Sonoelastography using Compensated Power Doppler

合集下载

A Mathematical Theory of Communication

Reprinted with corrections from The Bell System Technical Journal,V ol.27,pp.379–423,623–656,July,October,1948.A Mathematical Theory of CommunicationBy C.E.SHANNONI NTRODUCTIONHE recent development of various methods of modulation such as PCM and PPM which exchangebandwidth for signal-to-noise ratio has intensiﬁed the interest in a general theory of communication.A basis for such a theory is contained in the important papers of Nyquist1and Hartley2on this subject.In the present paper we will extend the theory to include a number of new factors,in particular the effect of noise in the channel,and the savings possible due to the statistical structure of the original message and due to the nature of theﬁnal destination of the information.The fundamental problem of communication is that of reproducing at one point either exactly or ap-proximately a message selected at another point.Frequently the messages have meaning;that is they refer to or are correlated according to some system with certain physical or conceptual entities.These semantic aspects of communication are irrelevant to the engineering problem.The signiﬁcant aspect is that the actual message is one selected from a set of possible messages.The system must be designed to operate for each possible selection,not just the one which will actually be chosen since this is unknown at the time of design.If the number of messages in the set isﬁnite then this number or any monotonic function of this number can be regarded as a measure of the information produced when one message is chosen from the set,all choices being equally likely.As was pointed out by Hartley the most natural choice is the logarithmic function.Although this deﬁnition must be generalized considerably when we consider the inﬂuence of the statistics of the message and when we have a continuous range of messages,we will in all cases use an essentially logarithmic measure.The logarithmic measure is more convenient for various reasons:1.It is practically more useful.Parameters of engineering importance such as time,bandwidth,numberof relays,etc.,tend to vary linearly with the logarithm of the number of possibilities.For example,adding one relay to a group doubles the number of possible states of the relays.It adds1to the base2logarithm of this number.Doubling the time roughly squares the number of possible messages,ordoubles the logarithm,etc.2.It is nearer to our intuitive feeling as to the proper measure.This is closely related to(1)since we in-tuitively measures entities by linear comparison with common standards.One feels,for example,thattwo punched cards should have twice the capacity of one for information storage,and two identicalchannels twice the capacity of one for transmitting information.3.It is mathematically more suitable.Many of the limiting operations are simple in terms of the loga-rithm but would require clumsy restatement in terms of the number of possibilities.The choice of a logarithmic base corresponds to the choice of a unit for measuring information.If the base2is used the resulting units may be called binary digits,or more brieﬂy bits,a word suggested by J.W.Tukey.A device with two stable positions,such as a relay or aﬂip-ﬂop circuit,can store one bit of information.N such devices can store N bits,since the total number of possible states is2N and log22N N.If the base10is used the units may be called decimal digits.Sincelog2M log10M log102332log10M1Nyquist,H.,“Certain Factors Affecting Telegraph Speed,”Bell System Technical Journal,April1924,p.324;“Certain Topics in Telegraph Transmission Theory,”A.I.E.E.Trans.,v.47,April1928,p.617.2Hartley,R.V.L.,“Transmission of Information,”Bell System Technical Journal,July1928,p.535.INFORMATIONSOURCE TRANSMITTER RECEIVER DESTINATIONNOISESOURCEFig.1—Schematic diagram of a general communication system.a decimal digit is about31physical counterparts.We may roughly classify communication systems into three main categories:discrete, continuous and mixed.By a discrete system we will mean one in which both the message and the signal are a sequence of discrete symbols.A typical case is telegraphy where the message is a sequence of lettersand the signal a sequence of dots,dashes and spaces.A continuous system is one in which the message and signal are both treated as continuous functions,e.g.,radio or television.A mixed system is one in which both discrete and continuous variables appear,e.g.,PCM transmission of speech.Weﬁrst consider the discrete case.This case has applications not only in communication theory,but also in the theory of computing machines,the design of telephone exchanges and otherﬁelds.In additionthe discrete case forms a foundation for the continuous and mixed cases which will be treated in the second half of the paper.PART I:DISCRETE NOISELESS SYSTEMS1.T HE D ISCRETE N OISELESS C HANNELTeletype and telegraphy are two simple examples of a discrete channel for transmitting information.Gen-erally,a discrete channel will mean a system whereby a sequence of choices from aﬁnite set of elementarysymbols S1S n can be transmitted from one point to another.Each of the symbols S i is assumed to have a certain duration in time t i seconds(not necessarily the same for different S i,for example the dots anddashes in telegraphy).It is not required that all possible sequences of the S i be capable of transmission on the system;certain sequences only may be allowed.These will be possible signals for the channel.Thus in telegraphy suppose the symbols are:(1)A dot,consisting of line closure for a unit of time and then line open for a unit of time;(2)A dash,consisting of three time units of closure and one unit open;(3)A letter space consisting of,say,three units of line open;(4)A word space of six units of line open.We might place the restriction on allowable sequences that no spaces follow each other(for if two letter spaces are adjacent, it is identical with a word space).The question we now consider is how one can measure the capacity of such a channel to transmit information.In the teletype case where all symbols are of the same duration,and any sequence of the32symbols is allowed the answer is easy.Each symbol representsﬁve bits of information.If the system transmits n symbols per second it is natural to say that the channel has a capacity of5n bits per second.This does not mean that the teletype channel will always be transmitting information at this rate—this is the maximum possible rate and whether or not the actual rate reaches this maximum depends on the source of information which feeds the channel,as will appear later.In the more general case with different lengths of symbols and constraints on the allowed sequences,we make the following deﬁnition:Deﬁnition:The capacity C of a discrete channel is given bylog N TC LimT∞and thereforeC log X0In case there are restrictions on allowed sequences we may still often obtain a difference equation of this type andﬁnd C from the characteristic equation.In the telegraphy case mentioned aboveN t N t2N t4N t5N t7N t8N t10as we see by counting sequences of symbols according to the last or next to the last symbol occurring. Hence C is log0where0is the positive root of12457810.Solving this weﬁnd C0539.A very general type of restriction which may be placed on allowed sequences is the following:We imagine a number of possible states a1a2a m.For each state only certain symbols from the set S1S n can be transmitted(different subsets for the different states).When one of these has been transmitted the state changes to a new state depending both on the old state and the particular symbol transmitted.The telegraph case is a simple example of this.There are two states depending on whether or not a space was the last symbol transmitted.If so,then only a dot or a dash can be sent next and the state always changes. If not,any symbol can be transmitted and the state changes if a space is sent,otherwise it remains the same. The conditions can be indicated in a linear graph as shown in Fig.2.The junction points correspond totheFig.2—Graphical representation of the constraints on telegraph symbols.states and the lines indicate the symbols possible in a state and the resulting state.In Appendix1it is shown that if the conditions on allowed sequences can be described in this form C will exist and can be calculated in accordance with the following result:Theorem1:Let b s i j be the duration of the s th symbol which is allowable in state i and leads to state j. Then the channel capacity C is equal to log W where W is the largest real root of the determinant equation:∑s W bsi j i j0where i j1if i j and is zero otherwise.For example,in the telegraph case(Fig.2)the determinant is:1W2W4W3W6W2W410On expansion this leads to the equation given above for this case.2.T HE D ISCRETE S OURCE OF I NFORMATIONWe have seen that under very general conditions the logarithm of the number of possible signals in a discrete channel increases linearly with time.The capacity to transmit information can be speciﬁed by giving this rate of increase,the number of bits per second required to specify the particular signal used.We now consider the information source.How is an information source to be described mathematically, and how much information in bits per second is produced in a given source?The main point at issue is the effect of statistical knowledge about the source in reducing the required capacity of the channel,by the useof proper encoding of the information.In telegraphy,for example,the messages to be transmitted consist of sequences of letters.These sequences,however,are not completely random.In general,they form sentences and have the statistical structure of,say,English.The letter E occurs more frequently than Q,the sequence TH more frequently than XP,etc.The existence of this structure allows one to make a saving in time(or channel capacity)by properly encoding the message sequences into signal sequences.This is already done to a limited extent in telegraphy by using the shortest channel symbol,a dot,for the most common English letter E;while the infrequent letters,Q,X,Z are represented by longer sequences of dots and dashes.This idea is carried still further in certain commercial codes where common words and phrases are represented by four-orﬁve-letter code groups with a considerable saving in average time.The standardized greeting and anniversary telegrams now in use extend this to the point of encoding a sentence or two into a relatively short sequence of numbers.We can think of a discrete source as generating the message,symbol by symbol.It will choose succes-sive symbols according to certain probabilities depending,in general,on preceding choices as well as the particular symbols in question.A physical system,or a mathematical model of a system which produces such a sequence of symbols governed by a set of probabilities,is known as a stochastic process.3We may consider a discrete source,therefore,to be represented by a stochastic process.Conversely,any stochastic process which produces a discrete sequence of symbols chosen from aﬁnite set may be considered a discrete source.This will include such cases as:1.Natural written languages such as English,German,Chinese.2.Continuous information sources that have been rendered discrete by some quantizing process.Forexample,the quantized speech from a PCM transmitter,or a quantized television signal.3.Mathematical cases where we merely deﬁne abstractly a stochastic process which generates a se-quence of symbols.The following are examples of this last type of source.(A)Suppose we haveﬁve letters A,B,C,D,E which are chosen each with probability.2,successivechoices being independent.This would lead to a sequence of which the following is a typicalexample.B DC B C E C C C AD C B D D A AE C E E AA B B D A E E C A C E E B A E E C B C E A D.This was constructed with the use of a table of random numbers.4(B)Using the sameﬁve letters let the probabilities be.4,.1,.2,.2,.1,respectively,with successivechoices independent.A typical message from this source is then:A A A C D CB DC E A AD A D A CE D AE A D C A B E D A D D C E C A A A A A D.(C)A more complicated structure is obtained if successive symbols are not chosen independentlybut their probabilities depend on preceding letters.In the simplest case of this type a choicedepends only on the preceding letter and not on ones before that.The statistical structure canthen be described by a set of transition probabilities p i j,the probability that letter i is followedby letter j.The indices i and j range over all the possible symbols.A second equivalent way ofspecifying the structure is to give the“digram”probabilities p i j,i.e.,the relative frequency ofthe digram i j.The letter frequencies p i,(the probability of letter i),the transition probabilities 3See,for example,S.Chandrasekhar,“Stochastic Problems in Physics and Astronomy,”Reviews of Modern Physics,v.15,No.1, January1943,p.1.4Kendall and Smith,Tables of Random Sampling Numbers,Cambridge,1939.p i j and the digram probabilities p i j are related by the following formulas:p i ∑j p i j∑j p j i ∑j p j p j ip i j p i p i j∑j p ij ∑i p i ∑i jp i j 1As a speciﬁc example suppose there are three letters A,B,C with the probability tables:p i j A B C 045i B 21151p i jA1518270C 274135A typical message from this source is the following:A B B A B A B A B A B A B A B B B A B B B B B A B A B A B A B A B B B A C A C A BB A B B B B A B B A B AC B B B A B A.The next increase in complexity would involve trigram frequencies but no more.The choice ofa letter would depend on the preceding two letters but not on the message before that point.A set of trigram frequencies p i j k or equivalently a set of transition probabilities p i j k would be required.Continuing in this way one obtains successively more complicated stochastic pro-cesses.In the general n -gram case a set of n -gram probabilities p i 1i 2i n or of transition probabilities p i 1i 2i n 1i n is required to specify the statistical structure.(D)Stochastic processes can also be deﬁned which produce a text consisting of a sequence of“words.”Suppose there are ﬁve letters A,B,C,D,E and 16“words”in the language with associated probabilities:.10A.16BEBE .11CABED .04DEB .04ADEB.04BED .05CEED .15DEED .05ADEE.02BEED .08DAB .01EAB .01BADD .05CA .04DAD .05EESuppose successive “words”are chosen independently and are separated by a space.A typical message might be:DAB EE A BEBE DEED DEB ADEE ADEE EE DEB BEBE BEBE BEBE ADEE BED DEED DEED CEED ADEE A DEED DEED BEBE CABED BEBE BED DAB DEED ADEB.If all the words are of ﬁnite length this process is equivalent to one of the preceding type,but the description may be simpler in terms of the word structure and probabilities.We may also generalize here and introduce transition probabilities between words,etc.These artiﬁcial languages are useful in constructing simple problems and examples to illustrate vari-ous possibilities.We can also approximate to a natural language by means of a series of simple artiﬁcial languages.The zero-order approximation is obtained by choosing all letters with the same probability and independently.The ﬁrst-order approximation is obtained by choosing successive letters independently but each letter having the same probability that it has in the natural language.5Thus,in the ﬁrst-order ap-proximation to English,E is chosen with probability .12(its frequency in normal English)and W with probability .02,but there is no inﬂuence between adjacent letters and no tendency to form the preferred5Letter,digram and trigram frequencies are given in Secret and Urgent by Fletcher Pratt,Blue Ribbon Books,1939.Word frequen-cies are tabulated in Relative Frequency of English Speech Sounds,G.Dewey,Harvard University Press,1923.digrams such as TH,ED,etc.In the second-order approximation,digram structure is introduced.After aletter is chosen,the next one is chosen in accordance with the frequencies with which the various lettersfollow theﬁrst one.This requires a table of digram frequencies p i j.In the third-order approximation, trigram structure is introduced.Each letter is chosen with probabilities which depend on the preceding twoletters.3.T HE S ERIES OF A PPROXIMATIONS TO E NGLISHTo give a visual idea of how this series of processes approaches a language,typical sequences in the approx-imations to English have been constructed and are given below.In all cases we have assumed a27-symbol “alphabet,”the26letters and a space.1.Zero-order approximation(symbols independent and equiprobable).XFOML RXKHRJFFJUJ ZLPWCFWKCYJ FFJEYVKCQSGHYD QPAAMKBZAACIBZL-HJQD.2.First-order approximation(symbols independent but with frequencies of English text).OCRO HLI RGWR NMIELWIS EU LL NBNESEBY A TH EEI ALHENHTTPA OOBTTV ANAH BRL.3.Second-order approximation(digram structure as in English).ON IE ANTSOUTINYS ARE T INCTORE ST BE S DEAMY ACHIN D ILONASIVE TU-COOWE AT TEASONARE FUSO TIZIN ANDY TOBE SEACE CTISBE.4.Third-order approximation(trigram structure as in English).IN NO IST LAT WHEY CRATICT FROURE BIRS GROCID PONDENOME OF DEMONS-TURES OF THE REPTAGIN IS REGOACTIONA OF CRE.5.First-order word approximation.Rather than continue with tetragram,,n-gram structure it is easierand better to jump at this point to word units.Here words are chosen independently but with their appropriate frequencies.REPRESENTING AND SPEEDILY IS AN GOOD APT OR COME CAN DIFFERENT NAT-URAL HERE HE THE A IN CAME THE TO OF TO EXPERT GRAY COME TO FURNISHESTHE LINE MESSAGE HAD BE THESE.6.Second-order word approximation.The word transition probabilities are correct but no further struc-ture is included.THE HEAD AND IN FRONTAL ATTACK ON AN ENGLISH WRITER THAT THE CHAR-ACTER OF THIS POINT IS THEREFORE ANOTHER METHOD FOR THE LETTERS THATTHE TIME OF WHO EVER TOLD THE PROBLEM FOR AN UNEXPECTED.The resemblance to ordinary English text increases quite noticeably at each of the above steps.Note that these samples have reasonably good structure out to about twice the range that is taken into account in their construction.Thus in(3)the statistical process insures reasonable text for two-letter sequences,but four-letter sequences from the sample can usually beﬁtted into good sentences.In(6)sequences of four or more words can easily be placed in sentences without unusual or strained constructions.The particular sequence of ten words“attack on an English writer that the character of this”is not at all unreasonable.It appears then that a sufﬁciently complex stochastic process will give a satisfactory representation of a discrete source.Theﬁrst two samples were constructed by the use of a book of random numbers in conjunction with(for example2)a table of letter frequencies.This method might have been continued for(3),(4)and(5), since digram,trigram and word frequency tables are available,but a simpler equivalent method was used.To construct(3)for example,one opens a book at random and selects a letter at random on the page.This letter is recorded.The book is then opened to another page and one reads until this letter is encountered. The succeeding letter is then recorded.Turning to another page this second letter is searched for and the succeeding letter recorded,etc.A similar process was used for(4),(5)and(6).It would be interesting if further approximations could be constructed,but the labor involved becomes enormous at the next stage.4.G RAPHICAL R EPRESENTATION OF A M ARKOFF P ROCESSStochastic processes of the type described above are known mathematically as discrete Markoff processes and have been extensively studied in the literature.6The general case can be described as follows:There exist aﬁnite number of possible“states”of a system;S1S2S n.In addition there is a set of transition probabilities;p i j the probability that if the system is in state S i it will next go to state S j.To make thisMarkoff process into an information source we need only assume that a letter is produced for each transition from one state to another.The states will correspond to the“residue of inﬂuence”from preceding letters.The situation can be represented graphically as shown in Figs.3,4and5.The“states”are thejunctionFig.3—A graph corresponding to the source in example B.points in the graph and the probabilities and letters produced for a transition are given beside the correspond-ing line.Figure3is for the example B in Section2,while Fig.4corresponds to the example C.In Fig.3Fig.4—A graph corresponding to the source in example C.there is only one state since successive letters are independent.In Fig.4there are as many states as letters. If a trigram example were constructed there would be at most n2states corresponding to the possible pairs of letters preceding the one being chosen.Figure5is a graph for the case of word structure in example D. Here S corresponds to the“space”symbol.5.E RGODIC AND M IXED S OURCESAs we have indicated above a discrete source for our purposes can be considered to be represented by a Markoff process.Among the possible discrete Markoff processes there is a group with special properties of signiﬁcance in communication theory.This special class consists of the“ergodic”processes and we shall call the corresponding sources ergodic sources.Although a rigorous deﬁnition of an ergodic process is somewhat involved,the general idea is simple.In an ergodic process every sequence produced by the process 6For a detailed treatment see M.Fr´e chet,M´e thode des fonctions arbitraires.Th´e orie des´e v´e nements en chaˆıne dans le cas d’un nombreﬁni d’´e tats possibles.Paris,Gauthier-Villars,1938.is the same in statistical properties.Thus the letter frequencies,digram frequencies,etc.,obtained from particular sequences,will,as the lengths of the sequences increase,approach deﬁnite limits independent of the particular sequence.Actually this is not true of every sequence but the set for which it is false has probability zero.Roughly the ergodic property means statistical homogeneity.All the examples of artiﬁcial languages given above are ergodic.This property is related to the structure of the corresponding graph.If the graph has the following two properties7the corresponding process will be ergodic:1.The graph does not consist of two isolated parts A and B such that it is impossible to go from junctionpoints in part A to junction points in part B along lines of the graph in the direction of arrows and also impossible to go from junctions in part B to junctions in part A.2.A closed series of lines in the graph with all arrows on the lines pointing in the same orientation willbe called a“circuit.”The“length”of a circuit is the number of lines in it.Thus in Fig.5series BEBES is a circuit of length5.The second property required is that the greatest common divisor of the lengths of all circuits in the graph beone.If theﬁrst condition is satisﬁed but the second one violated by having the greatest common divisor equal to d1,the sequences have a certain type of periodic structure.The various sequences fall into d different classes which are statistically the same apart from a shift of the origin(i.e.,which letter in the sequence is called letter1).By a shift of from0up to d1any sequence can be made statistically equivalent to any other.A simple example with d2is the following:There are three possible letters a b c.Letter a isfollowed with either b or c with probabilities13respectively.Either b or c is always followed by lettera.Thus a typical sequence isa b a c a c a c a b a c a b a b a c a cThis type of situation is not of much importance for our work.If theﬁrst condition is violated the graph may be separated into a set of subgraphs each of which satisﬁes theﬁrst condition.We will assume that the second condition is also satisﬁed for each subgraph.We have in this case what may be called a“mixed”source made up of a number of pure components.The components correspond to the various subgraphs.If L1,L2,L3are the component sources we may writeL p1L1p2L2p3L37These are restatements in terms of the graph of conditions given in Fr´e chet.where p i is the probability of the component source L i.Physically the situation represented is this:There are several different sources L1,L2,L3which are each of homogeneous statistical structure(i.e.,they are ergodic).We do not know a priori which is to be used,but once the sequence starts in a given pure component L i,it continues indeﬁnitely according to the statistical structure of that component.As an example one may take two of the processes deﬁned above and assume p12and p28.A sequence from the mixed sourceL2L18L2would be obtained by choosingﬁrst L1or L2with probabilities.2and.8and after this choice generating a sequence from whichever was chosen.Except when the contrary is stated we shall assume a source to be ergodic.This assumption enables one to identify averages along a sequence with averages over the ensemble of possible sequences(the probability of a discrepancy being zero).For example the relative frequency of the letter A in a particular inﬁnite sequence will be,with probability one,equal to its relative frequency in the ensemble of sequences.If P i is the probability of state i and p i j the transition probability to state j,then for the process to be stationary it is clear that the P i must satisfy equilibrium conditions:P j∑iP i p i jIn the ergodic case it can be shown that with any starting conditions the probabilities P j N of being in state j after N symbols,approach the equilibrium values as N∞.6.C HOICE,U NCERTAINTY AND E NTROPYWe have represented a discrete information source as a Markoff process.Can we deﬁne a quantity which will measure,in some sense,how much information is“produced”by such a process,or better,at what rate information is produced?Suppose we have a set of possible events whose probabilities of occurrence are p1p2p n.These probabilities are known but that is all we know concerning which event will occur.Can weﬁnd a measure of how much“choice”is involved in the selection of the event or of how uncertain we are of the outcome?If there is such a measure,say H p1p2p n,it is reasonable to require of it the following properties:1.H should be continuous in the p i.2.If all the p i are equal,p i12,p216.On the right weﬁrst choose between two possibilities each withprobability13,1216H121312is because this second choice only occurs half the time.In Appendix2,the following result is established:Theorem2:The only H satisfying the three above assumptions is of the form:H Kn∑i1p i log p iwhere K is a positive constant.This theorem,and the assumptions required for its proof,are in no way necessary for the present theory.It is given chieﬂy to lend a certain plausibility to some of our later deﬁnitions.The real justiﬁcation of these deﬁnitions,however,will reside in their implications.Quantities of the form H∑p i log p i(the constant K merely amounts to a choice of a unit of measure) play a central role in information theory as measures of information,choice and uncertainty.The form of H will be recognized as that of entropy as deﬁned in certain formulations of statistical mechanics8where p i isthe probability of a system being in cell i of its phase space.H is then,for example,the H in Boltzmann’s famous H theorem.We shall call H∑p i log p i the entropy of the set of probabilities p1p n.If x is a chance variable we will write H x for its entropy;thus x is not an argument of a function but a label for anumber,to differentiate it from H y say,the entropy of the chance variable y.The entropy in the case of two possibilities with probabilities p and q1p,namelyH p log p q log qis plotted in Fig.7as a function of p.HBITSpFig.7—Entropy in the case of two possibilities with probabilities p and1p.The quantity H has a number of interesting properties which further substantiate it as a reasonable measure of choice or information.1.H0if and only if all the p i but one are zero,this one having the value unity.Thus only when weare certain of the outcome does H vanish.Otherwise H is positive.2.For a given n,H is a maximum and equal to log n when all the p i are equal(i.e.,1。

催化量eda复合物

催化量eda复合物英文回答：Catalytic amounts of EDA complexes are widely used in various chemical reactions. EDA stands for electron donor-acceptor, and these complexes are formed by the interaction between an electron donor and an electron acceptor. The electron donor is usually a Lewis base, while the electron acceptor is typically a Lewis acid.One example of a catalytic reaction using EDA complexes is the hydroboration of alkenes. In this reaction, an EDA complex of borane and tetrahydrofuran (THF) is used as the catalyst. The THF molecule acts as the Lewis base, donating a pair of electrons to the boron atom, which acts as the Lewis acid. This EDA complex activates the boron atom, making it more reactive towards the alkene substrate. The reaction proceeds through the formation of a cyclic transition state, leading to the addition of boron and hydrogen across the double bond of the alkene.Another example is the catalytic reduction of ketones using EDA complexes of borane and amines. In this reaction, the amine acts as the Lewis base, donating a pair of electrons to the boron atom, which acts as the Lewis acid. This EDA complex activates the boron atom, making it more reactive towards the ketone substrate. The reactionproceeds through the formation of a cyclic transition state, leading to the reduction of the ketone to an alcohol.The use of EDA complexes as catalysts has several advantages. First, they can be used in catalytic amounts, which means that only a small amount of the complex is needed to catalyze the reaction. This makes them cost-effective and environmentally friendly. Second, EDA complexes can often be easily prepared from commercially available reagents, making them readily accessible for usein various reactions. Lastly, EDA complexes can exhibithigh selectivity and efficiency in catalytic reactions, leading to high yields of the desired products.中文回答：催化量的EDA复合物广泛应用于各种化学反应中。

simultaneous equation method

Simultaneous Equation MethodIntroductionIn mathematics, simultaneous equations play a crucial role in solving real-world problems and modeling various phenomena. The simultaneous equation method is a powerful technique used to find solutions for a system of equations. This method involves solving multiple equations together to determine the values of unknown variables. In this article, we will explore the simultaneous equation method in detail and discuss its applications.Understanding Simultaneous EquationsDefinitionSimultaneous equations, also known as a system of equations, are a set of equations that share the same variables. The solutions of these equations simultaneously satisfy each equation in the system. The general form of simultaneous equations can be written as:a1x + b1y = c1a2x + b2y = c2Here, x and y are the variables, while a1, a2, b1, b2, c1, and c2 are constants.Types of Simultaneous EquationsSimultaneous equations can be classified into three types based on the number of solutions they have:1.Consistent Equations: These equations have a unique solution,meaning there is a specific set of values for the variables thatsatisfy all the equations in the system.2.Inconsistent Equations: This type of system has no solution. Theequations are contradictory and cannot be satisfied simultaneously.3.Dependent Equations: In this case, the system has infinitely manysolutions. The equations are dependent on each other and represent the same line or plane in geometric terms.To solve simultaneous equations, we employ various methods, with the simultaneous equation method being one of the most commonly used techniques.The Simultaneous Equation MethodThe simultaneous equation method involves manipulating and combining the given equations to eliminate one variable at a time. By eliminating one variable, we can reduce the system to a single equation with one variable, making it easier to find the solution.ProcedureThe general procedure for solving simultaneous equations using the simultaneous equation method is as follows:1.Identify the unknow n variables. Let’s assume we have n variables.2.Write down the given equations.3.Choose two equations and eliminate one variable by employingsuitable techniques such as substitution or elimination.4.Repeat step 3 until you have a single equation with one variable.5.Solve the single equation to determine the value of the variable.6.Substitute the found value back into the other equations to obtainthe values of the remaining variables.7.Verify the solution by substituting the found values into all theoriginal equations. The values should satisfy each equation.If the system is inconsistent or dependent, the simultaneous equation method will also lead to appropriate conclusions.Applications of Simultaneous Equation MethodThe simultaneous equation method finds applications in numerous fields, including:EngineeringSimultaneous equations are widely used in engineering to model and solve various problems. Engineers employ this method to determine unknown quantities in electrical circuits, structural analysis, fluid mechanics, and many other fields.EconomicsIn economics, simultaneous equations help analyze the relationship between different economic variables. These equations assist in studying market equilibrium, economic growth, and other economic phenomena.PhysicsSimultaneous equations are a fundamental tool in physics for solving complex problems involving multiple variables. They are used in areas such as classical mechanics, electromagnetism, and quantum mechanics.OptimizationThe simultaneous equation method is utilized in optimization techniques to find the optimal solution of a system subject to certain constraints. This is applicable in operations research, logistics, and resource allocation problems.ConclusionThe simultaneous equation method is an essential mathematical technique for solving systems of equations. By employing this method, we can find the values of unknown variables and understand the relationships between different equations. The applications of this method span across various fields, making it a valuable tool in problem-solving and modeling real-world situations. So, the simultaneous equation method continues to be akey topic in mathematics and its practical applications in diverse disciplines.。

Advanced Circuit Simulation软件用户指南说明书

.SNNOISERuns periodic AC noise analysis on nonautonomous circuits in a large-signal periodic steady state..SNNOISE output insrc frequency_sweep [N1, +/-1]+ [LISTFREQ=(freq1 [freq2 ... freqN ]|none|all]) [LISTCOUNT=num ]+ [LISTFLOOR=val ] [LISTSOURCES=on|off].HBAC / .SNACRuns periodic AC analysis on circuits operating in a large-signal periodic steady state..HBAC frequency_sweep .SNAC frequency_sweep.HBXF / .SNXFCalculates transfer function from the given source in the circuit to the designated output..HBXF out_var frequency_sweep .SNXF out_var frequency_sweep.PTDNOISECalculates the noise spectrum and total noise at a point in time..PTDNOISE output TIME=[val |meas |sweep ] +[TDELTA=time_delta ] frequency_sweep+[listfreq=(freq1 [freq2 ... freqN ]|none|all)] [listcount=num ]+[listfloor=val ] [listsources=on|off]RF OptionsSIM_ACCURACY=x Sets and modifies the size of the time steps. The higher the value, thegreater the accuracy; the lower the value, the faster the simulation runtime. Default is 1.TRANFORHB=n 1 Forces HB analysis to recognize or ignore specific V/I sources, 0 (default) ignores transient descriptions of V/I sources.HBCONTINUE=n Specifies whether to use the sweep solution from the previous simulation as the initial guess for the present simulation. 0 restarts each simulation in a sweep from the DC solution, 1 (default) uses the previous sweep solution as the initial guess.HBSOLVER=n Specifies a preconditioner for solving nonlinear circuits. 0 invokes the direct solver. 1 (default) invokes the- matrix-free Krylov solver. 2 invokes the two-level hybrid time-frequency domain solver.SNACCURACY=n Sets and modifies the size of the time steps. The higher the value, the greater the accuracy; the lower the value, the faster the simulation runtime. Default is 10.SAVESNINIT=”filename ” Saves the operating point at the end of SN initialization.LOADSNINIT=”filename ” Loads the operating point saved at end of SN initialization.Output Commands.BIASCHK .MEASURE .PRINT .PROBEFor details about all commands and options, see the HSPICE ® Reference Manual: Commands and Control Options.Synopsys Technical Publications 690 East Middlefield Road Mountain View, CA 94043Phone (650) 584-5000 or (800) Copyright ©2017 Synopsys, Inc. All rights reserved.Signal Integrity Commands.LINCalculates linear transfer and noise parameters for a general multi-port network..LIN [sparcalc [=1|0]] [modelname=modelname ] [filename=filename ]+ [format=selem|citi|touchstone|touchstone2] [noisecalc [=1|0]]+ [gdcalc [=1|0]] [dataformat=ri|ma|db]+ [listfreq=(freq1 [freq2 ... freqN ]|none|all)] [listcount=num ]+ [listfloor=val ] [listsources=1|0|yes|no].STATEYEPerforms Statistical Eye Diagram analysis..STATEYE T=time_interval Trf=rise_fall_time [Tr=rise_time ] + [Tf=fall_time ] Incident_port=idx1[, idx2, … idxN ]+ Probe_port=idx1[, idx2, … idxN ] [Tran_init=n_periods ] + [V_low=val ] [V_high=val ] [TD_In=val ] [TD_PROBE=val ]+ [T_resolution=n ] [V_resolution=n ] [VD_range=val ]+ [EDGE=1|2|4|8] [MAX_PATTERN=n ] [PATTERN_REPEAT=n ] + [SAVE_TR=ascii] [LOAD_TR=ascii] [SAVE_DIR=string ]+ [IGNORE_Bits=n ] [Tran_Bit_Seg=n ]+ [MODE=EDGE|CONV|TRAN] [XTALK_TYPE = SYNC|ASYNC|DDP|NO|ONLY]+ [Unfold_Length=n ] [TXJITTER_MODE = 1|2]RF Analysis Commands.ACPHASENOISEHelps interpret signal and noise quantities as phase variables for accumulated jitter for closed-loop PLL analysis..ACPHASENOISE output input [interval ] carrier=freq+ [listfreq=(freq1 [freq2 ... freqN ]|none|all)][listcount=num ]+ [listfloor=val ] [listsources=1|0].HBRuns periodic steady state analysis with the single and multitone Harmonic Balance algorithm..HB TONES=F1[,F2,…,FN ] [SUBHARMS=SH ] [NHARMS=H1[,H2,…,HN ]]+ [INTMODMAX=n ] [SWEEP parameter_sweep ].SNRuns periodic steady state analysis using the Shooting Newton algorithm..SN TRES=Tr PERIOD=T [TRINIT=Ti ] [MAXTRINITCYCLES=integer ]+ [SWEEP parameter_sweep ] [NUMPEROUT=val ].SN TONE=F1 [TRINIT=Ti ] NHARMS=N [MAXTRINITCYCLES=integer ]+ [NUMPEROUT=val ] [SWEEP parameter_sweep ].HBOSC / .SNOSCPerforms analysis on autonomous oscillator circuits..HBOSC TONE=F1 NHARMS=H1+ PROBENODE=N1,N2,VP [FSPTS=NUM,MIN,MA X]+ [SWEEP parameter_sweep ] [SUBHARMS=I ] [STABILITY=-2|-1|0|1|2].SNOSC TONE=F1 NHARMS=H1 [TRINIT=Ti ]+ [OSCTONE=N ] [MAXTRINITCYCLES=N ]+ [SWEEP parameter_sweep ].PHASENOISEInterprets signal / noise quantities as phase variables for accumulated jitter in closed-loop PLL analysis..PHASENOISE output frequency_sweep [method= 0|1|2]+ [listfreq=(freq1 [freq2 ... freqN ]|none|all)] [listcount=num ]+ [listfloor=val ] [listsources=1|0] [carrierindex=int ].HBNOISEPerforms cyclo-stationary noise analysis on circuits in a large-signal periodic steady state..HBNOISE output insrc parameter_sweep [N1, N2, ..., NK ,+/-1]+ [LISTFREQ=(freq1 [freq2 ... freqN ]|none|all]) [LISTCOUNT=num ]+ [LISTFLOOR=val ] [LISTSOURCES=on|off].NOISERuns noise analysis in frequency domain..NOISE v(out ) vin [interval ] [listckt[=1|0]]+ [listfreq=freq1 [freq2 ... freqN ]|none|all]) [listcount=num ]+ [listfloor=val ] [listsources=1|0|yes|no]] [listtype=1|0].ALTERReruns a simulation using different parameters and data from a specified sequence or block. The .ALTER block can contain element commands and .AC, .ALIAS, .DATA, .DC, .DEL LIB, .HDL, .IC (initial condition), .INCLUDE, .LIB, .MODEL, .NODESET, .OP, .OPTION, .PARAM, .TEMP, .TF, .TRAN, and .VARIATION commands..ALTER title_string.DCPerforms DC analyses..DC var1 START=start1 STOP=stop1 STEP=incr1Parameterized Sweep.DC var1 start1 stop1 incr1 [SWEEP var2 type np start2 stop2].DC var1 START=[par_expr1] STOP=[par_expr2] STEP=[par_expr3]Data-Driven Sweep.DC var1 type np start1 stop1 [SWEEP DATA=datanm (Nums )].DC DATA=datanm [SWEEP var2 start2 stop2 incr2].DC DATA=datanm (Nums )Monte Carlo Analysis.DC var1 start1 stop1 incr1 [SWEEP MONTE=MCcommand ].DC MONTE=MCcommand.OPCalculates the operating point of the circuit..OP format_time format_time ... [interpolation].PARAMDefines parameters. Parameters are names that have associated numeric values or functions..PARAM ParamName = RealNumber | ‘AlgebraicExpression’ | DistributionFunction (Arguments ) | str(‘string’) | OPT xxx (initial_guess, low_limit, upper_limit )Monte Carlo Analysis.PARAM mcVar = UNIF(nominal_val , rel_variation [, multiplier ]) | AUNIF(nominal_val , abs_variation [, multiplier ])| GAUSS(nominal_val , rel_variation , num_sigmas [, multiplier ]) | AGAUSS(nominal_val , abs_variation , num_sigmas [, multiplier ]) | LIMIT(nominal_val , abs_variation ).STOREStarts creation of checkpoint files describing a running process during transient analysis..STORE [file=checkpoint_file ] [time=time1]+ [repeat=checkpoint_interval ].TEMPPerforms temperature analysis at specified temperatures..TEMP t1 [t2 t3 ...].TRANPerforms a transient analysis.Single-Point Analysis.TRAN tstep1 tstop1 [START=val ] [UIC]Multipoint Analysis.TRAN tstep1 tstop1 [tstep2 tstop2 ... tstepN tstopN ]+ RUNLVL =(time1 runlvl1 time2 runlvl2...timeN runlvlN )+ [START=val ] [UIC] [SWEEP var type np pstart pstop ]Monte Carlo Analysis.TRAN tstep1 tstop1 [tstep2 tstop2 ... tstepN tstopN ]+ [START=val ] [UIC] [SWEEP MONTE=MCcommand ]Invoking HSPICESimulation Modehspice [-i] input_file [-o [output_file ]] [-hpp] [-mt #num ][-gz] [-d] [-case][-hdl filename ] [-hdlpath pathname ] [-vamodel name ]Distributed-Processing Modehspice [-i] input_file [-o [output_file ]] -dp [#num ][-dpconfig [dp_configuration_file ]] [-dplocation [NFS|TMP][-merge]Measurement Modehspice -meas measure_file -i wavefile -o [output_file ]Help Modehspice [-h] [-doc] [-help] [-v]Argument Descriptions-i input_file Specifies the input netlist file name.-o output_file Name of the output file. HSPICE appends the extension .lis.-hpp Invokes HSPICE Precision Parallel.-mt #num Invokes multithreading and specifies the number of processors. Works best when -hpp is used.-gz Generates compression output on analysis results for these output types: .tr#, .ac#, .sw#, .ma#, .mt#, .ms#, .mc#, and .print*.-d (UNIX) Displays the content of .st0 files on screen while running HSPICE.-case Enable case sensitivity.-hdl filename Specifies a Verilog-A file.-hdlpath pathname Specifies the search path for Verilog-A files.-vamodel name Specifies the cell name for Verilog-A definitions.-dp #num -dpconfig dpconfig_file -dplocation [NFS|TMP] Invokesdistributed processing and specifies number of processes, the configuration file for DP, and the location of the output files.-merge Merge the output files in the distributed-processing mode.-meas measure_file Calculates new measurements from a previous simulation.-h Outputs the command line help message.-doc Opens the PDF documentation set for HSPICE (requires Adobe Acrobat Reader or other PDF document reader).-help Invokes the online help system (requires a Web browser).-v Outputs HSPICE version information.HSPICE is fully integrated with the Synopsys® Custom Compiler™ Simulation and Analysis Environment (SAE). See the Custom Compiler™ Simulation and Analysis Environment User Guide .To use the HSPICE integration to the Cadence® Virtuoso® Analog Design Environment, go to /$INSTALLDIR/interface/ and follow the README instructions.Analysis Commands.ACPerforms AC analyses.Single / Double Sweep.AC type np fstart fstop.AC type np fstart fstop [SWEEP var+ [START=]start [STOP=]stop [STEP=]incr ].AC type np fstart fstop [SWEEP var type np start stop ]Sweep Using Parameters.AC type np fstart fstop [SWEEP DATA=datanm (Nums )].AC DATA=datanm.AC DATA=datanm [SWEEP var [START=]start [STOP=]stop [STEP=]incr ].AC DATA=datanm [SWEEP var type np start stop ]Monte Carlo Analysis.AC type np fstart fstop [SWEEP MONTE=MCcommand ].LSTBInvokes loop stability analysis..LSTB [lstbname ] mode=[single|diff|comm + vsource=[vlstb |vlstbp,vlstbn ]Data-Driven Sweep.TRAN DATA=datanm.TRAN DATA=datanm [SWEEP var type np pstart pstop ].TRAN tstep1 tstop1 [tstep2 tstop2 ... tstepN tstopN ]+ [START=val ] [UIC] [SWEEP DATA=datanm (Nums )]Time Window-based Speed/Accuracy Tuning by RUNLVL.TRAN tstep tstop [RUNLVL=(time1 runlvl1...timeN runlvlN )]Circuit Block-based Speed/Accuracy Tuning by RUNLVL.TRAN tstep tstop+ [INST=inst_exp1 RUNLVL=(time11 runlvl11...time1N runlvl1N )]+ [SUBCKT=subckt_exp2 RUNLVL=(time21 runlvl21...time2N runlvl2N )]Time Window-based Temperature Setting.TRAN tstep tstop [tempvec=(t1 Temp1 t2 Temp2 t3 Temp3...)+[tempstep=val ]].TRANNOISEActivates transient noise analysis to compute the additional noise variables over a standard .TRAN analysis..TRANNOISE output [METHOD=MC] [SEED=val ] [SAMPLES=val ] [START=x ]+ [AUTOCORRELATION=0|1|off|on] [FMIN=val ] [FMAX=val ] [SCALE=val ]+ [PHASENOISE=0|1|2] [JITTER=0|1|2] [REF=srcName ] [PSD=0|1]HSPICE Options.OPTION opt1 [opt2 opt3 …]opt1 opt2 … Specify input control options.General OptionsALTCC=n Enables reading the input netlist once for multiple .ALTER statements. Default is 0.LIS_NEW=x Enables streamlining improvements to the *.lis file. Default is 0. SCALE=x Sets the element scaling factor. Default is 1.POSTTOP=n Outputs instances up to n levels deep. Default is 0.POSTLVL=n Limits data written to the waveform file to the level of nodes specified by n .POST=n Saves results for viewing by an interactive waveform viewer. Default is 0.PROBE=n Limits post-analysis output to only variables specified in .PROBE and .PRINTstatements. Default is 0.RC Reduction OptionsSIM_LA=name Starts linear matrix (RC) reduction to the PACT, PI, or LNE algorithm. Defaultis off.Transient OptionsAUTOSTOP=n Stops transient analysis after calculating all TRIG-TARG, FIND-WHEN, andFROM-TO measure functions. Default is 0.METHOD=name Sets numerical integration method for a transient analysis to GEAR, or TRAP(default), or BDF.RUNLVL=n Controls the speed and accuracy trade-off; where n can be 1 through 6. The higher the value, the greater the accuracy; the lower the value, the faster the simulation runtime. Default is 3.Variability and Monte Carlo Analysis.AC .DC .TRAN .MEASURE .MODEL .PARAM .ACMATCHCalculates the effects of variations on the AC transfer function, with one or more outputs..ACMatch Vm(n1) Vp(n1) Vr(n1) Vi(n1) Vm(n1,n2) Im(Vmeas ).DCMATCHCalculates the effects of variations on the DC operating point, with one or more outputs..DCMatch V(n1) V(n1,n2) I(Vmeas )。

超声波用于介入性疼痛管理说明书

357© Springer Nature Switzerland AG 2020P. Peng et al. (eds.), Ultrasound for Interventional Pain Management , https:///10.1007/978-3-030-18371-4AAbsorption, 5–7, 29Acoustic enhancement artifact, 18, 19Acoustic impedance, 7, 29Acoustic lens, 10Acoustic matching layer, 10Acoustic shadowing, 18, 19, 325Air artifact, 21Alcock’s canal, 100–102, 109, 110, 112Amplitude (A) mode, 5Anisotropy, 21–22, 209Anterior spinal artery, 149, 154Anterior superior iliac spine (ASIS), 75, 77,79, 81, 121, 125, 273, 340, 341Artifactacoustic enhancement artifact, 18acoustic shadowing, 18air artifact, 21anisotropy, 21edge shadowing, 20mirror imaging artifact, 20reverberation artifact, 18Ascending cervical arteries, 149BBeatty test, 96Border nerves, 75, 76Brightness (B), 4, 5CCalcific tendinitis calcific stage, 325causes, 325fenestration technique, 330, 331hard calcific phase, 326hard calcific phases, 325minimal invasive treatments, 325one needle barbotage technique, 328–330patient selection, 327phases of, 326postcalcific stage, 325precalcific stage, 325resorptive phase, 326soft calcific phase, 326ultrasound scan, 327Carpal tunnel syndrome causes, 247diagnosis, 247in-plane injection, 250median nerve, 247out-of-plane injection, 251ultrasound scan, 249Caudal canal injectioncomplications, 203, 204filum terminale and dura, 201needle placement, 199patient selection, 201sacral hiatus, 199, 200ultrasound guidance, 199ultrasound scan, 201–204Cervical epidural space, 150Cervical ganglion trunk, 45Cervical medial branch blocks (CMBBs)anatomy, 158patient selection, 158ultrasound scanC5, C6 medial branches, 164, 165C7 medial branches, 165coronal (long axis) scan, 160, 161needle placement, 165, 166procedure, 164TON, C3, C4 medial branches, 164transverse (short axis) scan, 161, 162Cervical nerve root block/transforaminalepidural injections, 151, 155Cervical spinal nerve, 149Index358Cervical sympathetic trunkclinical benefits, 49, 50contraindications, 46painful and non-painful conditions, 50patient selection, 45procedure, 48–49ultrasound scanning, 46–48Cervical transforaminal injections, 149, 154 Cervicogenic headache, 35, 41 Cervicothoracic ganglion, 43, 45, 50 Chronic pelvic pain (CPP), 93Cluster attacks, 41Color Doppler, 13–16, 46, 47, 165, 271–274 Complex regional pain syndrome (CRPS)type I, 59Cross-body adduction test, 59, 217DDeep cervical arteries, 149–151Deep gluteal syndrome, 100Depth, ultrasound, 12Doppler, 13–16, 37–39, 46, 47, 80, 97, 102,165, 298, 352EEdge shadowing, 20Elbow paincauses, 233lateral elbow anatomy, 234medial elbow anatomy, 235patient selection, 236posterior elbow anatomy, 236ultrasound scanelbow joint injection, 243, 244injection for common extensor tendon, 242injection for common flexor tendon,242, 243lateral elbow, 237medial elbow, 238, 239posterior elbow, 240, 241Electrical stimulation, 2, 95, 99Erector spinae plane (ESP) block, 131, 132 and transverse process, 144blockade area, 136catheter placement, 142clinical benefits, 143ligaments and muscles, 133mechanism of action, 133MRI scan, 134patient selection and the choice oflevel, 135randomized controlled trials, 144, 145single shot injection, 141ultrasound scanning, 137–139 Ergonomics, 23, 25, 27, 28EtOH, 70External iliac artery (EIA), 79, 83, 85–89FFocus, ultrasound, 14Foot and ankle painankle anatomy, 301, 302ankle joint, ultrasound scanprocedure, 312–314subtalar joint, 310–312tibiotalar joint, 310ankle nerves, ultrasound scandeep peroneal nerve, 307procedure, 309sural and superficial peroneal nerve,303–307tibial and saphenous nerve, 308, 309 anterior view of ankle, 303anteromedial view of ankle, 305etiology of, 301lateral view of ankle, 306medial view of ankle, 305musculoskeletal causes, 301patient selection, 303peripheral nerves, 301SaN, 302SuN, 302superficial peroneal nerve, 301, 304ultrasound scan, tibial and saphenousnerve, 309GGain, ultrasound, 13Genitofemoral nerve (GFN), 83clinical benefits, 91genital branch, 85, 91patient selection, 85procedure, 90ultrasound scanning, 85, 87–89Greater occipital nerve (GON)anatomy, 34blockade indication, 33clinical benefits, 40distal approach, 37, 38patient selection, 35procedure, 39, 40proximal approach, 36, 37ultrasound-guided technique, 41Index359HHand-shoulder syndrome (HSS), 59 Hematoma, 69, 203Hemoperitoneum, 69High-Intensity focused ultrasound (HIFU), 70 Hip jointanterior hipiliacus and psoas, 277patient selection, 278procedure, 279ultrasound scan, 278, 279blood supply, 268bones, cartilage, and ligamentousstructures, 267hip greater trochanteric (GT) complexgluteus minimus (GMin), 275muscles and tendons, 275patient selection, 276ultrasound scanning, 276–278hip intraarticular injectionin-plane needle insertion, 274out-plane needle insertion, 273, 274patient selection, 268ultrasound scanning, 270–273innervation, 268musculature, 268Hip painarticular branches of hip, 336, 340AON, 337, 338femoral nerve, 336, 337obturator nerve, 337, 339diagnostic block, 343–345patient selection, 338radiofrequency ablation, 344, 345RFA, 336ultrasound scan, 339–343 Hyperechoic, 15, 17, 29, 101, 114, 138, 139, 208 Hypoechoic, 15, 17, 29, 68, 201, 208, 209,222, 258, 292, 295IIliohypogastric nerves, 75–78clinical benefits, 81external oblique, 75internal oblique, 75patient selection, 77, 78procedure, 80–81techniques, 81ultrasound scanning, 79, 80Ilioinguinal nerves, 75, 76clinical benefits, 81external oblique, 75internal oblique, 75patient selection, 77, 78procedure, 80–81techniques, 81ultrasound scanning, 79, 80Iliotibial band (ITB) syndrome, 275, 277,295–297Image acquisition and processingtransducer, 9, 10transducer selection, 10, 11Inferior cluneal nerve, 110, 111clinical benefits, 117patient selection, 112procedure, 117sonoanatomy, 118ultrasound scan, 116Inferior epigastric artery (IEA), 83, 85, 88 Inferior oblique capitis muscle (IOC), 34, 36 In-plane approach, 24, 49, 67, 80, 90, 115,141, 243, 250, 273, 277, 313 Intercostal nerve block, 61, 69anatomy, 62caveats, 62, 64clincial benefits, 69HIFU, RFA, EtOH, ICNB studies, 70–72patientselectionadvantages, 65complications, 65contraindications, 64, 65indications, 64pneumothorax, 72post-procedure follow-up and issues, 68procedure, 67ultrasound scanning, 65, 67KKnee painarticular branches of knee, 347, 348diagnostic block, 350–352distal iliotibial band bursa injectionpathology, 295procedure, 296, 297ultrasound scan, 295, 296intra-articular injection, 287patient selection, 284procedure, 285, 286ultrasound scanning, 284–286patellar tendon injectionsprocedure, 298, 299ultrasound scan, 297, 298patient selection, 348pes anserinus bursa and peritendon injection procedure, 293, 294ultrasound scan, 292, 293Index360Knee pain (cont.)popliteal cyst/Baker’s cystprimary cysts, 287procedure, 289–291semimembranosus-gastrocnemiusbursa, 287, 288ultrasound scanning, 287–289radiofrequency ablation, 336, 352, 353ultrasound guidance, 283ultrasound scaninferomedial articular branches,349, 350superolateral articular branches, 350superomedial articular branches,348, 349LLateral femoral cutaneous nerve (LFCN),121, 124clinical benefits, 127patient selection, 122, 123procedure, 126, 127ultrasound application, 128ultrasound scanning, 124–126Lesser occipital nerve (LON), 34, 35patient selection, 35procedure, 40sonography, 39Long axis, 15, 17, 21, 24, 36, 48, 67,159–161, 222, 255, 259, 264, 273,277, 284, 292, 294, 297, 330, 349,350Low back paindefinitive diagnosis, 169lumbar medial branches (see Lumbarmedial branches)prevalence rate, 169Lumbar medial branchesanatomy, 169, 170patient selection, 170, 171ultrasound scanningL5 dorsal ramus, 176, 178L5 dorsal ramus block, 179–181lumbar medial branch (L1–4) block,179, 180medial branch L1-4, 176, 178paramedial sagittal articular processview, 171, 173paramedial sagittal oblique view,171, 174paramedial sagittal transverse process view, 171, 172procedure, 179sagittal view, 175, 177transverse interlaminar view, 173, 175transverse spinous process view, 173transverse view, 175Lumbar plexus, 75, 76, 83MMedian nerve neuralgia, 247Meralgia paresthetica (MP), 121, 125, 128 Middle cervical ganglion, 45Migraine, 34, 41Mirror imaging artifact, 20–21Motion (M) mode, 4, 5, 30 Musculoskeletal (MSK) scanningadvantages, 207, 208advantages image quality, 208anatomical landmarks, 208anisotropy, 209applications, 207Doppler effect, 209hyaluronic acid injections, 209hyperechoic images, 208image quality, 207injections setup, 209ozone injections, 209platelet-rich plasma injections, 209sonoelastography, 211three-dimensional ultrasound, 210ultrasound guidance, 207OObturatorinternus(OI) muscle, 100cadaveric study, 103clinical benefits, 103patient selection, 100procedure, 102ultrasound scan, 101Occipital artery, 33–35, 37–39Occipital muscle, 35Occipital neuralgia, 35Osteoarthritis (OA), 335Out-of-plane, 24, 27, 49, 105, 117, 127,179, 195, 202, 209, 224, 242, 243,250, 255, 256, 260, 261, 273, 274,309, 312PPACE, 96Paraspinal muscles, 132Patellar tendinopathy, 296, 297Pelvic musclesobturatorinternus muscle, 100–103obturatorinternusmuscle, 100Index361piriformis muscle, 94–96, 99quadratusfemoris, 104–106Peripheral nerve stimulation, 58, 59 Peritendon/bursa injection, 102–103 Piezoelectric elements, 10Piriformis muscle, 93–96, 98–100clinicalbenefits, 98insciatic neuropathy, 99and neurovascular structures, 95patient selection, 95procedure, 98ultrasound scan, 97Piriformis syndrome, 93–95, 99, 100 Platelet-rich plasma (PRP)anti-inflammatory and pro-inflammatoryeffects, 320clinical application, 321contraindications, 322growth factors, 318, 320mechanisms of effects, 318pattern of healing, 319platelet physiology, 318preparation, 322proteins, 319regulatory landscape, 319, 320research and clinical utilization, 317role of, 318supra-physiologic concentration ofplatelets, 317in tendinopathy treatment, 321on tissue regeneration, 322 Pneumothorax, 64, 65, 68, 72Posterior superior iliac spine (PSIS), 97, 112, 113, 175, 187Power Doppler, 13, 14Pudendal entrapment neuropathy, 109, 110 clinical benefits, 117patient selection, 112procedure, 115sonoanatomy, 118ultrasound scan, 113–115Pudendal nerve, 78, 84, 95, 109–115 Pudendal nerve block, 118Pudendal neuralgia, 109, 112Pulse length (PL), 3, 10Pulse repetition frequency (PRF), 3, 9 Pulsed radiofrequency, 41, 50, 55, 78QQuadratusfemoris (QF), 104fluoroscopy- and CT-guided injections, 106 patient selection, 104procedure, 105ultrasound scan, 105RRadiofrequency ablation (RFA), 70–72, 335,336, 347–349, 353, 354 Reflection, 7–8, 15, 208Reverberation artifact, 18, 19SSacral lateral branch (SLB)anatomy, 186clinical indication, 185patient selection, 186ultrasound scanningprocedure, 188sagittal plane scan, 188Sacroiliac joint (SIJ)anatomy, 185, 191–193clinical indication, 185patient selection, 186, 192radiofrequency ablation, 191, 193,195, 196ultrasound scanning, 192, 194procedure, 188, 189transverse plane scan, 186, 187 Scapular spine, 55, 57, 221Scattering, 5, 7–9Sciatic nerve, 93, 95, 96, 98–100, 102–105,110, 115, 116, 268Sciatic neuropathy, 99Semispinalis capitis muscle (SSC), 34, 36,161, 162, 166Short axis, 17, 24, 48, 58, 151, 161–163, 203, 208, 220, 223, 224, 249, 254, 259,260, 276–277, 289, 296, 298, 307,351Shoulder pain, 53–55, 58, 59, 213–216 lifetime prevalence, 213patient selection, 216, 217, 219shoulder girdle anatomyacromioclavicular joint, 216, 217coracohumeral ligament (CHL), 214GH joint capsule, 214glenohumeral (GH) joint, 214joint capsule, 216long head of biceps (LHB)tendon, 215rotator cuff muscles, 215subacromial impingement, 215subacromial subdeltoid(SASD), 215superior glenohumeral ligament(SGHL), 214ultrasound scanAC joint, 222–224anterior GH joint approach, 225, 226Index362Shoulder pain (cont.)LHB tendon, 224, 225LHB tendon and rotator interval, 219,220posterior glenohumeral joint, 221supraspinatus tendon and SASD bursa, 221, 222Sonoanatomy, 46, 91, 113, 114, 118, 139,237–240, 306–312tissue echogenicity, 15tissue features, 16–18Sonography, 39, 40, 47, 80, 81, 87, 99, 102,103, 116, 153Sound wave, 1Spermatic cord, 83, 87, 90Stellate ganglion block (SGB), 43Superior articular process (SAP), 154,161, 162, 165, 166, 170, 173,175, 179Superior cervical ganglion, 45 Suprascapular nerve (SN), 54anatomy, 53, 54clinical benefits, 58, 59diagnosis, 54diagnostic criteria, 55HSS and CRPS, 59pathophysiology and clinical presentation, 53, 55patient selection, 55procedure, 57, 58ultrasound guided peripheral nervestimulation of, 58ultrasound scanning, 55–57 Suprascapular nerve block (SNB), 55 Sympathetic fibers, 43TThenar atrophy, 248Third occipital nerve (TON)anatomy, 158patient selection, 158ultrasound scanC5, C6 medial branches, 164, 165C7 medial branches, 165coronal scan, 159–161needle placement, 165, 166procedure, 164TON, C3, C4 medial branches, 164transverse scan, 161–163Time motion, 5Transducer, 9, 10, 36handling, 22selection, 10, 11Transmission, 9, 18Transversus abdominis muscle, 75–77, 79–81 UUltrasoundimage acquisition and processingtransducer, 9, 10transducer selection, 10, 11machine operation, 12depth, 12, 13Doppler, 13focus, 13, 14gain, 12machine operation, Doppler, 14scanning and performanceand positioning terminology, 22, 23ergonomics, 23, 25ergonomics, 27, 28transducer handling, 22sonoanatomy and artifactacoustic enhancement artifact, 18acoustic shadowing, 18air artifact, 21anisotropy, 21edge shadowing, 20mirror imaging artifact, 20reverberation artifact, 18tissue echogenicity, 15tissue features, 16, 17sound wave, characteristic of, 1tissue interaction, 5absorption, 6, 7reflection, 7, 8scattering, 8transmission, 9transmission, 9ultrasound image, generation of, 4, 5ultrasound wave, generation of, 2, 3 Ultrasound-guided cervical nerve root block,151–153analgesic efficacy, 155in cadavers, 154clinical benefits, 154efficacy and safety, 155with fluoroscopy, 154fluoroscopy guided injection and, 155 procedure, 152, 154Index。

对油田电网进行无功补偿的动态优化算法及应用

刘洋：对油田电网进行无功补偿的动态优化算法及应用第14卷第3期（2024-03）据目前数据统计，采油行业的电能用量在采油行业总能耗的占比达到53%[1]，电能使用成本在生产成本的占比达到45％。

基于油田用电设备运行特性，因此经常会造成油田电网负荷起伏不定、负荷功率低与功率损耗多等问题，电网无功补偿技术可以将上述问题得到改善[2]，即在减少无功传输能耗的同时，增大有功传输容量，降低作业成本。

而传统的无功优化补偿方法具有一定局限性，实际补偿经济效益不佳，因此对油田电网的无功补偿优化方法进行研究，以便同时强化无功补偿的容量与位置。

迄今为止，关于油田电网无功补偿优化研究已有诸多学者进行了研究，并取得有效成果。

吴必章[3]在井口低压一侧放置电容器装置，在降低线损对油田电网进行无功补偿的动态优化算法及应用刘洋（大庆油田有限责任公司第七采油厂）摘要：为解决油田电网负荷高、电能损耗大的问题，提出对油田电网进行无功补偿的动态优化算法，首先分析出抽油机负荷特性，在此基础上利用电损修正系数调整抽油机分支导线线损与变压器线损，其次根据线损结果计算各节点上变压器的有功、无功电量以及功率，利用潮流方程建立无功补偿优化模型，确定需要补偿的节点以及补偿参数，最后利用最小目标函数计算无功优化补偿结果，通过对补偿优化的（更换120台变压器以及调整210台变压器容量）实际应用以及对实际应用的评估，有功功率损耗下降21.15%，电网线损率下降30.65%，电压合格率为100%。

无功补偿的优化，降低了运作费用，并提高了电网的安全性。

关键词：抽油机负荷特性；潮流方程；无功优化控制模型；线损DOI :10.3969/j.issn.2095-1493.2024.03.004Dynamic optimization algorithm and application of reactive power compensation in oil⁃field power grid LIU YangNo.7Oil Production Plant of Daqing Oilfield Co ．，Ltd ．Abstract：In order to solve the problem of high load and high power loss in oilfield power grid，the dynamic optimization algorithm of reactive power compensation in oilfield power grid is proposed ．Firstly，the load characteristics of pumping unit are analyzed，and then the branch wire loss and trans-former line loss of pumping unit are adjusted by using the power loss correction coefficient．Secondly，the active and reactive energy and power of the transformer at each node are calculated based on the line loss results，and the reactive power compensation optimization model is established by using the power flow equation．The nodes and compensation parameters that need to be compensated are determined ．Finally using the minimum objective function can be calculated the reactive power optimization com-pensation results.Through the practical application of compensation optimization （replacement of 120transformers and capacity adjustment of 210transformers ）and evaluation of the practical applica-tion，the active power loss is reduced by 21.15%，power grid line loss rate is reduced by 30.65%，and the voltage qualification rate is 100%.The optimization of reactive power compensation is reduced op-erating costs and improved grid security ．Keywords：load characteristics of pumping unit；power flow equation；reactive power optimization control model；line loss作者简介：刘洋，工程师，2006年毕业于上海东华大学（电气工程及其自动化专业），从事油田地面电力、自控专业的规划与设计工作，引文：刘洋．对油田电网进行无功补偿的动态优化算法及应用[J]．石油石化节能与计量，2024，14（3）：16-21.LIU Yang．Dynamic optimization algorithm and application of reactive power compensation in oilfield power grid[J]．Energy Conservation and Measurement in Petroleum &Petrochemical Industry，2024，14（3）：16-21.技术应用/TechnologyApplication与减少变压器损失的同时，提高电网功率数，实现对油田电网的无功补偿。

电力职称英语试题及答案

电力职称英语试题及答案一、选择题（每题2分，共20分）1. The primary function of a transformer is to:A. Convert voltage levelsB. Amplify electrical signalsC. Rectify alternating currentD. Filter electrical noise答案：A2. In an electric power system, the term "load" refers to:A. The source of electrical powerB. The electrical equipment that consumes powerC. The transmission lines that carry powerD. The protective devices for circuits答案：B3. Which of the following is not a type of electrical fault?A. Short circuitB. OverloadC. Ground faultD. Surge protection答案：D4. The unit of electrical power is the:A. VoltB. AmpereC. WattD. Ohm答案：C5. The purpose of a circuit breaker is to:A. Provide a path for excess currentB. Maintain a constant voltage levelC. Protect the circuit from overcurrentD. Convert AC to DC答案：C二、填空题（每题1分，共10分）6. The three main components of an electric power system are the _______, transmission, and distribution.答案：generation7. The SI unit for electrical resistance is the _______.答案：ohm8. In a parallel circuit, the total resistance is always_______ than any individual resistance.答案：lower9. The process of converting mechanical energy intoelectrical energy is known as _______.答案：generation10. A fuse is a type of protective device that operates by_______ when the current exceeds a safe level.答案：melting三、简答题（每题5分，共30分）11. Explain the difference between AC and DC power systems. 答案：AC (Alternating Current) power systems use a current that regularly reverses direction, while DC (Direct Current) power systems use a current that flows in one direction only.12. What is the significance of Ohm's Law in electrical engineering?答案：Ohm's Law is fundamental in electrical engineering asit relates the voltage (V), current (I), and resistance (R) in a simple electrical circuit, expressed as V = IR, allowing for calculations of these quantities.13. Describe the role of a generator in an electric power system.答案：A generator is a device that converts mechanical energy into electrical energy, serving as the primary source of power in an electric power system.14. What are the functions of a capacitor in an electrical circuit?答案：A capacitor in an electrical circuit can store energy, filter signals, and block direct current while allowing alternating current to pass.四、计算题（每题5分，共20分）15. Calculate the total resistance in a circuit with two resistors in parallel, where R1 = 100 ohms and R2 = 200 ohms.答案：$ R_{total} = \frac{R1 \times R2}{R1 + R2} = \frac{100 \times 200}{300} = \frac{20000}{300} = 66.67 $ ohms16. If a 12-volt battery is connected to a 3-ohm resistor, what is the current flowing through the resistor?答案：$ I = \frac{V}{R} = \frac{12}{3} = 4 $ amperes17. What is the power consumed by a 5-ohm resistor with a current of 2 amperes flowing through it?答案：$ P = I^2 \times R = 2^2 \times 5 = 4 \times 5 = 20 $ watts18. If a 240-volt AC motor draws a current of 5 amperes, what is the apparent power?答案：$ S = V \times I = 240 \times 5 = 1200 $ volt-amperes五、论述题（每题10分，共20分）19. Discuss the importance of energy efficiency in power systems and how it can be achieved.答案：Energy efficiency is crucial in power systems as it reduces energy consumption, lowers operational costs, and decreases environmental impact. It can be achieved through various means such as using high-efficiency equipment, optimizing system operations, and implementing demand-side management strategies.20. Explain the concept of smart grids and their advantages over traditional power systems.答案：Smart grids are advanced power systems that use digital technology and automation to improve the efficiency, reliability, and sustainability of electricity production anddistribution. They offer numerous advantages over traditional systems, including better demand response, enhanced grid stability, and the ability to integrate renewable energy sources more effectively.。

001 (ISSCC tutorial)Noise Analysis in Switched-Capacitor Circuits

PSD(f) f
© 2011 IEEE
IEEE International Solid-State Circuits Conference
© 2011 IEEE
Thermal Noise Power
• Nyquist showed that
PSD ( f ) = 4kT
• The total average noise power of a resistor in a certain frequency band is therefore
– Examples: Audio systems, wireless transceivers, sensor interfaces
• Electronic noise directly trades with power dissipation and speed • Electronic noise is a major concern in modern technologies with reduced VDD
• The noise of a MOSFET operating in the triode region is approximately equal to that of a resistor • In the saturation region, the thermal noise can be modeled using a drain current source with power spectral density
• We can model the noise using an equivalent voltage or current generator
2 vn
= Pn ⋅ R = 4kT ⋅ R ⋅ Δf

微芯片（Microchip）产品说明书

Microchip offers a broad portfolio of stand-alone analog and interface solutions that address the thermal management, power management, mixed-signal, linear, interface and safety and security markets.In addition to using low power CMOS technology, Microchip’s analog products are designed to optimize performance while minimizing power consumption.Non-volatile expertise is leveraged to achieve high accuracy specifications without additional manufacturing steps and cost. Chip select/shutdown/sleep features on many of our analog and interface parts enable systems to be selectively shut down to further reduce power consumption.Low operating voltages combined with small form factors such as SC70, DFN and SOT-23 make Microchip’s analog and interface portfolio well-suited for applications with tight power budgets.Typical Applications■Battery powered/Handheld■Consumer■PC Peripherals■Telecommunication■Automotive■IndustrialDesign Tools■CAD/CAE Schematic Symbols and Footprints/cadProduct Selection Tools■Microchip’s Advanced Product Selector/MAPS■Treelink presentation/treelinkStand-Alone Analog and Interface Portfolio Low Power Analog SolutionsPower Management LDO & Switching Regulators Charge PumpDC/DC Converters Power MOSFET DriversPWM Controllers System Supervisors Voltage Detectors Voltage References Li-Ion/Li-Polymer Battery ChargersMixed-SignalA/D ConverterFamiliesDigitalPotentiometersD/A ConvertersV/F and F/VConvertersEnergyMeasurementICsInterfaceCAN PeripheralsInfraredPeripheralsLIN TransceiversSerial PeripheralsEthernet ControllersUSB Peripheral LinearOp AmpsProgrammableGainAmpliﬁersComparatorsSafety & SecurityPhotoelectricSmoke DetectorsIonization SmokeDetectorsIonization SmokeDetector Front EndsPiezoelectricHorn DriversThermalManagementTemperatureSensorsFan SpeedControllers/Fan FaultDetectorsMotor DriveStepper and DC3Ф BrushlessDC Fan ControllerM i c r o c h i p T e c h n o l o g y I n c o r p o r a t e dInformation subject to change. The Microchip name and logo, the Microchip logo and PIC are registered trademarks of Microchip Technology Incorporated in the U.S.A. and other countries. © 2011 MicrochipTechnology Incorporated. All Rights Reserved. Printed in the U.S.A. 5/11DS22247B *DS22247B*Visit our web site for additional product information and to locate your local sales office.Microchip Technology Inc. • 2355 W. Chandler Blvd. • Chandler, AZ 85224-6199Low Power Analog & Interface Products/analog。

沙子吸附铅

Journal of Hazardous Materials B137(2006)384–395Removal of copper(II)and lead(II)from aqueoussolution by manganese oxide coated sand I.Characterization and kinetic studyRunping Han a ,∗,Weihua Zou a ,Zongpei Zhang a ,Jie Shi a ,Jiujun Yang baDepartment of Chemistry,Zhengzhou University,No.75of Daxue North Road,Zhengzhou 450052,PR ChinabCollege of Material Science and Engineering,Zhengzhou University,No.75of Daxue North Road,Zhengzhou 450052,PR ChinaReceived 8November 2005;received in revised form 25December 2005;accepted 13February 2006Available online 28February 2006AbstractThe preparation,characterization,and sorption properties for Cu(II)and Pb(II)of manganese oxide coated sand (MOCS)were investigated.A scanning electron microscope (SEM),X-ray diffraction spectrum (XRD)and BET analyses were used to observe the surface properties of the coated layer.An energy dispersive analysis of X-ray (EDAX)and X-ray photoelectron spectroscopy (XPS)were used for characterizing metal adsorption sites on the surface of MOCS.The quantity of manganese on MOCS was determined by means of acid digestion analysis.The adsorption experiments were carried out as a function of solution pH,adsorbent dose,ionic strength,contact time and temperature.Binding of Cu(II)and Pb(II)ions with MOCS was highly pH dependent with an increase in the extent of adsorption with the pH of the media inves-tigated.After the Cu(II)and Pb(II)adsorption by MOCS,the pH in solution was decreased.Cu(II)and Pb(II)uptake were found to increase with the temperature.Further,the removal efﬁciency of Cu(II)and Pb(II)increased with increasing adsorbent dose and decreased with ionic strength.The pseudo-ﬁrst-order kinetic model,pseudo-second-order kinetic model,intraparticle diffusion model and Elovich equation model were used to describe the kinetic data and the data constants were evaluated.The pseudo-second-order model was the best choice among all the kinetic models to describe the adsorption behavior of Cu(II)and Pb(II)onto MOCS,suggesting that the adsorption mechanism might be a chemisorption process.The activation energy of adsorption (E a )was determined as Cu(II)4.98kJ mol −1and Pb(II)2.10kJ mol −1,respectively.The low value of E a shows that Cu(II)and Pb(II)adsorption process by MOCS may involve a non-activated chemical adsorption and a physical sorption.©2006Elsevier B.V .All rights reserved.Keywords:Manganese oxide coated sand (MOCS);Cu(II);Pb(II);Adsorption kinetic1.IntroductionThe presence ofheavy metals in the aquatic environment is a major concern due to their extreme toxicity towards aquatic life,human beings,and the environment.Heavy metal ions from wastewaters are commonly removed by chemical precipitation,ion-exchange,reverse osmosis processes,and adsorption by activated carbon.Over the last few decades,adsorption has gained importance as an effective puriﬁcation and separation technique used in wastewater treatment,and the removal of heavy metals from metal-laden tap or wastewater∗Corresponding author.Tel.:+8637167763707;fax:+8637167763220.E-mail address:rphan67@ (R.Han).is considered an important application of adsorption processes using a suitable adsorbent [1,2].In recent years,many researchers have applied metal oxides to adsorption of heavy metals from metal-laden tap or wastewa-ter [3].Adsorption can remove metals over a wider pH range and lower concentrations than precipitation [4].Iron,aluminum,and manganese oxides are typically thought to be the most important scavengers of heavy metals in aqueous solution or wastewater due to their relatively high surface area,microporous structure,and possess OH functional groups capable of reacting with met-als,phosphate and other speciﬁcally sorbing ions [5].However,most metal oxides are available only as ﬁne powders or are gener-ated in aqueous suspension as hydroxide ﬂoc or gel.Under such conditions,solid/liquid separation is fairly difﬁcult.In addition,metal oxides along are not suitable as a ﬁlter medium because of0304-3894/$–see front matter ©2006Elsevier B.V .All rights reserved.doi:10.1016/j.jhazmat.2006.02.021R.Han et al./Journal of Hazardous Materials B137(2006)384–395385their low hydraulic conductivity.Recently,several researchers have developed techniques for coating metal oxides onto the surface of sand to overcome the problem of using metal oxides powers in water treatment.Many reports have shown the impor-tance of these surface coatings in controlling metal distribution in soils and sediments[3,6,7].In recent years,coated minerals have been studied because of their potential application as effective sorbents[3,8,9].Iron oxide coated meterials for heavy metal removal have been proved successful for the enhancement of treatment capacity and efﬁciency when compared with uncoatedﬁlter media,such as sil-ica sand[10–14],granular activated carbon[15]and polymeric media[16,17].For example,Edwards and Benjamin[7]found that coated media have similar properties to unattached coating materials in removing metals over a wide pH range,and that Fe oxide coated sand was more effective than uncoated sand.Bai-ley et al.[18]used iron oxide coated sand to remove hexavalent chromium from a synthetic waste stream.The inﬂuent contained 20mg l−1Cr(VI)and better than99%removal was achieved. Satpathi and Chaudhuri[19]and Viraraghavan et al.[20]have recently reported on the ability of this medium to adsorb metals from electroplating rinse waters and arsenic from drinking water sources,respectively.Green-Pedersen and Pind reported that a ferrihydrite-coated montmorillonite surface had a larger speciﬁc surface area and an increased sorption capacity for Ni(II)com-pared to the pure systems[21].Meng and Letterman[22]found that the adsorption properties of oxide mixtures are determined by the relative amount of the components.They also found that ion adsorption on aluminum oxide-coated silica was better mod-eled assuming uniform coverage of the oxide rather than using two distinct surfaces[23].Lo and Chen[8]determined the effect of Al oxide mineralogy,amount of oxide coating,and acid-and alkali-resistance on the removal of selenium from water.Bran-dao and Galembecket reported that the impregnation of cellulose acetates with manganese dioxide resulted in high removal efﬁ-cient of Cu(II),Pb(II),and Zn(II)from aqueous solutions[24]. Al-Degs and Khraisheh[25]also reported that diatomite and manganese oxide modiﬁed diatomite are effective adsorbents for removing Pb2+,Cu2+,and Cd2+ions.The sorption capac-ity of Mn-diatomite was considerably increased compared to the original material for removing the studied metals.Filtration quality of diatomite is signiﬁcantly increased after modiﬁcation with Mn-oxides.Merkle et al.[26–28]reported that manganese dioxide coated sand was effective for removal of arsenic from ground water in column experiments.Merkle et al.developed a manganese oxide coating method on anthracite to improve the removal of Mn2+from drinking water and hazardous waste efﬂuent.They generated aﬁlter media with an increased surface area after coating with manganese oxides and found manganese oxide coated media have the ability to adsorb and coprecipi-tate a variety of inorganic species.Stahl and James[29]found their manganese oxide coated sands generated a larger surface area and increased adsorption capability with increasing pH as compared to uncoated silica sand.Additional researchers have been investigated to evalu-ate coating characteristics.X-ray diffraction(XRD),X-ray photoelectron spectroscopy(XPS),Fourier transform infrared spectroscopy(FTIR),transmission electron microscopy(TEM), and scanning electron microscopy(SEM)have been used as well to identify components,distribution,and structure of surface oxide coating[7,9,30,31].An energy dispersive X-ray (EDAX)technique of analysis has been used to characterize metal adsorption sites on the sorbent surface.Typically,oxide was non-uniform over the surface as both the oxide and substratum had been observed[7].The research described here was designed to investigate characteristics of manganese oxide coated sand(MOCS)and test the properties of MOCS as an adsorbent for removing copper(II)and lead(II)from synthetic solutions in batch system.SEM/EDAX,XRD,XPS and BET analysis were employed to examine the properties of adsorption reactions for Cu(II)and Pb(II)ions on MOCS in water.The system variables studied include pH,MOCS dose,ionic strength,contact time and temperature.The kinetic parameters,such as E a,k1,k2, have been calculated to determine rate constants and adsorption mechanism.1.1.Kinetic parameters of adsorptionThe models of adsorption kinetics were correlated with the solution uptake rate,hence these models are important in water treatment process design.In order to analyze the adsorption kinetics of MOCS,four kinetic models including the pseudo-ﬁrst-order equation[32],the pseudo-second-order equation[33], Elovich equation[34],and intraparticle diffusion model[35] were applied to experimental data obtained from batch metal removal experiments.A pseudo-ﬁrst-order kinetic model of Lagergen is given as log(q e−q t)=log q e−K1t2.303(1)A pseudo-second-order kinetic model istq t=1(K2q2e)+tq e(2) andh=K2q2e(3) an intraparticle diffusion model isq t=K t t1/2+C(4) and an Elovich equation model is shown asq t=ln(αβ)β+ln tβ(5) where q e and q t are the amount of solute adsorbed per unit adsorbent at equilibrium and any time,respectively(mmol g−1), k1the pseudo-ﬁrst-order rate constant for the adsorption process (min−1),k2the rate constant of pseudo-second-order adsorption (g mmol−1min−1),K t the intraparticle diffusion rate constant (mmol g−1min−1),h the initial sorption rate of pseudo-second-order adsorption(mmol g−1min−1),C the intercept,αthe initial sorption rate of Elovich equation(mmol g−1min−1),and386R.Han et al./Journal of Hazardous Materials B137(2006)384–395the parameter βis related to the extent of surface coverage and activation energy for chemisorption (g mmol −1).A straight line of log(q e −q t )versus t ,t /q t versus t ,q t versus ln t ,or q t versus t 1/2suggests the applicability of this kinetic model and kinetic parameters can be determined from the slope and intercept of the plot.1.2.Determination of thermodynamic parametersThe activation energy for metal ions adsorption was calcu-lated by the Arrhenius equation [36]:k =k 0exp −E aRT (6)where k 0is the temperature independent factor ing mmol −1min −1,E a the activation energy of the reaction of adsorption in kJ mol −1,R the gas constant (8.314J mol −1K −1)and T is the adsorption absolute temperature (K).The linear form is:ln k =−E aRT+ln k 0(7)when ln k is plotted versus 1/T ,a straight line with slope –E a /R is obtained.2.Materials and methods 2.1.AdsorbentThe quartz sand was provided from Zhengzhou’s Company of tap water in China.The diameter of the sand was ranged in size from 0.99to 0.67mm.The sand was soaked in 0.1mol l −1hydrochloric acid solution for 24h,rinsed with distilled water and dried at 373K in the oven in preparation for surface coating.Manganese oxide coated sand was accomplished by utilizing a reductive procedure modiﬁed to precipitate colloids of man-ganese oxide on the media surface.A boiling solution containing potassium permanganate was poured over dried sand placed in a beaker,and hydrochloric acid (37.5%,W HCl /W H 2O )solution was added dropwise into the solution.After stirring for 1h,the media was ﬁltered,washed to pH 7.0using distilled water,dried at room temperature,and stored in polypropylene bottle for future use.2.2.Metal solutionsAll chemicals and reagents used for experiments and anal-yses were of analytical grade.Stock solutions of 2000mg l −1Pb(II)and Cu(II)were prepared from Cu(NO 3)2and Pb(NO 3)2in distilled,deionized water containing a few drops of concen-trated HNO 3to prevent the precipitation of Cu(II)and Pb(II)by hydrolysis.The initial pH of the working solution was adjusted by addition of HNO 3or NaOH solution.2.3.Mineral identiﬁcationThe mineralogy of the sample was characterized by X-ray diffraction (XRD)(Tokyo Shibaura Model ADG-01E).Pho-tomicrography of the exterior surface of uncoated sand and man-ganese oxide coated sand was obtained by SEM (JEOL6335F-SEM,Japan).The distribution of elemental concentrations for the solid sample can be analyzed using the mapping analysis of SEM/EDAX (JEOL SEM (JSM-6301)/OXFORD EDX,Japan).The existence of Cu(II)and Pb(II)ions on the surface of manganese oxide coated sand was also conﬁrmed by using EDAX.Samples for EDAX analysis were coated with thin carbon ﬁlm in order to avoid the inﬂuence of any charge effect during the SEM operation.The samples of MOCS and MOCS adsorbed with copper/lead ions were also analyzed by X-ray photoelectron spectroscopy (XPS)(ESCA3600Shimduz).2.4.Speciﬁc surface area and pore size distribution analysesAnalyses of physical characteristics of MOCS included spe-ciﬁc surface area,and pore size distributions.The speciﬁc sur-face area of MOCS and pore volumes were test using the nitrogen adsorption method with NOV A 1000High-Speed,Automated Surface Area and Pore Size Analyer (Quantachrome Corpora-tion,America)at 77K,and the BET adsorption model was used in the calculation.Calculation of pore size followed the method of BJH according to implemented software routines.2.5.Methods of adsorption studiesBatch adsorption studies were conducted by shaking the ﬂasks at 120rpm for a period of time using a water bath cum mechanical shaker.Following a systematic work on the sorp-tion uptake capacity of Cu(II)and Pb(II)in batch systems were studied in the present work.The experimental process was as following:put a certain quantity of MOCS into conical ﬂasks,then,added the solute of metals of copper or lead in single component system,vibrated sometime at a constant speed of 120rpm in a shaking water bath,when reached the sorption equilibrium after 180min,took out the conical ﬂasks,ﬁltrated to separate MOCS and the solution.No other solutions were provided for additional ionic strength expect for the effect of ionic strength.The concentration of the free metal ions in the ﬁltrate was analyzed using ﬂame atomic absorption spectrometer (AAS)(Aanalyst 300,Perkin Elmer).The uptake of the metal ions was calculated by the difference in their initial and ﬁnal concentrations.Effect of pH (1.4–6.5),quantity of MOCS,contact time,temperature (288–318K)was studied.The pH of the solutions at the beginning and end of experiments was measured.Each experiment was repeated three times and the results given were the average values.2.5.1.Effect of contact time and temperature on Cu(II)and Pb(II)adsorptionA 2.0g l −1sample of MOCS was added to each 20ml of Cu(II)or Pb(II)solutions with initial concentration of Cu(II)0.315mmol l −1and Pb(II)0.579mmol l −1,respectively.The temperature was controlled with a water bath at the temperature ranged from 294to 318K for the studies.Adsorbent of MOCS and metal solution were separated at pre-determined time inter-R.Han et al./Journal of Hazardous Materials B137(2006)384–395387 vals,ﬁltered and analyzed for residual Cu(II)and Pb(II)ionconcentrations.2.5.2.Effect of pH on the sorption of Cu(II)and Pb(II)byMOCSThe effect of pH on the adsorption capacity of MOCSwas investigated using solutions of0.157mmol l−1Cu(II)and0.393mmol l−1Pb(II)for a pH range of1.4–6.5at293K.A20g l−1of MOCS was added to20ml of Cu(II)and Pb(II)solu-tions.Experiments could not be performed at higher pH valuesdue to low solubility of metal ions.2.5.3.Effect of MOCS doseIt was tested by the addition of sodium nitrate and calciumnitrate to the solution of Cu(II)and Pb(II),respectively.The doseof adsorbents were varied from10to80g l−1keeping initial con-centration of copper0.157mmol l−1and lead0.393mmol l−1,respectively,and contact time was180min at the temperature of293K.2.5.4.Effect of ionic strength on Cu(II)and Pb(II)adsorptionThe concentration of NaNO3and Ca(NO3)2used rangedfrom0to0.2mol l−1.The dose of adsorbents were20g l−1,the initial concentration of copper0.157mmol l−1and lead0.393mmol l−1,respectively,and contact time was180min atthe temperature of293K.The data obtained in batch model studies was used to calculatethe equilibrium metal uptake capacity.It was calculated for eachsample of copper by using the following expression:q t=v(C0−C t)m(8)where q t is the amount of metal ions adsorbed on the MOCS at time t(mmol g−1),C0and C t the initial and liquid-phase concentrations of metal ions at time t(mmol l−1),v the volume of the aqueous phase(l)and m is the dry weight of the adsorbent(g).3.Results and discussion3.1.Mineralogy of manganese oxide coated sandThe samples of sand coated with manganese oxide were dark colored(brown–black)precipitates,indicating the presence of manganese in the form of insoluble oxides.The X-ray diffrac-tion spectrum(XRD)of the samples(data not shown)revealed that the manganese oxide were totally amorphous,as there was not any peak detected,indicative of a speciﬁc crystalline phase. SEM photographs in Fig.1were taken at10,000×magniﬁ-cations to observe the surface morphology of uncoated sand and manganese oxide coated sand,respectively.SEM images of acid-washed uncoated quartz sand in Fig.1(a)showed very ordered silica crystals at the surface.The virgin sand had a rela-tively uniform and smooth surface and small cracks,micropores or light roughness could be found on the sand -paring the images of virgin(Fig.1(a))and manganeseoxide Fig.1.SEM micrograph of sample:(a)sand;(b)manganese oxide coated sand. coated sand(Fig.1(b)),MOCS had a signiﬁcantly rougher sur-face than plain sand and the coated sand surfaces were apparently occupied by newborn manganese oxides,which were formed during the coating process.Fig.1(b)also showed manganese oxides,formed in clusters,apparently on occupied surfaces.At the micron scale,the synthetic coating was composed of small particles on top of a more consolidated coating.In most regions individual particles of manganese oxide(diameter=2–3␮m) appeared to be growing in clumps in surface depressions and coating cracks.The amount of manganese on the surface of the MOCS,measured through acid digestion analysis,was approx-imately5.46mg Mn/g-sand.3.2.SEM/EDAX analysisThe elements indicated as being associated with manganese oxide coated were detected by the energy dispersive X-ray spec-trometer system(EDAX)using a standardless qualitative EDAX analytical technique.The peak heights in the EDAX spectra are proportional to the metallic elements concentration.The quali-tative EDAX spectra for MOCS(Fig.2(a))indicated that Mn,O,388R.Han et al./Journal of Hazardous Materials B137(2006)384–395Fig.2.EDAX spectrum of MOCS under:(a)adsorbed without copper and lead ion;(b)adsorbed copper ions;(c)adsorbed lead ions.Si,and K are the main constituents.These had been known as the principal elements of MOCS.EDAX analysis yielded indirect evidence for the mechanism of manganese oxide on the surface of MOCS.The peak of Si occurred in EDAX showed that man-ganese oxides do not covered a full surface of the MOCS.If the solid sample of MOCS caused a change of elemental con-stitution through adsorption reaction,it could be inferred that manganese oxide has already brought about chemical interac-tion with adsorbate.The EDAX spectrum for copper and lead system was illustrated in Fig.2(b and c).It could be seen that copper and lead ion became one element of solid sample in this spectrum.The reason was that copper and lead ions were chemisorbed on the surface of MOCS.Dot mapping can provide an indication of the qualitative abundance of mapping elements.The elemental distribution mapping of EDAX for the sample of MOCS and MOCS adsorbed copper or lead ions is illustrated in Fig.3.The bright points represented the single of the element from the solid sam-ple.A laryer of manganese oxide coating is clearly shown in the dot map for Mn in Fig.3(a),and a high density of white dots indicates manganese is the most abundant element.Results indicated that manganese oxide was spread over the surface of MOCS,and was a constituent part of the solid sample.The ele-ment distribution mapping of EDAX for the sample ofMOCS Fig.3.EDAX results of MOCS(white images in mapping represent the cor-responding element):(a)adsorbed without copper and lead ion;(b)adsorbed copper ions;(c)adsorbed lead ions.R.Han et al./Journal of Hazardous Materials B137(2006)384–395389Fig.4.XPS wide scan of the manganese oxide coated sand. reacting with copper and lead ions is illustrated in Fig.3(b and c).Copper or lead ions were spread over the surfaces of MOCS. Results indicated that manganese oxide produces chemical bond with copper or lead ions.Thus,copper or lead element was a constituent part of the solid sample.3.3.Surface characterization using the X-ray photoelectron spectroscopy(XPS)XPS analyses were performed on samples of MOCS alone and reacting with copper or lead ions.The wide scan of MOCS is presented in Fig.4.It can be noticed that the major elements constituent are manganese,oxygen,and silicon.Detailed spectra of the peaks are shown in Fig.5.Manganese oxides are generally expressed with the chemical formula of MnO x,due to the multiple valence states exhibited by Mn.Therefore,it is reasonable to measure the average oxidation state for a manganese mineral[37].The observation of the Mn 2p3/2peak at641.9eV and the separation between this and the Mn2p1/2peak of11.4eV indicates the manganese exhibited oxidation between Mn3+and Mn4+as shown from the auger plot,but it can be seen to show Mn4+predominantly from the Mn2p3/2peaks[38].The large peak in Fig.5(b)is a sum of the two peaks at 529.3and533.1eV,which can be assigned to O1s;a low bind-ing energy at529.7eV,which is generally accepted as lattice oxygen in the form of O2−(metal oxygen bond).This peak is characteristic of the oxygen in manganese oxides.The second peak at533.4eV can be assigned to surface adsorbed oxygen in the form of OH−[38].As seen the XPS spectra of the sample of MOCS reacting with copper,Fig.6(a)shows the binding energies of the observed photoelectron peaks of Cu2p3/2,2p1/2.The binding energy of the Cu2p3/2peak at a value of933.9eV shows the presence of copper(+2).The XPS spectra obtained after Pb(II)adsorption on MOCS is presented in Fig.6(b).Fig.6(b)shows that doublets charac-teristic of lead appear,respectively,at138.3eV(assigned to Pb 4f7/2)and at143.8eV(assigned to Pb4f5/2)after loadingMOCSFig.5.XPS detailed spectra of MOCS:(a)Mn2p3/2;(b)O1s.with Pb(II)solution.The peak observed at138.3eV agrees with the138.0eV value reported for PbO[39].This shows aﬁxation of lead onto MOCS during the process.3.4.Speciﬁc surface area and pore size distribution analysesThe speciﬁc surface areas for sand and MOCS under un/adsorbed Pb(II)ions are summarized in Table1.Plain uncoated sand had a surface area of0.674m2g−1.A surface coating of manganese oxide increased the surface area of sand to0.712m2g−1,while average pore diameter decreased from 51.42to42.77˚A.This may be caused by the increase in both Table1Speciﬁc surface areas and average pore diameters for sand and various MOCSSurface area(m2g−1)Average pore diameter(˚A) Sand0.67451.42Unadsorbed a0.71242.77Adsorbed b0.55239.64Desorbed c0.70142.71a Without reacting with Pb(II)ions.b After reacting with Pb(II)ions.c After soaking with0.5mol l−1acid solution.390R.Han et al./Journal of Hazardous Materials B137(2006)384–395Fig.6.XPS detailed spectra of MOCS reacting with(a)copper;(b)lead. inner and surface porosity after adding the manganese oxides admixture.After reacting with Pb(II)ions,the pore size distribu-tion of MOCS had been changed,and parts of pores disappeared through the adsorption process.The results indicated the parts of pores were occupied with Pb(II)ions and average pore diameters decreased simultaneously,compared with unadsorbed MOCS, the surface area value of adsorbed MOCS is decreased,varying from of0.712to0.552m2g−1.Besides,pore size distribution of desorbed MOCS was similar to that of unadsorbed MOCS. The surface area of desorbed MOCS increased and average pore diameter also increased after regeneration with acid solution. The results indicated Pb(II)ions could be desorbed from the surface site of micropore and mesopores.3.5.Effect of contact time and temperature on Cu(II)andPb(II)adsorptionEffect of contact time and temperature on the adsorption of the copper(II)and lead(II)on MOCS was illustrated in Fig.7(a and b).The uptake equilibrium of Cu(II)and Pb(II) were achieved after180min and no remarkable changes were observed for higher reaction times(not shown in Fig.7).The shapes of the curves representing metal uptake versus time suggest that a two-step mechanism occurs.Theﬁrstportion Fig.7.Effect of contact time on Cu(II)and Pb(II)ions adsorption at pH4and various temperatures:(a)adsorption capacity vs.time;(b)adsorption percent vs.time(C0(Cu)=0.315mmol l−1,C0(Pb)=0.579mmol l−1).indicates that a rapid adsorption occurs during theﬁrst30min after which equilibrium is slowly achieved.Almost80%of total removal for both Cu(II)and Pb(II)occurred within60min.The equilibrium time required for maximum removal of Cu(II)and Pb(II)were90and120min at all the experimental temperatures, respectively.As a consequence,180min was chosen as the reac-tion time required to reaching pseudo-equilibrium in the present “equilibrium”adsorption experiments.Higher removal for cop-per and lead ions was also observed in the higher temperature range.This was due to the increasing tendency of adsorbate ions to adsorb from the interface to the solution with increasing temperature and it is suggested that the sorption of Cu(II)and Pb(II)by MOCS may involve not only physical but also chem-ical sorption.The metal uptake versus time curves at different temperatures are single,smooth and continuous leading to sat-uration,suggesting possible monolayer coverage of Cu(II)and Pb(II)on the surface of MOCS[40].3.6.Effect of pH on the sorption of Cu(II)and Pb(II)by MOCSIt is well known that the pH of the system is an important vari-able in the adsorption process.The charge of the adsorbate and the adsorbent often depends on the pH of the solution.The man-R.Han et al./Journal of Hazardous Materials B137(2006)384–395391 ganese oxide surface charge is also dependent on the solution pHdue to exchange of H+ions.The surface groups of manganeseoxide are amphoteric and can function as an acid or a base[41].The oxide surface can undergo protonation and deprotonationin response to changes in solution pH.As shown in Fig.8,the uptake of free ionic copper and leaddepends on pH,increasing with pH from1.4to5.1for Cu(II)and1.4to4.3for Pb(II).Above these pH levels,the adsorptioncurves increased very slightly or tended to level out.At low pH,Cu(II)and Pb(II)removal were inhibited possibly as result ofa competition between hydrogen and metal ions on the sorp-tion sites,with an apparent preponderance of hydrogen ions.Asthe pH increased,the negative charge density on MOCS sur-face increases due to deprotonation of the metal binding sitesand thus the adsorption of metal ions increased.The increase inadsorption with the decrease in H+ion concentration(high pH)indicates that ion exchange is one of major adsorption process.Above pH6.0,insoluble copper or lead hydroxide starts precip-itating from the solution,making true sorption studies impossi-ble.Therefore,at these pH values,both adsorption and precipita-tion are the effective mechanisms to remove the Cu(II)and Pb(II)in aqueous solution.At higher pH values,Cu(II)and Pb(II)inaqueous solution convert to different hydrolysis products.In order to understand the adsorption mechanism,the varia-tion of pH in a solution and the metal ions adsorbed on MOCSduring adsorption were measured,and the results are shown inFig.8.The pH of the solution at the end of experiments wasobserved to be decreased after adsorption by MOCS.Theseresults indicated that the mechanism by means of which Cu(II)and Pb(II)ion was adsorbed onto MOCS perhaps involved anexchange reaction of Cu2+or Pb2+with H+on the surface andsurface complex formation.According to the principle of ion-exchange,the more metalions that is adsorbed onto MOCS,the more hydrogen ions arereleased,thus the pH value was decreased.The complex reac-tions of Cu2+and Pb2+with manganese oxide may be writtenas follows(X=Cu,Pb and Y=Pb)[42]:MnOH+X2+ MnO−X2++H+(9)MnO−+X2+ MnO−X2+(10)Fig.8.Effect of pH on adsorption of Cu(II)and Pb(II)by MOCS.2(MnOH)+X2+ (MnO−)2X2++2H+(11)2(MnO−)+X2+ (MnO−)2X2+(12)MnOH+X2++H2O MnOXOH+2H+(13)MnOH+2Y2++H2O MnOY2OH2++2H+(14)Eqs.(9)–(14)showed the hydrogen ion concentration increasedwith an increasing amount of Cu(II)or Pb(II)ion adsorbed onthe MOCS surface.3.7.Effect of MOCS doseFig.9shows the adsorption of Cu(II)and Pb(II)as a functionof adsorbent dosage.It was observed that percent adsorptionof Cu(II)and Pb(II)increased from29to99%and19to99%with increasing adsorbent load from10to80g l−1,respectively.This was because of the availability of more and more bindingsites for complexation of Cu(II)ions.On the other hand,theplot of adsorption per unit of adsorbent versus adsorbent doserevealed that the unit adsorption capacity was high at low dosesand reduced at high dose.There are many factors,which can con-tribute to this adsorbent concentration effect.The most importantfactor is that adsorption sites remain unsaturated during theadsorption reaction.This is due to the fact that as the dosageof adsorbent is increased,there is less commensurate increasein adsorption resulting from the lower adsorptive capacity uti-lization of the adsorbent.It is readily understood that the numberof available adsorption sites increases by increasing the adsor-bent dose and it,therefore,results in the increase of the amountof adsorbed metal ions.The decrease in equilibrium uptake withincrease in the adsorbent dose is mainly because of unsaturationof adsorption sites through the adsorption process.The corre-sponding linear plots of the values of percentage removal(Γ)against dose(m s)were regressed to obtain expressions for thesevalues in terms of the m s parameters.This relationship is asfollows:for Cu(II):Γ=m s0.221+6.61×10−3m s(15)Fig.9.Effect of dosage of MOCS on Cu(II)and Pb(II)removal.。

National Instruments（NI）电路设计套餐版本10.0 Release Notes

RELEASE NOTESNI Circuit Design SuiteVersion 10.0These release notes contain system requirements for NI Circuit Design Suite 10.0,as well as information about product tiers, new features, documentation resources,and other changes since Multicap 9.0, Multisim 9.0, and Ultiboard 9.0.NI Circuit Design Suite includes the following familiar Electronics Workbenchsoftware products: NI Multisim, NI Ultiboard, and the NI Multisim MCU Module(formerly MultiMCU).ContentsInstalling NI Circuit Design Suite 10.0 (2)Minimum System Requirements (2)Installation Instructions (2)Product Activation (3)What’s New in NI Circuit Design Suite 10.0 (3)Mouse-Click Support for Interactive Components (3)Convergence Assistant (4)Increased Quality and Breadth of the Component Database (4)New Components from Leading Manufacturers (4)Generic Power Simulation Parts (4)Bipolar Sources (4)Graphical LCD (5)Single Symbol Representations of Standard Logic Components (5)Enhancements to Passive Components (5)Extended SPICE Modeling Capabilities (5)Parameterized SPICE models (5)Improved Support of Behavioral Sources (5)Support for BSIM 4 Parameters (6)Enhanced Data Visualization (6)Advanced Functionality of Static Probes (6)Add Traces to Grapher after Running Analyses (6)Display Initial Conditions on the Schematic (6)Current Probe Instrument (6)Enhanced Analysis Capabilities (6)Extended Language Support and File Management in the MCU Module (7)Improvements to Speed and Quality of NI Ultiboard (7)Advanced Options for Exported Data Interpolation (7)Miscellaneous Features (8)Unicode Characters (8)NI Installation and License Management (8)Product Tier Details (8)Documentation (14)Installing NI Circuit Design Suite 10.0This section describes the system requirements and installation procedures forNI Circuit Design Suite.Minimum System RequirementsTo run NI Circuit Design Suite 10.0, National Instruments recommends that yoursystem meet the following requirements:•Windows 2000 Service Pack 3 or later, or Windows XP•Pentium 4 class microprocessor or equivalent (Pentium III class minimum)•512 MB of memory (256 MB minimum)• 1.5 GB of free hard disk space (1 GB minimum)•Open GL® capable 3D graphics card recommended (SVGA resolution videoadapter with 800×600 video resolution minimum, 1024×768 or higherpreferred)•To develop custom LabVIEW based instruments for use in Multisim,LabVIEW 8.0.x or higher is requiredInstallation InstructionsThe NI Circuit Design Suite 10.0 installer installs all products in the suite:Multisim, Ultiboard, and the Multisim MCU Module.National Instruments recommends that you close all open applications before youinstall NI Circuit Design Suite.Unless you specify another location during installation, the NI Circuit DesignSuite installation program copies files to <Program Files>\NationalNI Circuit Design Suite Release Instruments\Circuit Design Suite10.0 after you complete thefollowing steps:1.Insert the NI Circuit Design Suite CD into the CD-ROM drive. If the CDstartup screen is not visible, select Run from the Windows Start menu and runsetup.exe from your CD.2.Follow the instructions in the dialog boxes.Product ActivationWhen you run a product in the NI Circuit Design Suite for the first time, it willprompt you to activate a license for that product.Note: To run the Multisim MCU Module, place a component from the MCUModule group on a Multisim circuit or open a Multisim file that contains acomponent from the MCU Module group.If you do not activate a valid license, the product will run in Evaluation Mode andcontinue to prompt you to activate a license on each subsequent run. EvaluationMode is valid for 30 days following the first run of the product.For information about how to activate your software product, please refer to theActivation Instructions for National Instruments Products Note to Users includedwith your NI Circuit Design Suite 10.0 package.What’s New in NI Circuit Design Suite 10.0This document describes the following new features ofNI Circuit Design Suite 10.0:•Mouse-Click Support for Interactive Parts•Convergence Assistant•Increased Quality and Breadth of the Component Database•Extended SPICE Modeling Capabilities•Enhanced Data Visualization•Extended Analysis Capabilities•Extended Programming and File Management in the MCU Module•Improvements to Speed and Quality of NI Ultiboard•Advanced Options for Exported Data Interpolation•Miscellaneous FeaturesMouse-Click Support for Interactive ComponentsNI Multisim 10.0 lets you use your mouse to control interactive componentsduring simulation. You can click on switches to toggle them, push keypad buttonswith the mouse, and adjust the value of the variable components, such asNational Instruments Corporation3NI Circuit Design Suite Release Notespotentiometers, with a slider bar. You may also continue to use keyboard controlsfor these devices.Convergence AssistantThe Convergence Assistant adjusts simulation settings when a "Time Step TooSmall" error occurs during interactive simulation. The assistant adjusts theminimum number of parameters required in order to allow convergence of thesimulation. The assistant adjusts the following parameters:1.Initial Condition2.TMAX3.RELTOL4.RSHUNT5.ITL16.Integration method7.GMINIncreased Quality and Breadth of the Component DatabaseNI Multisim 10.0 has a number of new additions and improvements to thecomponent database. These include: around 1,000 new components from leadingmanufacturers, generic power simulation parts, new bipolar sources, a GraphicalLCD, single symbol representations of standard logic components, andimprovements to passive components.New Components from Leading ManufacturersNI Multisim 10.0 has approximately 1,000 new components with models fromAnalog Devices, Texas Instruments, and Linear Technologies. These additionsinclude symbols, models, and IPC-standard landpatterns. Components includeoperational-amplifier, comparator, and voltage reference models.Generic Power Simulation PartsNI Multisim 10.0 includes models for all power simulation parts found in the"Switch-Mode Power Supply SPICE Cookbook" by Christophe Basso. Thesecomponents include Buck, Boost, Buck-Boost, and PWM controllers. Theirmodels include voltage and current mode controlled devices, and models foraverage and detailed transient operation.Bipolar SourcesNew bipolar pulse sources include both current and voltage sources.NI Circuit Design Suite Release Graphical LCDA Graphical LCD is available for users who purchase the MCU Module inconjunction with NI Multisim. The command system for the Graphical LCDfollows the Toshiba T6963C. The graphical LCD is a two-color device with 256 x256 pixel display resolution. This device supports three modes of operation:text-only, graphics-only, and mixed text and graphics.Single Symbol Representations of Standard LogicComponentsIn addition to the multi-section component representation of standard logiccomponents such as logic gates and flip-flops, the component database nowincludes single symbol representations of common components. Thesesingle-symbol representations show the power and ground pins of these devices.Enhancements to Passive ComponentsYou can now change the value of any resistor, capacitor, or inductor placed on theschematic without replacing it. You can also assign a landpattern to any passivecomponent. You can assign information about the type of component, for instancemetal-oxide, and this information propagates to the Bill of Materials. Thetolerance of the components is automatically available for Monte-Carlo and WorstCase analyses, and you can edit the tolerances in the spreadsheet.An advanced non-linear inductor model lets you define the inductor characteristicsbased on datasheet values.Extended SPICE Modeling CapabilitiesNI Multisim 10.0 introduces enhancements to its SPICE modeling capabilities,including parameters in SPICE subcircuit models, improved support of behavioralsources, and support for BSIM 4 parameters.Parameterized SPICE modelsYou may now define parameters in the .subcircuit line of SPICE macro-models inNI Multisim. The definition of parameters is as follows..subckt<subckt_name><node_list>PARAMS:param_name=value,...You may then use the parameter name in place of a value in the macro-model. Thevalue of the parameter is editable in the component dialog on the schematic.Improved Support of Behavioral SourcesBehavioral sources now support nested instances of IF statements.National Instruments Corporation5NI Circuit Design Suite Release NotesSupport for BSIM 4 ParametersNI Multisim 10.0 supports the standard BSIM 4 parameters for MOSFET models.BSIM 4 supports up to 400 parameters. More information about BSIM 4 isavailable at /~bsim3/bsim4.html.Enhanced Data VisualizationNI Multisim 10.0 includes a number of improvements to the way you configureand view results. These include: advanced functionality of the static probes, theability to add traces to the Grapher after running a simulation, the ability to displaythe initial conditions of components on the schematic, a current probe instrument,and improvements to the memory and register displays of MCUs.Advanced Functionality of Static ProbesPlaced (static) probes now include a reference designator, which allows you toselect another probe as a reference net. In previous versions of NI Multisim, allprobes referenced ground. You can also use probe reference designators to selectwhich traces to view in analyses.Add Traces to Grapher after Running AnalysesYou can add traces to the Grapher view after running an analysis, and select whattype of data you want NI Multisim to store.Display Initial Conditions on the SchematicYou can choose to display the initial conditions of capacitors and inductors on theschematic.Current Probe InstrumentThe current probe instrument is a virtual representation of a real current probe thatconnects to an oscilloscope. You connect one end of the probe to a net on theschematic and the other to the input to an oscilloscope. You can set the ratio ofamps to volts displayed on the instrument. Note that the units remain in volts onthe oscilloscope.Enhanced Analysis CapabilitiesNI Multisim 10.0 now allows you to evaluate more expressions before and afterrunning analyses. The definitions of the expressions are:1.avg(X) — Running average of the vector X2.avg(X, d) — Running average of the vector X over dNI Circuit Design Suite Release 3.envmax(X, n) — Upper envelope of the vector X where n is the number ofpoints on either side of a peak that must be less than the value for a peak to beidentified4.envmin(X, n) — Lower envelope of the vector X where n is the number ofpoints on either side of a peak that must be less than the value for a peak to beidentified5.grpdelay(X) — Group delay of X with results in seconds6.rms(X) — Running RMS average of vector X7.integral(X) — Running integral of vector X8.sgn(X) — The sign or signum of a real number. It is -1 for a negative number,0 for the number zero, and 1 for a positive number.Extended Language Support and File Management in the MCU ModuleThe MCU Module, formerly MultiMCU, supports C-code in addition to Assemblylanguage. It has a code manager that lets you use multiple files to define theoperation of the microcontrollers in the design. You can have header files and uselibraries. You can also load in externally assembled binary files and view them indisassembled format.Improvements to Speed and Quality of NI UltiboardNI Ultiboard 10.0 contains enhancements to the quality of the product that includeimprovements to the speed of trace-placment and the ability to select whether ornot to plate through-holes. Exported Gerber files do not contain mosaics in thepolygons. Quality improvements in the landpatterns include: pin mappings fromsymbols to IC pin-outs and landpattern shapes and sizes in the database. All newlandpatterns follow IPC standards.Advanced Options for Exported Data InterpolationWhen exporting simulation data from NI Multisim to other NI data formats suchas LVM or TDM files, you can choose the interpolation technique that best suitsthe signal. You can also control the interpolation method used when sendingsimulation data to NI LabVIEW based instruments running inside of NI Multisim.The interpolation methods include:•Coerce•Linear Interpolation•Spline InterpolationNational Instruments Corporation7NI Circuit Design Suite Release NotesMiscellaneous FeaturesSome of the other features added to the new suite include Unicode charactersupport and NI installation and license management.Unicode CharactersAll products in NI Circuit Design Suite 10.0 support Unicode characters. Thisfeature allows you to use Cyrillic and Asian fonts inside the products.NI Installation and License ManagementAll products in NI Circuit Design Suite adhere to the standard method used toinstall and activate National Instruments software. You can activate the softwareautomatically via the internet, or manually via a web browser, phone call, oremail.Product Tier DetailsThe following lists the schematic capture functionality available in MultisimStudent and Education editions:Functionality Student EducationCustomizable GUI X XScreen-capture utility X XComments on schematic X XCircuit annotations X XModeless part placement and wiring X XFast retrieval parts bins X XAuto and manual wiring X XVirtual wiring by node name X XRubber banding on part move X XFast auto-connect passives X XSubcircuits X X3-dimensional breadboarding X XVirtual NI ELVIS X XEmbedded questions - view and respond X XNI Circuit Design Suite Release Functionality Student EducationForward/Back annotation with Ultiboard X XCross-probing with Ultiboard X XBus-vector connect XSpreadsheet view XDesign constraints for layout XAdvanced search XZoom to selected part XCorporate database XUser defined fields XXSave components to database fromworkspaceMultiple circuits open XEmbedded questions - create and edit XElectrical rules check XGraphically mark no-connect pins XHierarchical designs XMultisheet designs XProject manager XReports - including bill of materials XPin and gate swap XExport to Mentor PADS layout XDevice library Partial CompleteMaximum components in design50UnlimitedNational Instruments Corporation9NI Circuit Design Suite Release NotesThe following lists the simulation functionality available in Multisim Student andEducation editions:Functionality Student EducationInteractive simulation X XFully mixed-mode A/D simulation X XStandard SPICE 3X5/XSPICE X XEnhanced model support X XPSPICE model simulation* X XSpeed/Accuracy tradeoffs X XSimulation advisor X XConvergence assistant X XVirtual, interactive, animated parts X XMouse click support for interactive parts X XRated components X XInsert faults into components X XMeasurement Probes X XComponent Wizard X XNI measurement data file sources X XNI measurement data file export X XX XNI LabVIEW VIs as instruments andsourcesMicrophone & speaker X XCircuit restrictions X XGrapher & Postprocessor X XRF design kit X XCircuit wizards XC-Code modeling XDescription box synced with simulation XLadder diagrams/components XModel makers XNI Circuit Design Suite Release Load and save simulation profiles XVirtual Instruments 2222Analyses1018Co-simulation of MCUs Add On Add On* Does not support all PSpice syntaxThe following lists the layout functionality available in Ultiboard Student andEducation editions:Functionality Student EducationPush and Shove trace placement X XReal-time & from copper ratsnest X XReal-time polygon update with voiding X XForward/Backward annotation X XCross-probing with Multisim X XReal-time DRC X X64 layers and 1 nanometer resolution X XComprehensive Footprint Wizard X XEnhanced 3D visualization with print X XUser annotations X XFull screen mode XGerber, DXF, IPC-D-356A, SVG output XDimensions on PCB and Landpatterns XDimensions in Database Manager XNet bridges X3D visualization inside circuit board XTurn off ratsnest for selected nets XGridless follow-me placement XLoad and save technology files XPolar Grids XNational Instruments Corporation11NI Circuit Design Suite Release NotesCustomizable layer viewing XSplit power-planes XKeep-in/Keep-out areas XPlace components in array XUnplace all components XRuler bar alignments and measurements XAuto-alignment XSave PCB Design as a component XPermanent grouping XPin & gate swapping XMultiple clearances XJump to Error XEquispace trace support XDifferential Impedance Calculator XTransmission Line Calculator XMicrovias XTest point insertion XAutomatic tear-dropping XPin necked trace support XAutomatic jumper insertion XCopy Route & Replica Place functions XIn-place footprint editor XMechanical CAD XExport 3D info in 3D IGES, DXF formats XCopper amount report XTest point report XCustomization of report generation XMultiple open documents XNI Circuit Design Suite Release National Instruments Corporation 13NI Circuit Design Suite Release NotesThe following lists the autorouting functionality available in Ultiboard Student and Education editions:Number of pins supported 3501,000Spreadsheet viewLimitedCompleteFunctionalityStudentEducationFully customizable cost factors X X Progressive Routing X X Interactive autorouting X X Constraint driven routingX X Manual pre-placement: components, vias, tracesX X Auto Block Capacitor recognition X X SMD mirroring X X Trace rubberbandingX X Follows keep-in/keep-out criteria X X Pin number limit3501,000Maximum number of layers24DocumentationNI Circuit Design Suite 10.0 includes a complete documentation set featuringprinted and electronic resources for your reference.The following printed and electronic resource is available:•Getting Started with NI Circuit Design Suite GuideThe following electronic resources are available in PDF files:•Multisim User Guide•Multisim Component Reference Guide•Multisim for Educators Guide•Multisim MCU Module User Guide•Ultiboard User GuideTo access the User Guides, select Start > All Programs > National Instruments >Circuit Design Suite 10.0 > Documentation and then select the file of interest.The following online help files are available from the installed software Helpmenu and from the Start Menu:•Multisim Education Edition Help File•Ultiboard Help FileTo access the Help Files, select Start > All Programs > National Instruments >Circuit Design Suite 10.0 > Documentation and then select the file of interest.The following online help files are available from the installed software Helpmenu:•Component Reference Education Edition Help File•Multisim Symbol Editor Help File•Multisim Title Block Editor Help FileNI Circuit Design Suite Release National Instruments, NI, , and LabVIEW are trademarks of National Instruments Corporation.Refer to the Terms of Use section on /legal for more information about National Instrumentstrademarks. Ultiboard is a registered trademark and Multisim and Electronics Workbench aretrademarks of Electronics Workbench. Other product and company names mentioned herein aretrademarks or trade names of their respective companies.374480A-01 Jan07© 2007 National Instruments Corp. All rights reserved.。

explanatory sequential mixed method

explanatory sequential mixed method Explanatory Sequential Mixed MethodsIntroduction:Research methodology plays a crucial role in informing decision-making and understanding complex phenomena. Mixed methods research designs have gained popularity in recent years due to their ability to provide a comprehensive and holistic understanding of a research problem. One such design is the explanatory sequential mixed methods approach, which incorporates both quantitative and qualitative components in a sequential manner. This article aims to explain the explanatory sequential mixed methods design, its components, advantages, and limitations, with examples from various research studies.Components of the Explanatory Sequential Mixed Methods Design:The explanatory sequential mixed methods design consists of two distinct phases, namely the quantitative phase and the qualitative phase. In this design, the quantitative component is conducted first and is followed by the qualitative component. The purpose of the quantitative phase is to explore relationships and identify patterns in the data, while the qualitative phase aims to provide a deeper understanding of these relationships and patterns.Quantitative Phase:During the quantitative phase, researchers collect and analyze quantitative data using structured surveys, experiments, orsecondary data sources. The goal is to generate numerical data that can be analyzed using statistical techniques to test hypotheses or patterns. The findings from the quantitative analysis inform the selection of participants and the focus of the qualitative phase.Qualitative Phase:The qualitative phase involves collecting and analyzing qualitative data, such as interviews, observations, or document analysis. The purpose of this phase is to understand the underlying reasons and processes behind the quantitative findings. Qualitative data collection methods allow researchers to gather rich and detailed information that provides context and meaning to the statistical results. The qualitative analysis involves coding, categorizing, and interpreting the data to identify themes and patterns.Integration of Findings:The integration of findings is a crucial step in the explanatory sequential mixed methods design. During this stage, researchers compare and contrast the findings from both the quantitative and qualitative phases to develop a comprehensive understanding of the research problem. This integration can occur in different ways, such as comparing the results side by side, using statistical findings to interpret qualitative data, or using qualitative findings to explain statistical patterns. The aim is to provide a richer and more nuanced understanding of the research topic than could be achieved through a single method or phase.Advantages of the Explanatory Sequential Mixed Methods Design:The explanatory sequential mixed methods design offers several advantages over traditional quantitative or qualitative approaches. Firstly, it provides a more comprehensive understanding of the research problem by combining quantitative and qualitative data. The sequential nature of the design allows researchers to build on the findings from the quantitative phase and explore them in more depth during the qualitative phase. This approach strengthens the validity and reliability of the research findings.Secondly, the design allows researchers to address research questions that require both numerical data and contextual information. Some phenomena cannot be fully understood or explained by numbers alone, and qualitative data can provide valuable insights into the underlying reasons and processes.Thirdly, the design enhances triangulation, which refers to the use of multiple data sources or methods to validate findings. By combining quantitative and qualitative data, researchers can compare and contrast the different perspectives and identify converging or conflicting evidence. This strengthens the overall validity and trustworthiness of the research.Limitations of the Explanatory Sequential Mixed Methods Design:Despite its advantages, the explanatory sequential mixed methods design also has some limitations. Firstly, it requires time and resources to implement both quantitative and qualitative components. Researchers need to consider the feasibility of conducting both phases and ensure that they have the necessaryskills and expertise in both quantitative and qualitative methods.Secondly, the design may face challenges in terms of data integration and interpretation. Combining quantitative and qualitative findings can be complex and may require expertise in both types of data analysis. Researchers need to carefully consider how to integrate the findings in a meaningful and coherent manner.Example Studies:To illustrate the application of the explanatory sequential mixed methods design, three example studies are presented below:1. A study on the effectiveness of a health intervention program uses a quantitative survey to measure participants' health outcomes and satisfaction levels. The qualitative phase involves in-depth interviews with a sub-sample of participants to explore their experiences and perceptions of the program.2. A study on the impact of a teacher training program uses a quantitative pre-test and post-test design to measure changes in students' academic performance. The qualitative phase involves focus group discussions with teachers to understand their perspectives on the program's effectiveness and challenges.3. A study on the factors influencing employee satisfaction and retention uses a quantitative survey to measure employee satisfaction levels. The qualitative phase involves semi-structured interviews with a subset of employees to explore the underlying reasons for their satisfaction or dissatisfaction.Conclusion:The explanatory sequential mixed methods design offers a powerful approach to research that combines the strengths of quantitative and qualitative methods. By integrating numerical data with contextual information, this design provides a comprehensive and holistic understanding of research problems. Despite its limitations, the design has gained popularity due to its ability to address complex research questions and enhance the validity and reliability of findings. Researchers should consider the feasibility and appropriateness of this design for their specific research objectives and resources.。

steinharmonic analysis

steinharmonic analysisStein's harmonic analysis, developed by mathematician Elias M. Stein, is a powerful mathematical tool used to study functions in signal processing, image analysis, and various other areas of mathematics. In this article, we will explore the key concepts and techniques involved in Stein's harmonic analysis.Harmonic analysis is a branch of mathematics that deals with the representation and decomposition of functions as a sum of simpler periodic functions called harmonics. Stein's harmonic analysis focuses on the study of functions and their properties using harmonic analysis techniques.One of the fundamental concepts in Stein's harmonic analysis is the Fourier transform. The Fourier transform of a function is a mathematical operation that decomposes the function into a collection of sinusoidal functions with varying frequencies and amplitudes. This decomposition provides valuable information about different components of the function, which can be useful in understanding and analyzing signals.The Fourier transform can be visualized as a way to transform afunction from the time/space domain to the frequency domain. In the frequency domain, the function is represented as a sum of sinusoidal functions, each associated with a particular frequency. This transformation allows us to analyze the function in terms of its frequency content, enabling us to identify important features and patterns that may be hidden in the time/space domain representation.Stein's harmonic analysis builds upon the Fourier transform by introducing techniques such as wavelet analysis andtime-frequency analysis. Wavelet analysis is a mathematical tool used to analyze signals at different resolutions. Unlike the Fourier transform, which provides a global frequency analysis, wavelet analysis allows for a localized analysis of the frequency components of a signal. This can be particularly useful when dealing with signals that contain transient or localized events.Time-frequency analysis, on the other hand, focuses on analyzing how the frequency content of a signal changes over time. This can be achieved using techniques such as the short-time Fourier transform or the spectrogram. These methods provide a representation of the signal that captures both its time andfrequency properties, allowing for a detailed analysis of transient events and changes in frequency content.Stein's harmonic analysis also incorporates concepts from functional analysis, which deals with the study of vector spaces of functions and operators. Functional analysis provides a rigorous mathematical framework for studying the properties and behavior of functions and operators in a more general context.One of the key contributions of Stein's harmonic analysis is the development of theory and techniques for dealing with non-linear and time-varying systems. Traditional harmonic analysis techniques often assume linearity and time-invariance, which may not hold in many practical applications. Stein's approach allows for the analysis of more complex systems that exhibit non-linear and time-varying behavior.In conclusion, Stein's harmonic analysis is a valuable mathematical tool for studying functions and their properties in various fields, including signal processing and image analysis. The concepts and techniques involved, such as Fourier transforms, wavelet analysis,and time-frequency analysis, provide powerful tools for analyzing and understanding the frequency content and behavior of functions. By incorporating ideas from functional analysis, Stein's approach also allows for the analysis of more complex andnon-linear systems. Overall, Stein's harmonic analysis has proven to be a versatile and powerful tool in the field of mathematics.。

Omega DRA-WVT-3 三相三线功率和 VAR 传感器说明书

U ± 0.1% Accuracy U G alvanically Isolated U T wo Simultaneous Outputs for Watt and VAR U S ingle Phase and Three Phase Models** Models with ±1mA or ±20mA outputs are also available. Consult engineering. Ordering Example: DRA-WVT-3-3A 3-phase, 3-wire watt/VAR transducer,115 Vac/5A 60 Hz input, 4-20 mA outputs for watt and VAR, 115 Vac power and OCW-1, OMEGACARE SM extends standard 2-year warranty to a total of 3 years.The DRA-WVT-3 Series combines watt and VAR transducers in one compact housing. Two simultaneous proportional dc current outputs are provided for watt and VAR parameters. The polarity of the watt output is positive for unity power factor (PF); polarity for the VAR output is positive for lagging power factor.SpecificationsGENERALAccuracy: ±0.1% of span typical for watt in 5-140% rangeTemperature Stability: < ±0.01%/°CResponse Time: < 200 millisecond (10-90% of span)Power Supply: 115 Vac -15/+25%, 230 Vac -15/+25%, 60 HzPower Overload: withstands 1.45 x nominal rating continuousInput Current Consumption: 0.26 VA @ 5 AacInput Voltage Consumption: 0.15 VA @150 Vac, 0.3 VA @ 300 VacFrequency: 60 HzFrequency Variation Effect: < ±0.02%/Hz (for watt output)Operating Ambient: -5 to 65°C (23 to 149°F); 5 to 95% RH, noncondensingStorage Temperature: -35 to 85°C (-31 to 185°F)Enclosure: polycarbonateMounting: standard 35 mm DIN rail or wall mountDimensions: 73 x 100 x 112 mm (2.87 x 3.94 x 4.41")Weight: 0.6 kg (1.3 lb)Combined Watt/Var TransducersINPUTSConnection: single phase or 3-phase, 3-wirePower Factor: unity-to, lead or lag, zeroPower Calibration Span: ±170 to ±10,000 watt/varOverrange: +42% (at full accuracy)Isolation: 2 KV RMS/1 minute for voltage and power inputs; 4 KV for current inputsCURRENT INPUTS Current Span: 5 AacCurrent Overrange: +20% (at full accuracy)Peak Overload: 40 Aac RMS for 5 seconds every 10 minutesVOLTAGE INPUTSVoltage Span: 115 Vac, 230 Vac Voltage Overrange: +20% (at full accuracy)Voltage Overload: 1.6 x nominal rating continuous, 600 Vac max OUTPUTS (WATT and VAR)Output Configuration: unipolar or bipolar currentOutput Span: 4-20 mA, 12 ± 8 mA Maximum Output Load: Rmax (KOhms) = 16/Iout (mA)Output Impedance: Z (K Ω) = 0.1 x Vo (Vdc)Load Variation Effect: < ±0.03% (for full change)DRA-WVT -3 SeriesOMEGACARE SM extendedwarranty program is available for models shown on this page. Ask your sales representative for fulldetails when placing an order.OMEGACARE SM covers parts,labor and equivalent loaners.DRA-WVT-3 shownsmaller than actual size.。

石墨烯的功能化

© XXXX American Chemical Society
A B B C D G H I K M N N Q R R S S S S S T T T
A
1. INTRODUCTION Graphene, the two-dimensional sp2-hybridized carbon, is currently, without any doubt, the most intensively studied material. This single-atom-thick sheet of carbon atoms arrayed in a honeycomb pattern is the world’s thinnest, strongest, and stiﬀest material, as well as being an excellent conductor of both heat and electricity. It is no wonder that this two-dimensional material is considered, from the application viewpoint, to be even more promising than other nanostructured carbon allotropes, that is, 1-dimensional nanotubes and 0-dimensional fullerenes. Since the ﬁrst experimental evidence of the electronic properties of graphene in 2004,1 a major focus of experimental research has been concentrated on the development of new synthetic routes enabling an eﬀective production of well-deﬁned sheets.2−18 The commonly applied methods include the micromechanical1 or chemical exfoliation of graphite,13 chemical

METHOD FOR OPTIMIZING AN ILLUMINATION SOURCE USING

专利名称：METHOD FOR OPTIMIZING ANILLUMINATION SOURCE USING FULL RESISTSIMULATION AND PROCESS WINDOWRESPONSE METRIC发明人：Steven George Hansen申请号：US10361831申请日：20030211公开号：US20040156029A1公开日：20040812专利内容由知识产权出版社提供专利附图：摘要：A method for optimizing the illumination conditions of a lithographic apparatus by computer simulation using full resist calculation, the lithographic apparatuscomprising an illuminator, a projection system, and a mask having a pattern to be printed in a layer of photoresist material formed on a substrate. This method includes defining a lithographic problem, which may include a lithographic pattern to be printed on a wafer;choosing a resist model of a resist process to be used to print a pattern in the layer of photoresist material; selecting a grid of source points in a pupil plane of the illuminator;calculating separate responses for individual source points, each of the responses representing a result of a single or series of simulations using the resist model; and adjusting an illumination arrangement based on analysis of accumulated results of the separate calculations.申请人：HANSEN STEVEN GEORGE更多信息请下载全文后查看。

中枢神经系统表面含铁血黄素沉积症的MRI表现并文献复习

[6]Xing P,Wu L,Zhang C,et al.Differentiation of benign from malignant thyroid lesions:calculation of the strain ra ⁃tio on thyroid sonoelastography[J].J Ultrasound Med,2011,30(5):663-669.[7]Wiest PW,Hartshorne MF,Inskip PD,et al.Thyroid pal ⁃pation versus high -resolution thyroid ultrasonography in the detection of nodules[J].J Ultrasound Med,1998,17(8):487-496.[8]Rago T,Vitti P,Chiovato L,et al.Role of conventional ul ⁃trasonography and color flow-doppler sonography in pre ⁃dicting malignancy in ‘cold ’thyroid nodules[J].Eur J En ⁃docrinol,1998,138(1):41-46.[9]燕山,詹维伟,周建桥.甲状腺与甲状旁腺超声影像学[M].北京:科学技术文献出版社,2009:240-252.[10]罗建文,白净.超声弹性成像的原理及理论分析[J].国外医学:生物医学工程分册,2003,26(3):97-102.[11]Krouskop TA,Wheeler TM,Kallel F,et al.Elastic moduli of breast and prostate tissues under compression[J].Ultra ⁃son Imaging,1998,20(4):260-274.[12]郭慕依,叶诸榕.病理学[M].2版.上海:上海医科大学出版社,2001:206.[13]Wong KT,Ahuja AT.Ultrasound of thyroid cancer [J].Cancer Imaging,2005,5:157-166.[收稿日期]2016-05-03*[通信作者]陆健,电话:139********,E-mail:blz1206@南通大学学报(医学版)Journal of Nantong University (Medical Sciences)2016∶36(4)中枢神经系统表面含铁血黄素沉积症(superfi -cial siderosis of the central nervous system,CNS SS)是一种罕见的中枢神经系统疾病,1908年由R.Hamill [1]首先描述。

糖尿病跟腱的超声研究的进展

糖尿病跟腱的超声研究的进展黄文慧;李彤;祝红晶;孙若雪;张伟静;杨春荣【期刊名称】《中国实验诊断学》【年(卷),期】2016(020)005【总页数】4页(P862-865)【作者】黄文慧;李彤;祝红晶;孙若雪;张伟静;杨春荣【作者单位】吉林大学第二医院电诊科，吉林长春 130041;吉林大学第二医院电诊科，吉林长春 130041;吉林大学第二医院电诊科，吉林长春 130041;吉林大学第二医院电诊科，吉林长春 130041;吉林大学第二医院电诊科，吉林长春130041;吉林大学第二医院电诊科，吉林长春 130041【正文语种】中文*通讯作者糖尿病足是糖尿病治疗的难题之一，是糖尿病患者下肢截肢致残的主要原因[1]。

许多糖尿病患者初诊后是有较长的存活期的[2]，案例报道和流行病学调查分析显示糖尿病与跟腱断裂是有明显关系的[3]，糖尿病导致的下肢综合征与糖尿病发病率和致死率有显著的相关性[2]，预防糖尿病下肢的病变是糖尿病患者晚期生活质量明显改善的关键之一，所以对糖尿病患者下肢早期异常改变的发现是至关重要的，可以极大程度上改善糖尿病患者后期的生活质量。

糖尿病下肢病变包括血管、肌肉、神经以及肌腱的变化[1]，影像诊断技术对肌腱的结构改变有一定的提示作用，这些技术包括肌骨的超声成像、计算机断层扫描技术以及核磁共振显像技术。

现今国内外对跟腱的研究相对较少，而影像学对糖尿病跟腱可显示出的改变相对较微小，大部分影像诊断医师也相对不熟悉该疾病的影像学表现。

这个综述目的是为大家提供糖尿病跟腱的超声改变，为糖尿病跟腱的超声研究做出初步总结。

1.1 二维高频超声(Ultrasonography,US) 根据超声医师的经验及肉眼对超声仪器屏幕显示二维图像的观察，分辨出跟腱的感兴趣区域的无回声、低回声、高回声、强回声，该技术主要缺点是受仪器先进性及检查者主观判断影响较大。

1.2 超声组织特征分型(Utrasonic Tissue Charateristic,UTC) 是半量化传统二维超声探查所得图像的结果，大致分为4种类型：(Ⅰ)完整、均匀、整齐的肌腱束；(Ⅱ)不连续或波浪状的肌腱束；(Ⅲ)毛糙状的肌腱束；(Ⅳ)表现为主要由细胞和基质组成的无特定形态的组织。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

Sonoelastography using Compensated Power DopplerStephen J.McKenna,Stuart Dickson,Ian W.Ricketts Department of Applied ComputingUniversity of DundeeDundee,Scotland{stephen,sdickson,ricketts}@Asif Iqbal,Tim Frank,Alfred Cuschieri Department of Surgery and Molecular OncologyUniversity of DundeeDundee,Scotland{a.y.iqbal,t.g.frank,a.cuschieri}@ABSTRACTSonoelastography is the visualisation of elastic properties using ultrasound.It can enable tumours to be detected and localised based on their elasticity when they are less elastic than the surrounding soft tissue.In vibration sonoelastog-raphy the target tissues are vibrated while simultaneously recording ultrasound images.A technique for imaging rel-ative elastic properties is proposed that uses a standard ul-trasound machine.It combines B-scan and power Doppler signals to produce images of relative vibration amplitude. Preliminary results using simulations and liver phantoms are presented and the potential of the method to highlight areas of differing elasticity within an organ such as the breast is mentioned.The possibility of combining such a method with freehand3D scanning,enabling B-scan and power Doppler signals to simultaneously populate a voxel array for subsequent visualisation is discussed.KEY WORDSSonoelastography,ultrasound,freehand scanning,power Doppler ultrasound1IntroductionThe most common clinical method for detecting lumps within tissue,palpation,is highly subjective and depen-dent on the skill of the practitioner.The method exists because certain pathological conditions,such as malignant tumours,manifest themselves as changes in the tissue’s mechanical stiffness.While X-ray imaging is well estab-lished for the detection of small,deeply located tumours, X-ray hazards and the desire for better performance have led to a continuing search for alternative techniques.Di-agnostic ultrasound is a potential alternative to X-rays,its limitation being that small pathological changes in tissue are difﬁcult to discern on normal ultrasound B-scans.If, however,ultrasonic echo data is collected before and af-ter a slight compression of the tissue,comparisons can be made between normal and pathological areas.This is pos-sible when normal tissues exhibit relatively more move-ment than stiffer pathological regions.It has been suggestd that benign and malignant tumours can be distinguished by elastography(imaging of elasticity)due to their differing uniformity of elastic properties[14].Elastography exam-ines the static elastic properties of tissue.Other authors and unpublished results from our own tissue property stud-ies suggest that differences between healthy and pathologi-cal tissue are highlighted more clearly using rapidly chang-ing strain.This time-dependent(i.e.viscous)response is analogous to the vibrational frequency response of the tis-sue.It is likely that a relatively narrow band of vibration frequencies exists for which the response in the tissue is optimum for distinguishing variations in viscoelastic prop-erties.Ultrasound imaging of elastic properties in the pres-ence of vibration is known as sonoelastography.A small, stiff zone will appear as a deﬁned region due to the dif-ference between its motion and that of the surrounding tis-sue.Ultrasound sonoelastography imaging has been com-pared to conventional ultrasound imaging for the detection of prostate cancer in vitro,with promising results[18].Al-though elastography and sonoelastography are not yet be-ing used in routine clinical practice,these imaging methods have the potential to give comparable spatial resolution to standard grey-scale imaging with enhanced tissue discrim-ination.Several authors have reported the use of phase-contrast magnetic resonance imaging(MRI)to visualise the mechanical properties of tissues[2,5].Images of tis-sue subjected to static or time varying displacement are obtained,yielding information on the3D distribution of elasticity and viscoelasticity respectively.The results from these techniques are very impressive in that small inho-mogeneities can be localised.However,the method may never become broadly applicable due to the very high cost of MRI and its lack of portability.In Doppler ultrasonography,shifts in returning ultra-sonic echoes due to the motion of reﬂecting features are detected.While this is commonly used to highlight blood ﬂow,variations in tissue motion can also be revealed.Ul-trasound imaging is particularly attractive as the basic im-age forming process due to its benign nature and low cost. In addition,the colour Doppler imaging modality offered in modern systems provides motion information when vi-bration is present.The technique described here,known as Doppler sonoelastography,produces images that can be interpreted in terms of elasticity variations.Sonoelastography has the potential to enhance the ef-ﬁcacy of screening for common cancers.A primary moti-vation for conducting the research described here is to lay the foundations for developing a new non-invasive,atrau-matic and painless system for breast tumour diagnosis and location.The technique is applicable to other common tu-mour sites such as the prostate.Elasticity imaging may also be used to detect other diseases that cause changes in tissue elasticity(e.g.atheromatous disease).Other applications include the measurement of tissue elasticity for use in tis-sue modelling studies and to provide data in virtual reality research in relation to surgical/interventional simulators.In this paper,we investigate the possibility of using the power Doppler imaging mode available as standard on many modern ultrasound machines in combination with co-registered B-scans to perform sonoelastography.Sec-tion2brieﬂy describes the methods that have previously been proposed for imaging elasticity using ultrasound.In Section3,a process for estimating the power Doppler sig-nal from tissue under vibration is described and simulated. Simulation results are presented to illustrate the effect of scatterer strength,vibration frequency and vibration ampli-tude on the power Doppler signal.Section4describes pre-liminary imaging experiments using the theory presented in the previous section.Section5describes our freehand3D scanning system and discusses its applicability to Doppler sonoelastography.Finally,some conclusions and directions for future work are given in Section6.2Elasticity Imaging using Ultrasound Several techniques for imaging tissue elasticity using ultra-sound have been proposed[1,4,10,12,13,20].The reader is refered to Gao et al.[7]for a review.Taylor et al.[19] classify existing methods as(i)compression elastography (strain imaging),(ii)transient elastography and(iii)vibra-tion sonoelastography.In compression elastography,ultra-sound images are compared before and after a compression is applied to the tissue in order to compute a strain map.In transient elastography,a low-frequency transient vibration is applied and the resulting tissue displacement is detected using ultrasound before echoes from tissue boundaries oc-cur.The third class,vibration sonoelastography,which is the topic of this paper,images the vibration patterns result-ing when low frequency vibration is applied to the tissue. Vibration propagation within a complex organ cannot be solved analytically.However,small,stiff lesions will tend to result in decreases in vibration amplitude.The extent to which they are contrasted with the surrounding tissue will depend on their size and stiffness and on the frequency of vibration.Losses at high frequencies impose an upper limit on the vibration frequencies that can be used in practice.Vibration amplitude imaging with low-frequency vi-bration wasﬁrst proposed in the late80’s[11].Tissue mo-tion can be estimated by tracking the two-dimensional im-age motion of the speckle produced by back-scattering in high frame-rate,real-time ultrasound.Such tracking is of-ten based on template matching methods(e.g.correlation-based motion estimation)although other opticalﬂow algo-rithms may also be applicable[3].Speckle tracking can be used to produce images of strain magnitude(e.g.[9]).Finite element methods have been proposed to enable re-construction of the spatial distribution of Young’s modulus [4].An alternative to speckle tracking is the use of real-time Doppler ultrasound.Doppler techniques measure the component of motion in the direction of ultrasound wave propagation and as such detect axial motion.Doppler ultra-sound machines typically use autocorrelation estimators to estimate the mean frequency and the variance of the power spectrum[6].Inﬂow Doppler,which is used for imag-ing bloodﬂow for example,the mean frequency is used to estimate the mean velocity.However,under sinusoidal vibration,mean velocity gives no indication of vibration amplitude since oscillation is about a rest position.Taylor et al.[19]make use of the relationship between vibration amplitude andﬂow Doppler variance.They used a scan-ner specially modiﬁed to display the real-time estimate of the variance of the power spectrum.Under reasonable as-sumptions the standard deviation of the power spectrum is linearly related to vibration amplitude.They were thus able to image the vibration amplitude by measuring this vari-ance.In contrast,we propose the use of power Doppler imaging in conjunction with co-registered B-scan images to image the vibration amplitude.Power Doppler is available as standard on many ultrasound machines since it is use-ful for imaging bloodﬂow and has the advantage of good sensitivity to very low velocities.3Power DopplerPower Doppler imaging encodes an estimate of the inte-grated power Doppler spectrum in pseudo-colour.It cannot be used directly to estimate the vibration amplitude because the power Doppler signal depends on the echo strength of the region being imaged as well as its vibration amplitude. The method proposed here uses standard B-scan imaging to compensate the power Doppler signal in order to image the relative vibration amplitudes in the tissue.3.1SimulationUltrasound scanners tend to use autocorrelation estimators for colourﬂow and power Doppler imaging.This estima-tion process was simulated in order to investigate its be-haviour at different vibration frequencies and vibration am-plitudes.The simulation was similar to that used by Taylor et al.[19]to investigate the effect of vibration amplitude on estimates of the variance of the Doppler power spectrum as used forﬂow imaging.Here we investigate estimation of vibration amplitude from the integrated power spectrum.In pulsed Doppler ultrasound,a sequence of ultra-sound pulses which together form a packet are used.The number of pulses in a packet is usually user-controlled and here it was set to N=16.These pulses are emitted at in-tervals of T p.Each pulse was modelled as a real wavelet(Equation(1))whereσ=173ns and f c was the centre frequency.p(t)=1(2πσ2)12exp(−t22σ2)cos(2πf c t)(1)The round-trip time taken from the ultrasound transducerto a scatterer at distance d0and back is t d0=2d0/c wherec is the speed of sound.The mean speed of sound in tis-sue varies from approximately1446ms−1in fat to approx-imately1556ms−1in spleen,for example.The simulations reported here used c=1540ms−1,an average value used in some scanners[8].A scatterer under forced vibration was modelled as undergoing sinusoidal motion about a rest position at distance d0from the ultrasound transducer with peak vibration amplitude m and vibration frequency f v. Its distance,d(t),from the transducer at time t is therefore given by Equation(2).d(t)=d0− m sin2πf v t(2) The backscatter,e(t),received from a single pulse at time t is:e(t)=Ap(t−2d(t)/c)(3) where A is the amplitude of the backscatter and models the echogenicity,the scattering coefﬁcient and attenuation in the tissue.Aﬁrst-difference FIRﬁlter was applied to the backscattered pulse signals.This simulated a wallﬁlter and attenuated the ponent.Quadrature demodulation was simulated by sampling the N returning,ﬁltered,backscattered pulses in a packet with theﬁrst pulse emitted at time t=0.Samples I nwere taken at times t I(n)=nT p+t d0and samples Q nwere taken a quarter of a cycle later at times t Q(n)= t I(n)+1/(4f c),where n=1...N.In the experiments described here,T p=1ms.The average power,R,of the backscattered signal is given by the autocorrelation func-tion at zero lag:R=1N(I2n+Q2n)(4)Note that R is proportional to A2.Doubling the amplitude of the backscatter,for example,will quadruple the power Doppler signal.3.2Simulation ResultsFigure1shows power,R,plotted against vibration ampli-tude, m for a scatterer vibrated at a frequency of f v= 200Hz at mean distance d0=2cm from a7.5MHz trans-ducer.Three curves are plotted corresponding to scatterer strengths of A=0.1,A=0.2and A=0.3.Together these curves illustrate that R increases with A2.If the power signal can be compensated using an estimate of the scatterer strength these three curves become the same.The power Doppler signal increases monotonically with vibra-tion amplitude over this range(≤1mm)except at veryFigure1.Simulated power Doppler versus vibration am-plitude for A=0.1(solid),A=0.2(dashed)and A=0.3 (dotted).The power Doppler signal has been normalised. Other parameters were d0=2cm,f c=7.5MHz and f v=200Hzlow power.Therefore an appropriately compensated power Doppler signal could be used to image vibration ampli-tude in this situation.Note that larger vibration amplitudes would not be properly imaged.The amplitude and frequency of the vibration source should be selected to be appropriate for the ultrasound transducer used and the depth d0of the tissue of interest. This is necessary in order to ensure that the relationship be-tween R and m is approximately monotonic and produces a meaningful image for the range of vibration amplitudes induced.Figures2and3show three curves generated as in Fig-ure1but with the vibration frequency decreased to40Hz. Note that the ranges of vibration amplitudes that can now be imaged reliably are different.Figure2shows that the range m=0to m=5mm could in theory be imaged reasonably well.However,Figure3shows that vibration amplitudes in the range m=0to m=250µm could also be imaged at this depth and frequency.4Sonoelastographic ImagingAn Aloka SSD220ultrasound system with a7.5MHz linear array probe was used for preliminary imaging experiments. This system has a power Doppler mode as standard.Several vibration systems have been constructed for experimental use with tissue phantoms.They all consist of a single source using a signal generator and an acoustic speaker.The oscillator incorporated a trigger circuit to al-low phase-locking of the image acquisition.The range of vibration frequencies that can be used is limited by loss at higher frequencies.Frequencies need to be selected to en-able imaging of the vibration amplitude as described in the previous section.An alternative to sinusoidal vibration isFigure2.Simulated(nomalised)power Doppler versus vi-bration amplitude for A=0.1(solid),A=0.2(dashed) and A=0.3(dotted).Parameters were as for Figure1 with the exception of vibration frequency which was f v= 40Hz.Figure3.The previous Figure with the abscissa scaled. to use some form of polychromatic vibration(e.g.square wave vibration).This can help avoid modal patterns and the vibration systems are currently being used to conduct empirical investigation of various forms of vibration over arange of frequencies and amplitudes.Figure4shows co-registered B-scan and power Doppler images of a slice through a commercially available synthetic breast phantom(supplied by Computing Imaging Reference Systems,Inc.).Vibration was applied at the base in the Figures and the transducer was at the top.The fre-quency of the applied vibration was30Hz.The images were obtained by keeping the ultrasound probe clamped in aﬁxed position while switching from B-scan mode to power Doppler mode.Aﬂuidﬁlled cyst can be seen at the lower right and a stiff lesion at the lower left.The cyst ap-pears as a void in the B-scanandtherefore also as a voidin the power Doppler image.Since there is no signiﬁcantbackscattered signal from this region,there is no powerDoppler signal.The lesion at the lower left appears con-trasted in the B-scan indicating that it scatters with greateramplitude.It also appears contrasted in the power Dopplersignal and the extent of this contrast is due to both the in-creased scatter and the increased stiffness.Figure4.Mean B-scan(left)and power Doppler(right)images of the same slice of a commercial breast phantomwith an applied vibration.Figure5shows co-registered B-scan,power Dopplerand sonoelastographic images.The sonoelastographic im-age was obtained by compensating the power Doppler datawith squared B-scan data.The square root of the resultingpixel data is shown for better visualisation.The images areof a liver phantom with a simulated tumour in the centre.This tumour appears hyperechoic in the B-scan but is notapparent in the power Doppler signal as a result,despiteits lower elasticity.However,it appears as a void in so-noelastographic image indicating that it is stiffer than thesurrounding tissue.5Freehand3D SonoelastographyStandard two-dimensional ultrasound scanners can be usedto provide three-dimensional images if the3D position andorientation of the transducer is known for each of the2Dimages recorded.Free-hand3D scanning can be used toconstruct a3D volume(voxel array)while the physicianperforms an examination in a normal manner.Visualisa-tion software can then provide an operator with the abilityto explore the3D volume using techniques such as any-slice imaging,rendering with transparency and3D view-point control.5.1Calibration and VisualisationA freehand scanning system has been constructed in whichthe ultrasound probe’s3D position and orientation are mea-sured using a Polhemus Fastrak electromagnetic sensorwith an angular and positional accuracy of0.5◦and0.5mmrespectively.The Polhemus device is portable and accurateFigure5.Top:B-Scan,Middle:Power Doppler,Bot-tom:Sonoelastographic image.The sonoelastographic im-age was obtained by compensating the Dopper image with squared B-scan data and then taking the square root of each pixel to improve visualisation.as long as reasonable precautions are taken to avoid elec-tromagnetic interference.Once attached to the ultrasound probe,the Polhemus sensing system is spatially calibrated with respect to the B-scans using an object of known ge-ometry.This spatial calibration was performed using the StradX software and a phantom constructed using a sim-ilar design to that described by Prager et al.[15].This phantom is shown in Figure6.The measurements from the Polhemus sensor and the ultrasound images capturedwere Figure6.Left:the calibration phantom with the probe and Polhemus sensor attached.Right:a calibration image temporally aligned using a trigger signal supplied via a footswitch.This system can be used to reconstruct3D vol-umes from freehand scans and is being used to investigate the possibility of3D sonoelastography based on simultane-ously acquired B-scan and power Doppler data.High qual-ity3D reconstruction requires accurate calibration of the free-hand scanning device,accurate registration and data fusion.Image-based registration and fusion can improve the quality of the reconstruction and reduce speckle noise, shadowing and signal dropout[16,17].5.2Current Research Issues for3D DopplerSonoelastographyDoppler imaging only measures the component of velocity in the direction of wave propagation i.e.only axial motion can be detected.However,freehand scanning can be used to register and fuse Doppler signals from different trans-ducer orientations.The process of forming a power Doppler image is rel-atively slow since multi-pulse packets are used for estima-tion.This means that the probe can move signiﬁcantly dur-ing acquisition of a single image.Probe position and orien-tation measurements therefore need to be interpolated over time so that columns in the2D images obtained from the linear array probe can be aligned appropriately in3D.The frame-rate for power Doppler imaging is often increased by reducing the area over which Doppler signals are estimated, the remaining area being imaged in B-scan mode.During such a scan,the B-scan and Doppler data can be recorded and registered in two separate3D voxel arrays.Fusion of these B-scan and Doppler volumes then compensates the power Doppler data to produce3D sonoelastographic vol-ume data.Each voxel in this volume could be assigned an uncertainty value based on the amount of evidence avail-able from the2D scans and the extent of the interpolation used.This uncertainty data could in turn provide useful in-formation for subsequent data fusion and provide feedback to the physician performing the scan.Three-dimensional sonoelastographic imaging has the potential application of measurement of the volume distribution of tissue elastic properties.This data is required by researchers developing mathematical models of tissue and,in particular,for use in electronic tissue representation in surgical simulators.6ConclusionsA method for vibration sonoelastography has been pro-posed based on compensating power Doppler images with B-scan image data.Simulations were presented to explore the feasibility of the method and the sensitivity to vibration amplitude and frequency.An experimental imaging system was described and the potential beneﬁts of its extension to freehand3D scanning systems were outlined.Future work could extend the simulation usingﬁnite element shear wave vibration modelling combined with models of ultrasound propagation.As demonstrated in the simulations presented here,sonoelastographic scanning re-quires the determination of optimal frequency ranges for the externally applied vibration.Modal patterns(stand-ing waves)can occur,especially for regular shapes,and these can make image interpretation difﬁcult[19].The use of polychromatic vibration should be explored to alleviate such artefacts.We are also studying Doppler imaging in the non-power mode.Here the image acquisition times are shorter and allow us to synchronise the image to an ad-justable phase position within one vibration cycle.This is revealing information about vibration mode structures and will help to develop methods for avoiding them.An objective of this research is to improve detec-tion of subclinical breast cancer by breast sonoelastogra-phy.The sonoelastographic imaging modality is painless, risk free and uses equipment that is relatively cheap and portable.References[1]J.C.Bamber and N.L.Bush.Freehand Elasticity Imag-ing Using Speckle Decorrelation Rate.Plenum,New York, 1995.[2]J.Bishop,M.Leitch,G.Poole,and D.Plewes.Magneticresonance imaging of shear wave propagation in excised tissue.Journal of Magnetic Resonance Imaging,8:1257–1265,1998.[3] D.H.Cooper and J.Graham.Estimating motion in noisy,textured images:Opticalﬂow in medical ultrasound.In British Machine Vision Conference(BMVC),pages585–594,1996.[4]M.M.Doyley,P.M.Meaney,and J.C.Bamber.Evalu-ation of an iterative reconstruction method for quantitative elastography.Phys.Med.Biol.,45:1521–1540,2000. [5]R.Ehman.Magnetic resonance elastography:‘palpation’by imaging.Proc.Int.Workshop on Soft Tissue Deforma-tion and Tissue Palpation,October1998.[6] D.H.Evans and W.N.McDicken.Doppler Ultrasound:Physics,Instrumentation and Signal Processing.Wiley,2nd edition,1999.[7]L.Gao,S.K.Alam,R.M.Lerner,and S.F.Levinson.Imag-ing of the elastic properties of tissue-a review.Ultrasound Med.Biol.,22:959–77,1996.[8]J.A.Jensen.Ultrasound imaging and its modeling.In Imag-ing of Complex Media with Acoustic and Seismic Waves, Topics in Applied Physics.Springer Verlag,2000.[9]K.Kaluzynski,X.Chen,Y.Emelianov,A.R.Skovoroda,and M.O’Donnell.Strain rate imaging using two-dimensional speckle tracking.IEEE Transcations on Ultra-sonics,Ferroelectrics and Frequency Control,48(4):1111–1123,July2001.[10]R.M.Lerner and K.J.Parker.Sonoelasticity images,ultra-sonic tissue characterization and echographic imaging.In 7th European Communities Workshop,Nijmegen,Nether-lands,1987.[11]R.M.Lerner,K.J.Parker,J.Holen,R.Gramiak,and R.C.Waag.Sono-elasticity:medical elasticity images derived from ultrasound signals in mechanically vibrated targets.In Proc.16th int.Symp.Acoustical Imaging,vol.19,pages 317–327,New York,1988.Plenum.[12]M.O’Donnell,A.R.Skovoroda,B.M.Shapo,and S.Y.Emelianov.Internal displacement and strain imaging using ultrasonic speckle tracking.IEEE Trans.Ultrason.Ferro-electr.Freq.Control,41:314–325,1994.[13]J.Ophir.Elastography:ultrasonic imaging of tissue strainand elastic modulus in vivo.Eur.J.Ultrasound,3:49–70, 1996.[14]J.Ophir.Scientists useﬁnite element method in developingnew cancer detection technique.NASA Tech.Briefs,pages 86–87,August1998.[15]R.W.Prager,R.N.Rohling,A.H.Gee,and L.Berman.Rapid calibration for3-d freehand ultrasound.Ultrasound in Medicine and Biology,24(6):855–869,1998.[16]R.N.Rohling,A.H.Gee,and L.Berman.Spatial com-pounding of3d ultrasound images.Technical Report Tech.Rep.CUED/F-INFENG/TR270,Univ.of Cambridge,Oc-tober1996.[17]R.N.Rohling,A.H.Gee,and L.Berman.Automatic reg-istration of3d ultrasound images.Technical Report Tech.Rep.CUED/F-INFENG/TR290,Univ.of Cambridge,May 1997.[18] D.Rubens,M.Hadley,and et al.Sonoelasticity imaging ofprostate cancer:in vitro results.Radiology,195:379–383, 1995.[19]L.Taylor,B.C.Porter,D.J.Rubens,and K.J.Parker.Three-dimensional sonoelastography:Principles and prac-tices.Phys.Med.Biol.,2000.[20]Y.Yamakoshi,J.Sato,and T.Satoa.ultrasonic imagingof internal vibration of soft tissue under forced vibration.IEEE Trans.Ultrason.Ferroelectr.Freq.Control,17:45–53,1990.。