In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under...In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.展开更多
From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of t...From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a 'by-product' in the computation of the conjugate gradient if a computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on AT A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.展开更多
A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided proje...A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.展开更多
In order to avoid unnecessary failure in crystal growth experiments aboard spacecraft, an implicit alternating directions iterative (ADI) method was suggested to simulate the Marangoni convection (due to surface tensi...In order to avoid unnecessary failure in crystal growth experiments aboard spacecraft, an implicit alternating directions iterative (ADI) method was suggested to simulate the Marangoni convection (due to surface tension) with emphasis on investigating application of the technique numerically. Numerical experiments turned out both accurate in mathematics and reasonable in physics. It is easier to treat the boundary conditions for intermediate variables by using this method, furthermore, the requirements in choosing (boundary) relaxation factor are not so severe for medium Reynolds numbers. Hence, ADI scheme is expected to be extended to the study of other convection processes related to material manufacturing.展开更多
In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform Holder condition, and obtain the uniform packing dimension of mu...In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform Holder condition, and obtain the uniform packing dimension of multiparameter stable processes. If Z is a stable （N, d, α）-process and αN ≤ d, then the following holds with probability 1 Dim Z（E）=α Dim E for any Borel setE ∈B（R ＋^N）, where Z（E）={x：E←t∈E,Z（t）=x}, Dim （E） denotes the packing dimension of E.展开更多
This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimi...This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimization, area minimization, placement problem, routing problem, etc. are especially discussed with new results and theoretical ideas for treating them. Finally, a number of problems for further research are mentioned.展开更多
Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, dual polarization interferometry, etc. are indeed very powerful tools to determine the 3-Dimensional structure of a protein (including...Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, dual polarization interferometry, etc. are indeed very powerful tools to determine the 3-Dimensional structure of a protein (including the membrane protein);theoretical mathematical and physical computational approaches can also allow us to obtain a description of the protein 3D structure at a submicroscopic level for some unstable, noncrystalline and insoluble proteins. X-ray crystallography finds the X-ray final structure of a protein, which usually need refinements using theoretical protocols in order to produce a better structure. This means theoretical methods are also important in determinations of protein structures. Optimization is always needed in the computer-aided drug design, structure-based drug design, molecular dynamics, and quantum and molecular mechanics. This paper introduces some optimization algorithms used in these research fields and presents a new theoretical computational method—an improved LBFGS Quasi-Newtonian mathematical optimization method—to produce 3D structures of prion AGAAAAGA amyloid fibrils (which are unstable, noncrystalline and insoluble), from the potential energy minimization point of view. Because the NMR or X-ray structure of the hydrophobic region AGAAAAGA of prion proteins has not yet been determined, the model constructed by this paper can be used as a reference for experimental studies on this region, and may be useful in furthering the goals of medicinal chemistry in this field.展开更多
This paper provides a functional equation satisfied by the dichromatic sum function of rooted outer-planar maps. By the equation, the dichromatic sum function can be found explicitly.
In this paper, some new oscillation criteria for a second order nonlinear differential equation with dampings are established. These criteria improve and generalize the related results given in [1-4].
The infinite-dimensional algebras on two-dimensional torus are developed.In particular the diffeomorphism algebra and the Beltrami algebra on torus with their central extensions have been presented.It is shown that th...The infinite-dimensional algebras on two-dimensional torus are developed.In particular the diffeomorphism algebra and the Beltrami algebra on torus with their central extensions have been presented.It is shown that these algebras are corresponding to the diffeomorphism and the quasiconformal transformation of torus,respectively.展开更多
The two-stage tandem queueing system M(z)/M/c→/PH(r)/1/K is studied in this paper. Customers arrive at stage-Ⅰ system in batches according to a Poisson process, and the size of the batch, x , is a r. v. within a ran...The two-stage tandem queueing system M(z)/M/c→/PH(r)/1/K is studied in this paper. Customers arrive at stage-Ⅰ system in batches according to a Poisson process, and the size of the batch, x , is a r. v. within a range of a finite number of positive integers. The stage- Ⅱ ststem has finite capacity, where customers are served in batches with a PH-distribution and the size of the batch is a positive integer r. Only after served in stage- Ⅰ system, and then served in stage- Ⅱ system, can the customers depart from the whole system. Several definitions such as the stage- Ⅰ service blocked time, the first-class and the second-class batch waiting times, and the batch sojourn time are introduced, and their distributions are obtained respectively.展开更多
In this paper, the authors give some applications of F-uniformly distributedsequences, which are suggested in their previous paper under the same title, in experimen-tal design, experiments with mixtures, geometric pr...In this paper, the authors give some applications of F-uniformly distributedsequences, which are suggested in their previous paper under the same title, in experimen-tal design, experiments with mixtures, geometric probability and simulation.展开更多
This paper gives some applications of number-theoretic method(or quasi Monte Carlomethod)for numerical evaluation of probabilities and moments of a continuous multivariatedistribution over a special domain such as cub...This paper gives some applications of number-theoretic method(or quasi Monte Carlomethod)for numerical evaluation of probabilities and moments of a continuous multivariatedistribution over a special domain such as cube, ball, sphere, simplex, etc., where theuniformly distributed sets of points’in such domains,which are useful in experimentaldesign,simulation,geometry probability,etc.,are suggested.Some applications of number-theoretic method in optimization are discussed also.展开更多
In this paper,we present a family of gradient projection method with arbitrary initialpoint.The formula of search direction in the method is unitary.The convergent conditions ofthe method are given.When the initial po...In this paper,we present a family of gradient projection method with arbitrary initialpoint.The formula of search direction in the method is unitary.The convergent conditions ofthe method are given.When the initial point is feasible,the family of the method contains severalknown algorithms.When the initial point is infeasible,the method is exactly that given in[6].Finally,we give a new method which has global convergence property.展开更多
Consider an AMG for the linear system Au=f. Up to now, only the uniform convergence of two-level AMG is proved for symmetric and positive definite L-matrices with weak diagonal dominance. Using the new form (1), we ex...Consider an AMG for the linear system Au=f. Up to now, only the uniform convergence of two-level AMG is proved for symmetric and positive definite L-matrices with weak diagonal dominance. Using the new form (1), we extend the results in [1] to the case that A is a general symmetric and positive definite matrix with weak diagonal dominance. In the following, we shall use the same notations as in [1].展开更多
The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are a...The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are also discussed.展开更多
Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal wit...Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal with the ess. inf case, the transplantation of results to the ess. sup case being trivial.展开更多
I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are pr...I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are proposed, referring to Anderson, for example.展开更多
If X has the exponential distribution, we write X～E(λ), where λ>0 is a parameter. Due to its importance in statistics, various multivariate extensions of the exponential distribution have been given. In this let...If X has the exponential distribution, we write X～E(λ), where λ>0 is a parameter. Due to its importance in statistics, various multivariate extensions of the exponential distribution have been given. In this letter, a new multivariate extension of E (λ) is suggested and its related properties are investigated thoroughly.展开更多
基金This work is supported by the National Natural Science Foundation of China
文摘In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.
文摘From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determined by the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a 'by-product' in the computation of the conjugate gradient if a computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on AT A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.
文摘A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.
基金The project supported by the National Natural Science Foundation of China
文摘In order to avoid unnecessary failure in crystal growth experiments aboard spacecraft, an implicit alternating directions iterative (ADI) method was suggested to simulate the Marangoni convection (due to surface tension) with emphasis on investigating application of the technique numerically. Numerical experiments turned out both accurate in mathematics and reasonable in physics. It is easier to treat the boundary conditions for intermediate variables by using this method, furthermore, the requirements in choosing (boundary) relaxation factor are not so severe for medium Reynolds numbers. Hence, ADI scheme is expected to be extended to the study of other convection processes related to material manufacturing.
基金Supported by the National Natural Science Foundation of China.
文摘In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform Holder condition, and obtain the uniform packing dimension of multiparameter stable processes. If Z is a stable （N, d, α）-process and αN ≤ d, then the following holds with probability 1 Dim Z（E）=α Dim E for any Borel setE ∈B（R ＋^N）, where Z（E）={x：E←t∈E,Z（t）=x}, Dim （E） denotes the packing dimension of E.
文摘This paper is basically a survey to show a number of combinatorial optimization problems arising from VLSI circuit design. Some of them including the existence problem, minimax problem, net representation, bend minimization, area minimization, placement problem, routing problem, etc. are especially discussed with new results and theoretical ideas for treating them. Finally, a number of problems for further research are mentioned.
文摘Experimental X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, dual polarization interferometry, etc. are indeed very powerful tools to determine the 3-Dimensional structure of a protein (including the membrane protein);theoretical mathematical and physical computational approaches can also allow us to obtain a description of the protein 3D structure at a submicroscopic level for some unstable, noncrystalline and insoluble proteins. X-ray crystallography finds the X-ray final structure of a protein, which usually need refinements using theoretical protocols in order to produce a better structure. This means theoretical methods are also important in determinations of protein structures. Optimization is always needed in the computer-aided drug design, structure-based drug design, molecular dynamics, and quantum and molecular mechanics. This paper introduces some optimization algorithms used in these research fields and presents a new theoretical computational method—an improved LBFGS Quasi-Newtonian mathematical optimization method—to produce 3D structures of prion AGAAAAGA amyloid fibrils (which are unstable, noncrystalline and insoluble), from the potential energy minimization point of view. Because the NMR or X-ray structure of the hydrophobic region AGAAAAGA of prion proteins has not yet been determined, the model constructed by this paper can be used as a reference for experimental studies on this region, and may be useful in furthering the goals of medicinal chemistry in this field.
基金Supported by the National Natural Science Foundation of China
文摘This paper provides a functional equation satisfied by the dichromatic sum function of rooted outer-planar maps. By the equation, the dichromatic sum function can be found explicitly.
基金The Project supported by the Science Foundation of Yunnan State Education Commission
文摘In this paper, some new oscillation criteria for a second order nonlinear differential equation with dampings are established. These criteria improve and generalize the related results given in [1-4].
基金Contribution to the Beijing Workshop on String Theories,July 6-Sept.51987,Beijing,China.
文摘The infinite-dimensional algebras on two-dimensional torus are developed.In particular the diffeomorphism algebra and the Beltrami algebra on torus with their central extensions have been presented.It is shown that these algebras are corresponding to the diffeomorphism and the quasiconformal transformation of torus,respectively.
基金This paper is supported by the National Natural Science Foundation of China
文摘The two-stage tandem queueing system M(z)/M/c→/PH(r)/1/K is studied in this paper. Customers arrive at stage-Ⅰ system in batches according to a Poisson process, and the size of the batch, x , is a r. v. within a range of a finite number of positive integers. The stage- Ⅱ ststem has finite capacity, where customers are served in batches with a PH-distribution and the size of the batch is a positive integer r. Only after served in stage- Ⅰ system, and then served in stage- Ⅱ system, can the customers depart from the whole system. Several definitions such as the stage- Ⅰ service blocked time, the first-class and the second-class batch waiting times, and the batch sojourn time are introduced, and their distributions are obtained respectively.
基金This work was supported by The Chinesse National Science Fund and Academia Sinics.
文摘In this paper, the authors give some applications of F-uniformly distributedsequences, which are suggested in their previous paper under the same title, in experimen-tal design, experiments with mixtures, geometric probability and simulation.
基金This Work is supported by the Chinese National science Foundation and the Science Foundation of the Chinese Academy of Sciences.
文摘This paper gives some applications of number-theoretic method(or quasi Monte Carlomethod)for numerical evaluation of probabilities and moments of a continuous multivariatedistribution over a special domain such as cube, ball, sphere, simplex, etc., where theuniformly distributed sets of points’in such domains,which are useful in experimentaldesign,simulation,geometry probability,etc.,are suggested.Some applications of number-theoretic method in optimization are discussed also.
基金Project supported by the National Natural Science Foundation of China
文摘In this paper,we present a family of gradient projection method with arbitrary initialpoint.The formula of search direction in the method is unitary.The convergent conditions ofthe method are given.When the initial point is feasible,the family of the method contains severalknown algorithms.When the initial point is infeasible,the method is exactly that given in[6].Finally,we give a new method which has global convergence property.
基金Project supported by the National Natural Science Foundation of China.
文摘Consider an AMG for the linear system Au=f. Up to now, only the uniform convergence of two-level AMG is proved for symmetric and positive definite L-matrices with weak diagonal dominance. Using the new form (1), we extend the results in [1] to the case that A is a general symmetric and positive definite matrix with weak diagonal dominance. In the following, we shall use the same notations as in [1].
基金This project is supported partially by the National Natural Science Foundation of China Grant 18971061
文摘The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are also discussed.
文摘Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal with the ess. inf case, the transplantation of results to the ess. sup case being trivial.
基金Project supported by the National Natural Science Foundation of China.
文摘I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are proposed, referring to Anderson, for example.
文摘If X has the exponential distribution, we write X～E(λ), where λ>0 is a parameter. Due to its importance in statistics, various multivariate extensions of the exponential distribution have been given. In this letter, a new multivariate extension of E (λ) is suggested and its related properties are investigated thoroughly.
