The Property of Bair in r-Space

ＴｈｅＰｒｏｐｅｒｔｙｏｆＢａｉｒｉｎｒ－ＳｐａｃｅＳｏｎｇＺｈｅｎｍｉｎｇ（宋振明）（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：ＩｎｔｈｉｓＰａｐｅｒ，ｗｅＳｔｕｄｙｐｒｏｐｅｒｔｉｅｓｏｆＢａｉｒｂｙｓｙｍｍｅｔｒｉｃｄｉｆｆｅｒｅｎｃｅ...     

M-N Fuzzy Number Space and properties

Ｍ－ＮＦｕｚｚｙＮｕｍｂｅｒＳｐａｃｅａｎｄＰｒｏｐｅｒｔｉｅｓＭ－ＮＦｕｚｚｙＮｕｍｂｅｒＳｐａｃｅａｎｄＰｒｏｐｅｒｔｉｅｓ￥／／ＸｕＸｉａｏＧｕａｎｇ；ＬｕＦｅｎｇ（ＢａｓｉｃＢｒａｎｃｈ，ＣｈａｎｇｃｈｕｎＴａｘ（ＤｅｐａｒｔｍｅｎｔｏｆＭａ...     

On the Solvability of x∈Ax＋λBx in a General Cone with A and B Multivalued k－set－contractive

ＯｎｔｈｅＳｏｌｖａｂｉｌｉｔｙｏｆｘ∈Ａｘ＋λＢｘｉｎａＧｅｎｅｒａｌＣｏｎｅ　ｗｉｔｈＡａｎｄＢＭｕｌｔｉｖａｌｕｅｄ　ｋ－ｓｅｔ－ｃｏｎｔｒａｃｔｉｖｅＺｈａｎｇＱｉｎｇｙｏｎｇ（张庆雍）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｉｃ...     

WELL-BEHAVED BASIS AND LR ARRAYS

ＷＥＬＬ－ＢＥＨＡＶＥＤＢＡＳＩＳＡＮＤＬＲＡＲＲＡＹＳＬＩＮＤＯＮＧＤＡＩ（林东岱）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

A New Characterization of the Analytic Radon-Nikodym Property for Bounded S

ＡＮｅｗＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆｔｈｅＡｎａｌｙｔｉｃＲａｄｏｎ－ＮｉｋｏｄｙｍＰｒｏｐｅｒｔｙｆｏｒＢｏｕｎｄｅｄＳｕｂｓｅｔｓＢｕＳｈａｎｇｑｕａｎ（步尚全）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇｈ...     

S~1 × S~1-Borsuk-Ulam Theorem on Product Spaces

Ｓ~１×Ｓ~１－Ｂｏｒｓｕｋ－ＵｌａｍＴｈｅｏｒｅｍｏｎＰｒｏｄｕｃｔＳｐａｃｅｓＺｈｏｎｇＣｈｅｎｇｋｕｉ（钟承奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ，７３００００）Ａｂｓｔｒａｃｔ：...     

Bernstein-Bezier Surface Patches on Arbitrary Spatial Triangulation

Ｂｅｒｎｓｔｅｉｎ－ＢéｚｉｅｒＳｕｒｆａｃｅＰａｔｃｈｅｓｏｎＡｒｂｉｔｒａｒｙＳｐａｔｉａｌＴｒｉａｎｇｕｌａｔｉｏｎＺｈｏｕＹｕｎｓｈｉ（周蕴时）；ＺｈａｎｇＸｕｅｍｅｉ（张雪梅）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，Ｕｎｉｖｅｒｓｉ...     

Non-singularSaffman-taylorFinger1

Ｎｏｎ－ｓｉｎｇｕｌａｒＳａｆｆｍａｎ－ｔａｙｌｏｒＦｉｎｇｅｒ１ＫａｉＨｕａＺＨＡＯＨｕｉｄａｎＹＵ（Ｄｅｐａｒｔｍｅｎｔｏｆｐｈｙｓｉｃｓ，ＣｅｎｔｅｒｆｏｒＮｏｎｌｉｎｅａｒＳｃｉｅｎｃｅ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００...     

Phase-lockinginaConnectedSystemofNonlinearlyCoupledOscillators

Ｐｈａｓｅ－ｌｏｃｋｉｎｇｉｎａＣｏｎｎｅｃｔｅｄＳｙｓｔｅｍｏｆＮｏｎｌｉｎｅａｒｌｙＣｏｕｐｌｅｄＯｓｃｉｌｌａｔｏｒｓＭｉｎＱＩＡＮ，ＳｈｕＺＨＵ￣２（ＳｃｈｏｏｌｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓ，ＰｅｋｉｎｇＵｎｉｖ．，Ｂｅｋｊｉ...     

A J-CONVEX SUBSET WHICH IS NOT PSH-CONVEX

ＡＪ－ＣＯＮＶＥＸＳＵＢＳＥＴＷＨＩＣＨＩＳＮＯＴＰＳＨ－ＣＯＮＶＥＸＢｕＳｈａｎｇｑｕａｎ（步尚全）（Ｄｅｐａｒｔｍｅｎｔｏｆａｐｐｌｉｅｄｍａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１０００８４，Ｃｈｉｎａ）Ａｂｓ...     

Dual simplex method for GUB problems

The dual simplex method for generalized upper bound (GUB) problems is presented. One of the major operations in the dual simplex method is to update the elements of therth row, wherer is the index for the leaving basic variable. Those updated elements are used for the ratio test to determine the entering basic variabble. A very simple formula for therth row update for the dual simplex method for a GUB problem is derived, which is similar to the formula for the standard linear program. This derivation is based on the change key operation, which is to exchange the key column and its counterpart in the nonkey section. The change key operation is possible because of a theorem that guarantees the existence of such a counterpart.     

Matrix correction of a dual pair of improper linear programming problems

A matrix is sought that solves a given dual pair of systems of linear algebraic equations. Necessary and sufficient conditions for the existence of solutions to this problem are obtained, and the form of the solutions is found. The form of the solution with the minimal Euclidean norm is indicated. Conditions for this solution to be a rank one matrix are examined. On the basis of these results, an analysis is performed for the following two problems: modifying the coefficient matrix for a dual pair of linear programs (which can be improper) to ensure the existence of given solutions for these programs, and modifying the coefficient matrix for a dual pair of improper linear programs to minimize its Euclidean norm. Necessary and sufficient conditions for the solvability of the first problem are given, and the form of its solutions is described. For the second problem, a method for the reduction to a nonlinear constrained minimization problem is indicated, necessary conditions for the existence of solutions are found, and the form of solutions is described. Numerical results are presented.     

Analysis of ordered categorical data from repeated measurements assuming a quantitative latent variable

Summary The purpose of the present paper is to propose an analytical method for ordered categorical responses obtained from a repeated measurement/longitudinal experiment. The ordered categorical scale is assumed to be a manifestation of a latent quantitative variable. A linear model is assumed for location parameters of the underlying distributions. Weighted least square method is applied to parameter estimation and subsequent analysis. Two data sets are analyzed to show several aspects of analysis by the proposed model and to discuss comparative characteristics of analysis compared with earlier analysis. A mention is made for a computer software program for the proposed model.     

A NEW STEPSIZE FOR THE STEEPEST DESCENT METHOD

The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.     

Half Space and Quarter Space Dirichlet Problems for the Partial Differential Equation

A customary, heuristic, method, by which the Poisson integral formula for the Dirichlet problem, for the half space, for Laplace's equation is obtained, involves Green's function, and Kelvin's method of images. Although this heuristic method leads one to guess the correct result, this Poisson formula still has to be verified directly, independently of the method by which it was arrived at, in order to be absolutely certain that a solution of the Dirichlet problem for the half space, for Laplace's equation, has been actually obtained. A similar heuristic method, as seems to be generally known, could be followed in solving the Dirichlet problem, for the half space, for the equation where is a real constant. However, in Part 1, a different, labor-saving, method is used to study Dirichlet problems for the equation. This method is essentially based on what Hadamard called the method of descent. Indeed, it is shown that he who has solved the half space Dirichlet problem for Laplace's equation has already solved the half space Dirichlet problem for the equation In Part 2, the solution formula for the quarter space Dirichlet problem for Laplace's equation is obtained from the Poisson integral formula for the half space Dirichlet problem for Laplace's equation. A representation theorem for harmonic functions in the quarter space is deduced. The method of descent is used, in Part 3, to obtain the solution formula for the quarter space Dirichlet problem for the equation by means of the solution formula for the quarter space Dirichlet problem for Laplace's equation. So that, indeed, it is also shown that he who has solved the quarter space Dirichlet problem for Laplace's equation has already solved the quarter space Dirichlet problem for the " equation" For the sake of completeness and clarity, and for the convenience of the reader, the appendix, at the end of Part 3, contains a detailed proof that the Poisson integral formula solves the half space Dirichlet problem for Laplace's equation. The Bibliography for Parts 1,2, 3 is to be found at the end of Part 1.     

Analysis of a mathematical model for tumor growth under indirect effect of inhibitors with time delay in proliferation

In this paper, a mathematical model for tumor growth with time delay in proliferation under indirect effect of inhibitor is studied. The delay represents the time taken for cells to undergo mitosis. Nonnegativity of solutions is investigated. The steady-state analysis is presented with respect to the magnitude of the delay. Existence of Hopf bifurcation is proved for some parameter values. Local and global stability of the stationary solutions are proved for other ones. The analysis of the effect of inhibitor's parameters on tumor's growth is presented. The results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding non-retarded problems for some parameter values.     

文物腐蚀程度分级规范的理论模型

一方面,需要全面了解馆藏文物腐蚀现状,科学分析和评估造成馆藏文物腐蚀损失的原因,为馆藏文物长期保护提供科学依据和对策;另一方面,文物的腐蚀又是具有多样性、复杂性及不间断性的,每一腐蚀程度之间的界限并非十分清晰,而是连续模糊的,这为全面了解馆藏文物腐蚀现状带来了很大困难.因此,建立科学的模型对文物遭受腐蚀侵害的真实情况做出准确的描述迫在眉睫,利用模糊综合评判及其逆问题给出了科学严谨的具体模型.     

Empirical likelihood for semiparametric regression model with missing response data

A bias-corrected technique for constructing the empirical likelihood ratio is used to study a semiparametric regression model with missing response data. We are interested in inference for the regression coefficients, the baseline function and the response mean. A class of empirical likelihood ratio functions for the parameters of interest is defined so that undersmoothing for estimating the baseline function is avoided. The existing data-driven algorithm is also valid for selecting an optimal bandwidth. Our approach is to directly calibrate the empirical log-likelihood ratio so that the resulting ratio is asymptotically chi-squared. Also, a class of estimators for the parameters of interest is constructed, their asymptotic distributions are obtained, and consistent estimators of asymptotic bias and variance are provided. Our results can be used to construct confidence intervals and bands for the parameters of interest. A simulation study is undertaken to compare the empirical likelihood with the normal approximation-based method in terms of coverage accuracies and average lengths of confidence intervals. An example for an AIDS clinical trial data set is used for illustrating our methods.     

Testing for increasing convex order in several populations

Increasing convex order is one of important stochastic orderings. It is very often used in queueing theory, reliability, operations research and economics. This paper is devoted to studying the likelihood ratio test for increasing convex order in several populations against an unrestricted alternative. We derive the null asympotic distribution of the likelihood ratio test statistic, which is precisely the chi-bar-squared distribution. The methodology for computing critical values for the test is also discussed. The test is applied to an example involving data for survival time for carcinoma of the oropharynx.     

A necessary and sufficient condition for Pareto-optimal security strategies in multicriteria matrix games

In this paper, a scalar game is derived from a zero-sum multicriteria matrix game, and it is proved that the solution of the new game with strictly positive scalarization is a necessary and sufficient condition for a strategy to be a Pareto-optimal security strategy (POSS) for one of the players in the original game. This is done by proving that a certain set, which is the extension of the set of security level vectors in the criterion function space, is convex and polyhedral. It is also established that only a finite number of scalarizations are necessary to obtain all the POSS for a player. An example is included to illustrate the main steps in the proof.This work was done while the author was a Research Associate in the Department of Electrical Engineering at the Indian Institute of Science and was financially supported by the Council of Scientific and Industrial Research, Delhi, India.The author wishes to express his gratefulness to Professor U. R. Prasad for helpful discussions and to two anonymous referees for suggestions which led to an improved presentation.