程有序，只是在几个原子范围内存在着短程有序，故非晶体材料的X 射线衍射（XRD ）图谱为一些漫散射馒头峰。
n λ=2dsin θ应用已知波长的X射线来测量θ角，从而计算出晶面间距d，这是用于X射线结构分析；另一个是应用已知d的晶体来测量θ角，从而计算出特征X射线的波长，进而可在已有资料中查出试样中所含的元素。
电影分类-英文版
202X
Thank You!
Hale Waihona Puke SadakoThe War Film
War film which is also called “military”. For history major military action films, through war events, campaigns and battles scenes, depicting characters, establishing the image of hero.
TITANIC
Cartoon
A cartoon is a form of twodimensional illustrated visual art. While the specific definition has changed over time, modern usage refers to a typically non-realistic or semi-realistic drawing or painting
单击此处添加正文，文字是您思想的提炼，请尽量言简意赅的阐 述观点。
the classification of film? Do you kown
Film Classification
Action Movie Comedy Documentary Science Fiction Film Horror Movie The War Film The Romantic Cartoon
人教版选择性必修三reading and thinking选三unit1
Picasso Others Still others
Cubism: analyse the shapes Realistic but dream-like quality Abstract art
characteristic: Not realistic, primitive and two-dimensional,
Nboyt ?realistic,
larger
primNitoivte,rtewaol-disimtiecn,siroenlail,gmioaiunsc,hparracimtersitwiveree
oafntedn
two-dimensional
For painters in the Middle Ages, art is ____________________ _p_r_i_m_i_ti_v_e_a_n__d_m__o_s_tl_y_f_o_r_r_e_l_ig_i_o_u_s________________________ .
Nboyt ?realistic,
larger
primNitoivte,rtewaol-disimtiecn,siroenlail,gmioaiunsc,hparracimtersitwiveree
oafntedn
two-dimensional
Religious themes, but showed real people in a real environment.
Impressionism
Subjective impression, not a detailed record
For artists in the Impression period, art is _m__o_r_e_a_b_o_u_t_t_h_e__su__b_je_c_t_iv_e__im__p_r_e_s_si_o_n_r_a_t_h_e_r_t_h_a_n__a_________ _d_e_t_a_il_e_d_r_e_c_o_r_d__o_f _th__in_g_s_.___.
Chinese art
Chinese artImportant components of Chinese culture include literature, music, visual arts, martial arts, cuisine, religion etc. Early "stone age art" dates back to 10,000 BC, mostly consisting of simple pottery and sculptures. After this early period Chinese art, like Chinese history, is typically classified by the succession of ruling dynasties of Chinese emperors, most of which lasted several hundred years.Chinese art has arguably the oldest continuous tradition in the world, and is marked by an unusual degree of continuity within, and consciousness of, that tradition, lacking an equivalent to the Western collapse and gradual recovery of classical styles.PaintingTraditional Chinese painting involves essentially the same techniques as Chinese calligraphy and is done with a brush dipped in black or colored ink; oils are not used. As with calligraphy, the most popular materials on which paintings are made of paper and silk. The finished work can be mounted on scrolls, such as hanging scrolls or handscrolls. Traditional painting can also be done on album sheets, walls, lacquerware, folding screens, and other media.Gong-bi (工筆), meaning "meticulous", uses highly detailed brushstrokes that delimits details very precisely.Ink and wash painting, in Chinese Shui-mo or (水墨also loosely termed watercolour or brush painting, and also known as "literati painting", as it was one of the "Four Arts" of the Chinese Scholar-official class ArtistsFrom the Han (202 BC) to the Tang (618–906) dynasties mainly painted the human figure.The time from the Five Dynasties period to the Northern Song period (907–1127) is known as the "Great age of Chinese landscape".SculptureChinese ritual bronzes from the Shang and Western Zhou Dynasties come from a period of over a thousand years from c. 1500, and have exerted a continuing influence over Chinese art.The spectacular Terracotta ArmySmaller figures in pottery or wood were placed in tombs for many centuries afterwards, reaching a peak of quality in the Tang DynastyPotteryThe first types of ceramics were made during the Palaeolithic era, and in later periods range from construction materials such as bricks and tiles, to hand-built pottery vessels fired in bonfires or kilns, to the sophisticated Chinese porcelain wares made for the imperial court.Decorative arts.Bronze, gold and silver, rhinoceros horn, Chinese silk, ivory, lacquer, cloisonne enamel and many other materials had specialist artists working in them.Folding screen(Chinese: 屏风; pinyin: píngfēng) is also a form of decorative art in ChinaHistorical development to 221 BCNeolithic pottery Yangshao cultureJade cultureThe Liangzhu Jade良渚文化The Liangzhu culture was the last Neolithic Jade culture in the Yangtze River deltaBronze casting The Bronze Age in China began with the Xia DynastyThe function and appearance of bronzes changed gradually from the Shang to the Zhou. They shifted from been used in religious rites to more practical purposes. By the Warring States period, bronze vessels had become objects of aesthetic enjoyment.Early Imperial China (221 BC–AD 220)The Terracotta Army, inside the Mausoleum of the First Qin Emperor, consists of more than 7,000 life-size tomb terra-cotta figures of warriors and horses buried with the self-proclaimed first Emperor of Qin (Qin Shi Huang) in 210–209 BC.The Han Dynasty was known for jade burial suitsCalligraphyCalligraphy was thought to be the highest and purest form of painting. The implements were the brush pen, made of animal hair, and black inks, made from pine soot and animal glue Wang Xizhi was a famous Chinese calligrapher who lived in the 4th century AD. His most famous work is the Lanting Xu, the preface of a collection of poems written by a number of poets when gathering at Lan Ting near the town of Shaoxing in Zhejiang province and engaging in a game called "qu shui liu shang".曲水流觞，是中国古代流传的一种游戏。
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i +j
(1)
k, h ∈ Z, where the coefficients Pk,j (x) and g (x, y ) have the two dimensional Taylor series expansions and Z denotes the set of integer numbers. The main importance of our work is considering the general second order linear PDDE (1), wherein the other papers only considered particular cases of our general problem. Also using the general shifted Jacobi polynomials as the basic functions for numerical approximation wherein the shifted Chebyshev (first to fourth kinds) and Legendre polynomials are particular cases of them, is the other superiority of our paper. The remainder of this paper is organized as follows: In Section 2, we introduce the properties of the one and two dimensional shifted Jacobi polynomials and the basic formulation of them is required for our subsequent development. Section 3, is devoted to the operational matrix of the one and two dimensional shifted Jacobi polynomials (derivative and moment) with some useful theorems. Section 4, summarizes the application of the two dimensional shifted Jacobi matrix method to the solution of problem (1). Thus, a set of algebraic equations is formed and a solution of the considered problem is introduced. In Section 5, we present the approximation with Jacobi polynomials. In section 6, the proposed method is applied to the two numerical experiments. The applications of the new method for the high order linear PDDEs is presented in Section 7. Finally, we have monitored a brief conclusion in section 8. Note, that we have computed the numerical results by Matlab (version 2013) programming.
1
Introduction
PDDEs arise in many branches of science and technology. For instance, in electromagnetic theory, physics, elasticity, fluid mechanics, heat transfer, acoustics, quantum mechanics, and so on [1-15]. In physics for example, the heat flow and the wave propagation phenomena are well described by PDDEs [5]. In ecology, most population models are governed by PDDEs [5]. The dispersion of a chemically reactive material is characterized by PDDEs [5]. In addition, most physical phenomena of fluid dynamics, quantum mechanics, electricity, plasma physics, propagation of shallow water waves, and many other models are controlled within its domain of validity by PDDEs [5]. Also the essential behavior of most physical systems can be modeled by the second order linear PDDEs with variable coefficients. There is no general theory known concerning the solvability of all PDDEs. Such a theory is extremely unlikely to exist, given the rich variety of physical, geometric, and probabilistic phenomena which can be modeled with PDDEs [2]. Instead research focuses on various particular PDDEs that are important for applications within and outside of mathematics, with the hope that insight from the origins of these PDDEs can give clues as to their solutions [2]. In particular case, the second order linear PDDEs with variable coefficients and their solutions play a major role in the branch of modern mathematics and arise frequently in many applied areas. Therefore, a reliable and efficient technique for the solution of them is too important. For a review of some applications of the second order linear PDDEs with variable coefficients, one can see [1-16]. The analytic results on the existence and uniqueness of solutions to the second order linear PDDEs have been investigated by many authors [1-16], however the existence and uniqueness of the solution for PDDEs under their conditions is beyond the scope of this article. We assume that the PDDEs which we consider in this paper with their conditions have solutions. During the last decades, several methods have been used to solve the second order linear PDDEs such as Chebyshev and Taylor method [17, 18], Adomian’s decomposition method [19, 20], the differential transform method [21-23], the finite element method [24-27], the finite volume method [28], the spectral element method [28], and the Jacobi operational matrix method [29], using generalized Jacobi polynomials/functions [30]. In this paper, we develop a new and efficient scheme (the general two dimensional shifted Jacobi matrix method) for numerical
Universal Journal of Applied Mathematics 1(2): 142-155, 2013
143
approximation of the second order linear PDDE (with the initial and boundary conditions which has a solution which is expressible as a known elementary function) in the following form