A Crop Planning Problem with Fuzzy Random Profit Coefficients

The main purpose of this paper is to present a crop planning problem for agricultural management under uncertainty. It is significant that agricultural managers assign their limited farmlands to cultivation of which crops in a season. This planning is called the crop planning problem and influences their incomes for the season. Usually, the crop planning problem is formulated as a linear programming problem. But there are many uncertain factors in agricultural problems, so future profits for crops are not certain values. A linear programming model with constant profit coefficients may not reflect the environment of decision making properly. Therefore, we propose a model of crop planning with fuzzy profit coefficients, and an effective solution procedure for the model. Furthermore, we extend this fuzzy model, setting the profit coefficients as discrete randomized fuzzy numbers. We show concrete optimal solutions for each models.     

André-Quillen cohomology and rational homotopy of function spaces

We develop a simple theory of André-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework.     

Shannon sampling II: Connections to learning theory

We continue our study [S. Smale, D.X. Zhou, Shannon sampling and function reconstruction from point values, Bull. Amer. Math. Soc. 41 (2004) 279–305] of Shannon sampling and function reconstruction. In this paper, the error analysis is improved. Then we show how our approach can be applied to learning theory: a functional analysis framework is presented; dimension independent probability estimates are given not only for the error in the L² spaces, but also for the error in the reproducing kernel Hilbert space where the learning algorithm is performed. Covering number arguments are replaced by estimates of integral operators.     

用偏倚缩减法检测壁湍流相干结构的时空尺度

提出了用偏倚缩减法计算壁湍流信号自相关函数,提高了自相关函数的计算精度。用壁湍流脉动速度的时间序列的自相关函数达到第二峰值对应的延迟时间检测壁湍流相干结构的平均周期。用槽道流直接数值模拟近壁区脉动速度自相关函数达到第二个峰值对应延迟长度检测壁湍流相干结构的空间平均尺度。     

模糊一次方程求解的实际研究

传统的加法,减法,乘法和除法运算都属于自然运算,因此不能用于区间数（interval）的分析中,故需要进一步研究区间数的特殊的运算规律。本文介绍模糊集合理论中的区间数进行加、减、乘、除等特殊的算术运算规律为基础,主要介绍并提出模糊一次方程bx＋a=c的求解过程及方法,并给出其模糊方程的解。     

Embedding with a Lipschitz function

We investigate a new notion of embedding of subsets of {?1,1}ⁿ in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {?1, 1}ⁿ, the vast majority of such sets do not embed in a better way than the entire cube in any normed space that satisfies a minor structural assumption. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Extensions of algorithmic senstivity calculations nonlinear programming using barrier and penalty functions

We provide a theoretical basis for approximating the sensitivity of a perturbed solution and the local optimalvalue function, using information generated by a sequential unconstrained minimization technique in the normal course of solving a mathematical program. We show that various algorithmic sensitivity results can be obtained without other assumptions than those needed for the corresponding nonalgorithmic results. Our results extend the algorithmic calculation of sensitivity information introduced by Fiacco, utilizing the logarithmic barrier function and quadratic penalty function     

Fourier Method for Riemann-Hilbert-Poincaré Problem of Analytic Function

Spectrum problem with Riemann-Hilbert-Poincaré boundary condition is studied. This problem will lead to inhomogeneous Fuchsian differential equations with its right hand side depending on some constants to be determined simultaneously. We find out that the multiplicities of eigenfunctions for different eigenvalues are not necessary the same, which are in sharp contrast to the known results of Riemann-Hilbert problem for analytic functions.     

Similar Transposed Sets of Polynomials

This paper studies the effectiveness of another kind of transposed sets of polynomials of one complex variable in closed regions, open discs, at the origin and for all entire functions. In addition, an upper bound for the order of these sets in this case is obtained.     

Unbounded Components in the Solution Sets of Strictly Quasiconcave Vector Maximization Problems

Let (P) denote the vector maximization problem