Paul S. Wang, H. Tan, A. Saleeb, Tse-Yung P. Chang
Recently developed techniques for the symbolic derivation of formulas and the automatic generation of code for numerical computation are applied to formulate the hybrid mixed model in finite element analysis. The hybrid mixed model is a promising approach to overcome several difficulties associated with the more traditional displacement models for the analysis of “constrained-media” problems. Applying the FINGER (FINite element GEneratoR) system, FORTRAN code has been generated for computing the strain-displacement coefficients and the stiffness coefficients for a sample hybrid mixed plate bending element. Attention is paid to improving the efficiency of code generated and the generality of the approach. Described is the first full-scale problem which subject the approach to stringent conditions and requirements of an actual engineering application.
近年来发展起来的公式符号推导技术和数值计算代码自动生成技术被应用于有限元分析中的混合混合模型。混合模型是一种很有前途的方法，可以克服与传统位移模型相关的一些困难，用于分析“受限介质”问题。应用FINGER (FINite element GEneratoR)系统，编制了计算混合板弯曲单元的应变-位移系数和刚度系数的FORTRAN程序。注意提高代码生成的效率和方法的通用性。描述的是第一个全面的问题，该问题使该方法符合实际工程应用的严格条件和要求。
{"title":"Code generation for hybrid mixed mode formulation in finite element analysis","authors":"Paul S. Wang, H. Tan, A. Saleeb, Tse-Yung P. Chang","doi":"10.1145/32439.32448","DOIUrl":"https://doi.org/10.1145/32439.32448","url":null,"abstract":"Recently developed techniques for the symbolic derivation of formulas and the automatic generation of code for numerical computation are applied to formulate the hybrid mixed model in finite element analysis. The hybrid mixed model is a promising approach to overcome several difficulties associated with the more traditional displacement models for the analysis of “constrained-media” problems. Applying the FINGER (FINite element GEneratoR) system, FORTRAN code has been generated for computing the strain-displacement coefficients and the stiffness coefficients for a sample hybrid mixed plate bending element. Attention is paid to improving the efficiency of code generated and the generality of the approach. Described is the first full-scale problem which subject the approach to stringent conditions and requirements of an actual engineering application.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123083094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The majority of today's computer algebra systems are huge programs that are only available on mainframe computers. One of the rare exceptions is the muMATH system which can be run on the variety of microcomputers. It was primarily designed to be used by students in high school or college. However, muMATH is meant to be a tool for the person who already knows relevant mathematics, but who wants to avoid tedious calculations.
{"title":"Edusym—educational symbolic manipulator on a microcomputer","authors":"Neven Jurkovic","doi":"10.1145/32439.32470","DOIUrl":"https://doi.org/10.1145/32439.32470","url":null,"abstract":"The majority of today's computer algebra systems are huge programs that are only available on mainframe computers. One of the rare exceptions is the muMATH system which can be run on the variety of microcomputers. It was primarily designed to be used by students in high school or college. However, muMATH is meant to be a tool for the person who already knows relevant mathematics, but who wants to avoid tedious calculations.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131095176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We devise several procedures based on signatures (or hashing functions) to determine equivalence of expressions in Random Polynomial Time (also called Probabilistic Polynomial Time) (RPT). We extend the previous results known to include various new functions that can be tested. These procedures return as result: “equivalent” or “not-equivalent”. The result “not-equivalent” is always correct, while the result “equivalent” is correct with probability at least 1 — ε. This probability depends on a random number generator and is independent of the problem being solved. In all our procedures, the value ε can be made arbitrarily small. This method works for determining equivalence over an important class of functions as well as answering other questions like linearity, polynomial dependence, squareness, independence, etc. The general scheme for all these algorithms is to use a basic heuristic “test” several times. I.e. solve( problem, epsilon ) repeat select suitable characteristic p randomly; assign random values to all variables; t := test( problem, p ); if t = “not-equivalent” then return( t ) until Prob of cumulative failures >= epsilon; return( “equivalent” ); It is assumed that “test” gives a wrong answer with probability δ, where δ remains bounded below 1. For all our “test” procedures, δ ≤ 1/2. In what follows we will describe the “test” part of the different procedures, it is always assumed that these are used in the above context. Without loss of generality we will assume that equivalence of expressions (A ≡ B) can be transformed into testing for 0 (A — B ≡ 0). This test can be performed “quickly” in the sense that it can run in polynomial time on the size of the dag (directed acyclic graph) representation of the expression, also known as “linear program representation” of an expression.
{"title":"New results for random determination of equivalence of expressions","authors":"G. Gonnet","doi":"10.1145/32439.32465","DOIUrl":"https://doi.org/10.1145/32439.32465","url":null,"abstract":"We devise several procedures based on signatures (or hashing functions) to determine equivalence of expressions in Random Polynomial Time (also called Probabilistic Polynomial Time) (RPT). We extend the previous results known to include various new functions that can be tested. These procedures return as result: <italic>“equivalent”</italic> or <italic>“not-equivalent”</italic>. The result “not-equivalent” is always correct, while the result “equivalent” is correct with probability at least 1 — ε. This probability depends on a random number generator and is <italic>independent</italic> of the problem being solved. In all our procedures, the value ε can be made arbitrarily small. This method works for determining equivalence over an important class of functions as well as answering other questions like linearity, polynomial dependence, squareness, independence, etc.\u0000The general scheme for all these algorithms is to use a basic heuristic <italic>“test”</italic> several times. I.e. solve( problem, epsilon ) repeat select suitable characteristic p randomly; assign random values to all variables; t := test( problem, p ); if t = “not-equivalent” then return( t ) until Prob of cumulative failures >= epsilon; return( “equivalent” );\u0000It is assumed that <italic>“test”</italic> gives a wrong answer with probability δ, where δ remains bounded below 1. For all our <italic>“test”</italic> procedures, δ ≤ 1/2.\u0000In what follows we will describe the <italic>“test”</italic> part of the different procedures, it is always assumed that these are used in the above context.\u0000Without loss of generality we will assume that equivalence of expressions (<italic>A ≡ B</italic>) can be transformed into testing for 0 (<italic>A — B ≡ 0</italic>).\u0000This test can be performed “quickly” in the sense that it can run in polynomial time on the size of the <italic>dag</italic> (directed acyclic graph) representation of the expression, also known as “linear program representation” of an expression.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128163982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Applications of a software interconnection system in mathematical problem solving environments","authors":"James M. Purtilo","doi":"10.1145/32439.32443","DOIUrl":"https://doi.org/10.1145/32439.32443","url":null,"abstract":"","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134328046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Formal solutions of linear difference equations: method of Pincherle-Ramis","authors":"J. Dora, E. Tournier","doi":"10.1145/32439.32477","DOIUrl":"https://doi.org/10.1145/32439.32477","url":null,"abstract":"","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133907259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Macaulay is a system for computing in algebraic geometry and cummutative algebra; it is capable of a variety of computations which are tedious or impossible to perform by hand. The primitive types in the system are polynomials, matrices, ideals, polynomial rings, modules, maps between rings, and complexes of modules. The system performs algebraic manipulation on objects of these types. The possible manipulations include the computation of standard (Gröbner) bases, modules of syzygies, finite free resolutions, Hilbert polynomials and functions. Using these basic operations, a variety of derived operations are possible, such as projections, ideal intersections, and the computation of coherent sheaf cohomology groups. The algorithm used for constructing standard (Gröbner) bases and syzygies is described in ([Buc76], [Zac78], [Sch80], [Bay82], [BaSt86a]). Macaulay is intended to provide a computational research tool for working mathematicians. Macaulay is designed primarily to aid in generating non-trivial examples in algebraic geometry and commutative algebra. Such examples help mathematicians to gain intuition, and formulate or gather evidence for conjectures. In certain cases, an example can provide a step in the proof of a theorem. This system has been continuously evolving since 1977 where it was first developed at the University of Illinois by the second author. The algorithms have become substantially more sophisticated and efficient and the scope and power of the system has increased dramatically since its inception. Macaulay differs in a number of significant ways from other computer algebra systems. The computation of standard bases is its fundamental operation, rather than simplification and factoring. Unlike other systems which provide for the computation of standard bases, submodules of free modules can uniformly be used wherever ideals can be used. Macaulay is written in the language C and its design has been optimized for execution on small systems; Macaulay is available, and reasonably powerful, on a Macintosh microcomputer. Macaulay uses a novel encoding scheme for monomials which considerably reduces the storage requirements for polynomials, further enhancing its viability on small systems. Computations in Macaulay are interruptible, with the full power of the system available to study and use partial results. Macaulay is command-driven, and is quickly learned by mathematicians having no experience with computers. The basic data types of Macaulay are highly structured, reflecting its focus on the construction of standard bases and syzygies, not the simplification of general expressions. This design allows Macaulay to outperform more general systems, within its problem domain. Macaulay is capable of many computations that are not available in more general systems. These include the computation of syzygies, finite free resolutions of modules and ideals, and coherent sheaf cohomology groups. The set of commands provided allow the user
{"title":"The design of Macaulay: a system for computing in algebraic geometry and commutative algebra","authors":"D. Bayer, M. Stillman","doi":"10.1145/32439.32471","DOIUrl":"https://doi.org/10.1145/32439.32471","url":null,"abstract":"Macaulay is a system for computing in algebraic geometry and cummutative algebra; it is capable of a variety of computations which are tedious or impossible to perform by hand. The primitive types in the system are polynomials, matrices, ideals, polynomial rings, modules, maps between rings, and complexes of modules. The system performs algebraic manipulation on objects of these types. The possible manipulations include the computation of standard (Gröbner) bases, modules of syzygies, finite free resolutions, Hilbert polynomials and functions. Using these basic operations, a variety of derived operations are possible, such as projections, ideal intersections, and the computation of coherent sheaf cohomology groups. The algorithm used for constructing standard (Gröbner) bases and syzygies is described in ([Buc76], [Zac78], [Sch80], [Bay82], [BaSt86a]).\u0000Macaulay is intended to provide a computational research tool for working mathematicians. Macaulay is designed primarily to aid in generating non-trivial examples in algebraic geometry and commutative algebra. Such examples help mathematicians to gain intuition, and formulate or gather evidence for conjectures. In certain cases, an example can provide a step in the proof of a theorem.\u0000This system has been continuously evolving since 1977 where it was first developed at the University of Illinois by the second author. The algorithms have become substantially more sophisticated and efficient and the scope and power of the system has increased dramatically since its inception.\u0000Macaulay differs in a number of significant ways from other computer algebra systems. The computation of standard bases is its fundamental operation, rather than simplification and factoring. Unlike other systems which provide for the computation of standard bases, submodules of free modules can uniformly be used wherever ideals can be used. Macaulay is written in the language C and its design has been optimized for execution on small systems; Macaulay is available, and reasonably powerful, on a Macintosh microcomputer. Macaulay uses a novel encoding scheme for monomials which considerably reduces the storage requirements for polynomials, further enhancing its viability on small systems. Computations in Macaulay are interruptible, with the full power of the system available to study and use partial results. Macaulay is command-driven, and is quickly learned by mathematicians having no experience with computers.\u0000The basic data types of Macaulay are highly structured, reflecting its focus on the construction of standard bases and syzygies, not the simplification of general expressions. This design allows Macaulay to outperform more general systems, within its problem domain. Macaulay is capable of many computations that are not available in more general systems. These include the computation of syzygies, finite free resolutions of modules and ideals, and coherent sheaf cohomology groups. The set of commands provided allow the user ","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122186111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Conform consists of a collection of LISP routines that permit the real time manipulation and display of conformal mappings of one complex plane onto another.
由一组LISP例程组成，这些例程允许实时操作和显示一个复平面到另一个复平面的保角映射。
{"title":"Conform: a conformal mapping system","authors":"H. R. Seymour","doi":"10.1145/32439.32472","DOIUrl":"https://doi.org/10.1145/32439.32472","url":null,"abstract":"Conform consists of a collection of LISP routines that permit the real time manipulation and display of conformal mappings of one complex plane onto another.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131321639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An operator algebra for Macsyma","authors":"J. Golden","doi":"10.1145/32439.32488","DOIUrl":"https://doi.org/10.1145/32439.32488","url":null,"abstract":"","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"87 20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126298232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Critical-pair criteria for the Knuth-Bendix completion procedure","authors":"L. Bachmair, N. Dershowitz","doi":"10.1145/32439.32481","DOIUrl":"https://doi.org/10.1145/32439.32481","url":null,"abstract":"","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134418474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I$ is well known that finding the greatest common divisor (GCD) of two integers is one of the fundamental computations in exact rational arithmetic, factorization and cryptography. Euclid3 algorithm and its variants are the widely used for GCD computations [Knu 811. However they are not suitable in the parallel computation. Since the whole-word comparisons is required. G.B. Purdy /Pur 831 proposed a different way to compute GCD which requires no comparison. The advantage of the Purdy’s algorithm is provided a possible way to speed up the period of each iteration time by using carry save technique. However, it requires 0( n2) iterations in its worst case where n denotes the number of bits of two inputs. In addition, it requires the additional hardware support to handle the overflow problem. R. P. Brent and H. T. Kung [B&K 85) have developed a plus-minus (PM) algorithm that test only the two least significant bits of two integers. The advantage of the PM algorithm is that the number of the iteration is at most 3.012*n units. In particular, this gives a linear time implementation on a systolic array [B&K 851. Although reaaonabl efficient in its use of silicon area, the delay between first input and first output of a computation for the serial-in-serial-out GCD is great than 3 n time units which may be undesirable long depending on the application. The basic idea in our algorithm is to combine two sequence operations of PM algorithm of BrenbKung into one basic operation, and also to avoid swap operations during the iterations to achieve higher parallelism. It has been proved that for any two n bit integers, the number of iterations of the new algorithm is less than 1.51*n+ 1 time units. A preliminary hardware design shows that the algorithm can be implemented in a simple way which consists of several conventional computer components such ss shift registers, borrow save adder, counter and a small PLA as controller. The algorithm can be extended to find not only the greatest common divisor of two numbers A and B, but also to find a pair of integers (2, y) such that AZ + By =GCD(A,B) with the same time complexity. A scheme to cascade a number of such GCD chips to compute very large GCD’s is also at hand, which alleviates a critical difficulty in such fields as cryptography.
众所周知，寻找两个整数的最大公约数(GCD)是精确有理数算术、因式分解和密码学中的基本计算之一。Euclid3算法及其变体被广泛用于GCD计算[Knu 811]。然而，它们并不适用于并行计算。因为需要对整个单词进行比较。G.B. Purdy /Pur 831提出了一种不需要比较的计算GCD的不同方法。Purdy算法的优点是利用进位保存技术为加快每次迭代周期提供了可能的途径。然而，在最坏的情况下，它需要0(n2)次迭代，其中n表示两个输入的位数。此外，它还需要额外的硬件支持来处理溢出问题。R. P. Brent和H. T. Kung [B&K 85]开发了一种加减(PM)算法，该算法仅测试两个整数的两个最低有效位。PM算法的优点是迭代次数最多为3.012*n个单元。特别是，这给出了一个在收缩数组[B&K 851]上的线性时间实现。虽然在使用硅面积方面是合理有效的，但是串行输入串行输出GCD计算的第一次输入和第一次输出之间的延迟大于3n个时间单位，这可能是不希望的长，具体取决于应用。我们算法的基本思想是将BrenbKung的PM算法的两个序列操作合并为一个基本操作，并且在迭代过程中避免交换操作，以实现更高的并行性。证明了对于任意两个n位整数，新算法的迭代次数小于1.51*n+ 1时间单位。初步的硬件设计表明，该算法可以以一种简单的方式实现，它由几个传统的计算机组件组成，如移位寄存器、借用保存加法器、计数器和一个小型PLA作为控制器。该算法不仅可以推广到求两个数A和B的最大公约数，而且可以求出具有相同时间复杂度的AZ + By =GCD(A,B)的一对整数(2,y)。一种将许多这样的GCD芯片级联以计算非常大的GCD的方案也在手边，这缓解了密码学等领域的关键困难。
{"title":"A fast carry-free algorithm and hardware design for extended integer GCD computation","authors":"D. Yun, Chang Nian Zhang","doi":"10.1145/32439.32455","DOIUrl":"https://doi.org/10.1145/32439.32455","url":null,"abstract":"I$ is well known that finding the greatest common divisor (GCD) of two integers is one of the fundamental computations in exact rational arithmetic, factorization and cryptography. Euclid3 algorithm and its variants are the widely used for GCD computations [Knu 811. However they are not suitable in the parallel computation. Since the whole-word comparisons is required. G.B. Purdy /Pur 831 proposed a different way to compute GCD which requires no comparison. The advantage of the Purdy’s algorithm is provided a possible way to speed up the period of each iteration time by using carry save technique. However, it requires 0( n2) iterations in its worst case where n denotes the number of bits of two inputs. In addition, it requires the additional hardware support to handle the overflow problem. R. P. Brent and H. T. Kung [B&K 85) have developed a plus-minus (PM) algorithm that test only the two least significant bits of two integers. The advantage of the PM algorithm is that the number of the iteration is at most 3.012*n units. In particular, this gives a linear time implementation on a systolic array [B&K 851. Although reaaonabl efficient in its use of silicon area, the delay between first input and first output of a computation for the serial-in-serial-out GCD is great than 3 n time units which may be undesirable long depending on the application. The basic idea in our algorithm is to combine two sequence operations of PM algorithm of BrenbKung into one basic operation, and also to avoid swap operations during the iterations to achieve higher parallelism. It has been proved that for any two n bit integers, the number of iterations of the new algorithm is less than 1.51*n+ 1 time units. A preliminary hardware design shows that the algorithm can be implemented in a simple way which consists of several conventional computer components such ss shift registers, borrow save adder, counter and a small PLA as controller. The algorithm can be extended to find not only the greatest common divisor of two numbers A and B, but also to find a pair of integers (2, y) such that AZ + By =GCD(A,B) with the same time complexity. A scheme to cascade a number of such GCD chips to compute very large GCD’s is also at hand, which alleviates a critical difficulty in such fields as cryptography.","PeriodicalId":314618,"journal":{"name":"Symposium on Symbolic and Algebraic Manipulation","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134576225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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