The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, ...The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, mathematics has permeated from natural scientific technology to agricultural construction, from economic activities to all areas of social life. Generally, when the actual problem requires us to provide quantitative results of analysis, forecasting, decision making, control and other aspects for real object under study, we are often inseparable from the application of mathematics. Mathematical modeling is the key to this process, whose purpose is to make mathematics applied to social and social services, and using mathematics to solve practical problems is through mathematical models. When using mathematical methods to solve some practical problems, we usually first transfer practical problems into mathematical language, and then abstract them into a mathematical model.展开更多
The use of questionnaires, rating scales and other kinds of ordered classifications is unlimited and interdisciplinary, so it can take long time before novel statistical methods presented in statistical journals reach...The use of questionnaires, rating scales and other kinds of ordered classifications is unlimited and interdisciplinary, so it can take long time before novel statistical methods presented in statistical journals reach researchers of applied sciences. Therefore. teaching is an effective way of introducing novel methods to researchers at an early stage. Assessments on scales produce ordinal data having rank-invariant properties only, which means that suitable statistical methods are non-parametric and often rank-based. These limited mathematical properties have been taken into account in the research regarding development of statistical methods for paired ordinal data. The aim is to present a statistical method for paired ordinal data that has been successfully implemented to researchers from various disciplines together with statisticians attending interactive problem solving courses of biostatistics.展开更多
This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry fora Birkhoffian system in the event space.The Birkhoffian parametric equations for the system are established,and thedet...This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry fora Birkhoffian system in the event space.The Birkhoffian parametric equations for the system are established,and thedetermining equations of Lie symmetry for the system are obtained.The conditions under which a Lie symmetry ofBirkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojmanconserved quantity are given.An example is given to illustrate the application of the results.展开更多
The problem of computing the greatest common divisor（GCD） of multivariate polynomials, as one of the most important tasks of computer algebra and symbolic computation in more general scope, has been studied extensiv...The problem of computing the greatest common divisor（GCD） of multivariate polynomials, as one of the most important tasks of computer algebra and symbolic computation in more general scope, has been studied extensively since the beginning of the interdisciplinary of mathematics with computer science. For many real applications such as digital image restoration and enhancement,robust control theory of nonlinear systems, L1-norm convex optimization in compressed sensing techniques, as well as algebraic decoding of Reed-Solomon and BCH codes, the concept of sparse GCD plays a core role where only the greatest common divisors with much fewer terms than the original polynomials are of interest due to the nature of problems or data structures. This paper presents two methods via multivariate polynomial interpolation which are based on the variation of Zippel＇s method and Ben-Or/Tiwari algorithm, respectively. To reduce computational complexity, probabilistic techniques and randomization are employed to deal with univariate GCD computation and univariate polynomial interpolation. The authors demonstrate the practical performance of our algorithms on a significant body of examples. The implemented experiment illustrates that our algorithms are efficient for a quite wide range of input.展开更多
It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. ...It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.展开更多
This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions...This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions and, using the methods of quasilinear hyperbolic systems, prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li, T. T., Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Ser. Appl. Math., vol 3,American Institute of Mathematical Sciences and Higher Education Press, 2010] existing in a neighborhood of the equilibrium solution. The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.展开更多
文摘The application level of mathematics in each science discipline signs the level of development of this science. With the advancement of science and technology, especially the rapid development of computer technology, mathematics has permeated from natural scientific technology to agricultural construction, from economic activities to all areas of social life. Generally, when the actual problem requires us to provide quantitative results of analysis, forecasting, decision making, control and other aspects for real object under study, we are often inseparable from the application of mathematics. Mathematical modeling is the key to this process, whose purpose is to make mathematics applied to social and social services, and using mathematics to solve practical problems is through mathematical models. When using mathematical methods to solve some practical problems, we usually first transfer practical problems into mathematical language, and then abstract them into a mathematical model.
文摘The use of questionnaires, rating scales and other kinds of ordered classifications is unlimited and interdisciplinary, so it can take long time before novel statistical methods presented in statistical journals reach researchers of applied sciences. Therefore. teaching is an effective way of introducing novel methods to researchers at an early stage. Assessments on scales produce ordinal data having rank-invariant properties only, which means that suitable statistical methods are non-parametric and often rank-based. These limited mathematical properties have been taken into account in the research regarding development of statistical methods for paired ordinal data. The aim is to present a statistical method for paired ordinal data that has been successfully implemented to researchers from various disciplines together with statisticians attending interactive problem solving courses of biostatistics.
基金Natural Science Foundation of Higher Education Institute of Jiangsu Province of China under Grant No.04KJA130135
文摘This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry fora Birkhoffian system in the event space.The Birkhoffian parametric equations for the system are established,and thedetermining equations of Lie symmetry for the system are obtained.The conditions under which a Lie symmetry ofBirkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojmanconserved quantity are given.An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China under Grant Nos.11471209,11561015,and 11301066Guangxi Key Laboratory of Cryptography and Information Security under Grant No.GCIS201615
文摘The problem of computing the greatest common divisor（GCD） of multivariate polynomials, as one of the most important tasks of computer algebra and symbolic computation in more general scope, has been studied extensively since the beginning of the interdisciplinary of mathematics with computer science. For many real applications such as digital image restoration and enhancement,robust control theory of nonlinear systems, L1-norm convex optimization in compressed sensing techniques, as well as algebraic decoding of Reed-Solomon and BCH codes, the concept of sparse GCD plays a core role where only the greatest common divisors with much fewer terms than the original polynomials are of interest due to the nature of problems or data structures. This paper presents two methods via multivariate polynomial interpolation which are based on the variation of Zippel＇s method and Ben-Or/Tiwari algorithm, respectively. To reduce computational complexity, probabilistic techniques and randomization are employed to deal with univariate GCD computation and univariate polynomial interpolation. The authors demonstrate the practical performance of our algorithms on a significant body of examples. The implemented experiment illustrates that our algorithms are efficient for a quite wide range of input.
基金supported by the National Natural Science Foundation of China under Grant No.71271128the State Key Program of National Natural Science Foundation of China under Grant No.71331006+4 种基金NCMISKey Laboratory of RCSDSCAS and IRTSHUFEPCSIRT(IRT13077)supported by Graduate Innovation Fund of Shanghai University of Finance and Economics under Grant No.CXJJ-2011-429
文摘It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier（K-M） estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly.The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.
基金supported by the National Basic Research Program of China(No.2103CB834100)the National Science Foundation of China(No.11121101)+1 种基金the National Natural Sciences Foundation of China(No.11101273)the DFG-Cluster of Excellence:Engineering of Advanced Materials
文摘This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions and, using the methods of quasilinear hyperbolic systems, prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li, T. T., Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Ser. Appl. Math., vol 3,American Institute of Mathematical Sciences and Higher Education Press, 2010] existing in a neighborhood of the equilibrium solution. The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.
