(n-1,1)-型分数阶共轭边值问题的正解

本文研究了(n?1,1)–型分数阶共轭边值问题正解的存在性与多解性问题。利用Krasnoselskii–Zabreiko不动点定理,结合与Green函数相关的不等式,获得了几个存在性结果,推广了一些现有的结果。     

A deteriorating multi-item inventory model with fuzzy costs and resources based on two different defuzzification techniques

Normally inventory models of deteriorating items, such as food products, vegetables, etc. involve imprecise parameters, like imprecise inventory costs, fuzzy storage area, fuzzy budget allocation, etc. In this paper, we aim to provide two defuzzification techniques for two fuzzy inventory models using (i) extension principle and duality theory of non-linear programming and (ii) interval arithmetic. On the basis of Zadeh’s extension principle, two non-linear programs parameterized by the possibility level α are formulated to calculate the lower and upper bounds of the minimum average cost at α-level, through which the membership function of the objective function is constructed. In interval arithmetic technique the interval objective function has been transformed into an equivalent deterministic multi-objective problem defined by the left and right limits of the interval. This formulation corresponds to the possibility level, α = 0.5. Finally, the multi-objective problem is solved by a multi-objective genetic algorithm (MOGA). The model has been illustrated through a numerical example and solved for different values of possibility level, α through extension principle and for α = 0.5 via MOGA. As a particular case, the results have been obtained for the inventory model without deterioration. Results from two methods for α = 0.5 are compared.     

Limiting Absorption Principle for Stratified Operators with Thresholds: A General Method

Out problem is about propagation of waves in stratified strips. The operators are quite general, a typical example being a coupled elasto-acoustic operator H defined in ?² × I where I is a bounded interval of ? with coefficients depending only on z ∈ I. The “conjugate operator method” will be applied to an operator obtained by a spectral decomposition of the partial Fourier transform ? of H. Around each value of the spectrum (except the eigenvalues) including the thresholds, a conjugate operator is constructed which permits to get the ”good properties“ of regularity for H. A limiting absorption principle is then obtained for a large class of operators at every point of the spectrum (except eigenvalues).     

A Nonlinear Version of Noether's Type Theorem

Abstract

Let L be a line bundle on a smooth curve C, which defines a birational morphism onto Φ(C) ? P ^r . We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H ⁰(C, L ²) can be written as α² + β² + γ², with α, β, γ ∈ H ⁰(C, L). If there are no quadrics of rank 3 containing Φ(C), this is true for any section. For canonical curves, this gives a non linear version of Noether's Theorem.     

Compact supported endographs and fuzzy sets

A metric is defined on a space of functions from a locally compact metric space X into the unit interval I in terms of the Hausdorff metric distance between their compact supported endographs in X × I. Convergence in this metric is shown to be equivalent to the conjunction of the Hausdorff metric convergence of supports in X and two conditions involving numerical values of the functions. The space of nonempty compact subsets of X with the Hausdorff metric is imbedded in the above function space by the characteristic function on subsets of X. Applications of these results to fuzzy subsets of X and fuzzy dynamical systems on X are indicated.     

On Φ-Derivation in Banach Algebras

Using Bre?ar and ?emrl approach, we give a proof of the extended Jacobson density theorem for Φ-derivations. Further, some applications on Banach algebras will be given. Precisely, for d being a continuous Φ-derivation on a given Banach algebra ?, we show that: d(?) ? rad (?) ? [b,[a, d(a)]] ∈ rad (?) for all a, b ∈ ? and d leaves invariant all maximal ideals of codimension one?for every a ∈ ? there exists a positive integer n such that (d(a)) ⁿ is quasi-nilpotent ? [d, Φ](?) ? rad (?) and d ²(a) ∈ rad (?) for all a ∈ ?. Finally, we characterize all pairs d, δ of continuous Φ-derivations such that dδ(a) is quasi-nilpotent for all a ∈ ? and [d, δ](?), [d, Φ](?), [δ,Φ](?) are subsets of rad (?).     

The analysis of structured qualitative data

The aim of this paper is to give an overview of the methodological contribution given by Italian researchers in introducing a priori information into multidimensional data analysis techniques, paying special attention to categorical variables. The basic method is Non‐Symmetrical Correspondence Analysis, which enables the analysis of a contingency table when the behaviour of one variable is supposed to be dependent on the other cross‐classified variable. As usual correspondence analysis decomposes an association index (Pearson's Φ²), in a principal component sense, the proposed method is based on a decomposition of a predictability index (Goodman and Kruskal's τ_b). Non‐symmetrical correspondence analysis has been extended to more than one dependent/explanatory variable(s), by means of proper flattening procedures, i.e. by the use of multiple tables, and the decomposition of Gray and Williams' multiple and partial τ_b's. In doing so multiple and partial versions have been proposed. A forward selection procedure for choosing the variables with higher predictive power is presented. After a brief review of non‐symmetrical correspondence analysis confirmatory approach, the problem of validating results in terms of analytical stability and replication stability is faced by means of influence functions and resampling techniques. Copyright © 1999 John Wiley & Sons, Ltd.     

基于Choquet积分的直觉模糊联盟合作博弈的Shapley值

本文针对联盟是直觉模糊集的合作博弈Shapley值进行了研究.通过区间Choquet积分得到直觉模糊联盟合作博弈的特征函数为区间数,并研究了该博弈特征函数性质。根据拓展模糊联盟合作博弈Shapley值的计算方法,得到直觉模糊联盟合作博弈Shapley值的计算公式,该计算公式避免了区间数的减法。进一步证明了其满足经典合作博弈Shapley值的公理性。最后通过数值实例说明本文方法的合理性和有效性。     

An asymptotic decomposition for multivariate distribution-free tests of independence

In the multivariate case, the empirical dependence function, defined as the empirical distribution function with reduced uniform margins on the unit interval, can be shown for an i.i.d. sequence to converge weakly in an asymptotic way to a limiting Gaussian process. The main result of this paper is that this limiting process can be canonically separated into a finite set of independent Gaussian processes, enabling one to test the existence of dependence relationships within each subset of coordinates independently (in an asymptotic way) of what occurs in the other subsets. As an application we derive the Karhunen-Loeve expansions of the corresponding processes and give the limiting distribution of the multivariate Cramer-Von Mises test of independence, generalizing results of Blum, Kiefer, Rosenblatt, and Dugué. Other extensions are mentioned, including a generalization of Kendall's τ.     

On the powers of 3/2 and other rational numbers

Letp > q > 1 be two coprime integers. In this paper, we prove several results about subsets of the interval [0, 1) which does or does not contain all the fractional parts {ξ (p /q)ⁿ }, n = 0, 1, 2, …, for certain non‐zero real number ξ. We show, for instance, that there are no real ξ for which the union of two intervals [8/39, 18/39] ∪ [21/39, 31/39] contains the set {ξ (3/2)ⁿ }, n ∈ N . The most important aspect of this result is that the total length of both intervals 20/39 is greater than 1/2: the same result as above for [0, 1/2) would imply that there are no Mahler's Z ‐numbers which the best known unsolved problem in this area. On the other hand, it is shown that there are infinitely many ξ for which {ξ (3/2)ⁿ } ∈ (5/48, 43/48) for each integer n ≥ 0. We also give simpler proofs of few recent results in this area. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time-cost trade-off analysis of project networks in fuzzy environments

This paper proposes a novel approach for time-cost trade-off analysis of a project network in fuzzy environments. Different from the results of previous studies, in this paper the membership function of the fuzzy minimum total crash cost is constructed based on Zadeh’s extension principle and fuzzy solutions are provided. A pair of two-level mathematical programs parameterized by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy minimum total crash cost at α. By enumerating different values of α, the membership function of the fuzzy minimum total crash cost is constructed, and the corresponding optimal activity time for each activity is also obtained at the same time. An example of time-cost trade-off problem with several fuzzy parameters is solved successfully to demonstrate the validity of the proposed approach. Since the minimum total crash cost is expressed by a membership function rather than by a crisp value, the fuzziness of parameters is conserved completely, and more information is provided for time-cost trade-off analysis in project management. The proposed approach also can be applied to time-cost trade-off problems with other characteristics.     

Mutual information in Gaussian channels

In the Gaussian channel Y(t) = Φ(t) + X(t) = message + noise, where Φ(t) and X(t) are mutually independent, the information I(Y, Φ) is evaluated. One of the results is that I(Y, Φ) < ∞ if and only if Φ ? $\text{H}$(X) = the reproducing kernel Hilbert space for X(·). And the causal formula of I(Y, Φ) is given.     

基于GMRES(m)法的双连通区域数值保角变换的计算法

本文研究了基于模拟电荷法的双连通区域的数值保角变换问题.利用限制Krylov子空间最大维数的算法–GMRES(m)算法,求解基于模拟电荷法的双连通区域数值保角变换中的约束方程,获得了模拟电荷和变换半径,构造了近似保角变换函数.数值实验表明了本文算法的有效性.     

Maps preserving product X*Y + YX* on factor von Neumann algebras

Let 𝒜 and ? be two factor von Neumann algebras. In this article, we prove that a nonlinear bijective map Φ?:?𝒜?→?? satisfies Φ(X*?Y?+?YX*)?=Φ(X)*Φ(Y)?+?Φ(Y)Φ(X)* (?X,?Y?∈?𝒜), if and only if Φ is a *-ring isomorphism. In particular, if 𝒜 and ? are type I factors, then Φ is a unitary isomorphism or conjugate unitary isomorphism.     

Distinction between several subsets of fuzzy measures

In this paper, we place several fuzzy measure subsets in relation one with the other. The subsets under study are those corresponding to the definitions of probability measure. Sugeno's g_λ-measure, Shafer's belief function and Zadeh's possibility measure. We study the intersection of these subsets and we show the particular role of Dirac's measures in this comparison. We limit ourself to the case of mappins whose domain is the collection of all subsets of a finite set.Finally, the obtained partial results are summarized in only one figure which shoul clarify the specificity of each of the above definitions.     

Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method

This paper proposes a mathematical programming method to construct the membership functions of the fuzzy objective value of the cost-based queueing decision problem with the cost coefficients and the arrival rate being fuzzy numbers. On the basis of Zadeh’s extension principle, three pairs of mixed integer nonlinear programs (MINLP) parameterized by the possibility level α are formulated to calculate the lower and upper bounds of the minimal expected total cost per unit time at α, through which the membership function of the minimal expected total cost per unit time of the fuzzy objective value is constructed. To provide a suitable optimal service rate for designing queueing systems, the Yager’s ranking index method is adopted. Two numerical examples are solved successfully to demonstrate the validity of the proposed method. Since the objective value is completely expressed by a membership function rather than by a crisp value, it conserves the fuzziness of the input information, thus more information is provided for designing queueing systems. The successful extension of queueing decision models to fuzzy environments permits queueing decision models to have wider applications in practice.     

Improved confidence intervals for the scale parameter of Burr XII model based on record values

In this paper some different sorts of confidence intervals are considered for the scale parameter of the Burr type XII distribution based on the upper record values. In this regard, the coverage probability is adopted as a measure of improvement when the endpoints are the same for all types of confidence intervals. Proposed confidence intervals are based on the preliminary test estimator, Thompson shrinkage estimator and Bayes estimator with conjugate prior information. It is nicely demonstrated that the confidence intervals based on the above methodologies are superior to the equal tail confidence interval on specific intervals. Subsequently, to construct a uniformly dominant confidence interval, the result of Kubokawa (Ann Stat 22(1):290–299, 1994) is extended for dependent observations by making use of the information that exists in a covariate record value.     

Interval Non‐edge‐Colorable Bipartite Graphs and Multigraphs

An edge‐coloring of a graph G with colors is called an interval t‐coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In 1991, Erd?s constructed a bipartite graph with 27 vertices and maximum degree 13 that has no interval coloring. Erd?s's counterexample is the smallest (in a sense of maximum degree) known bipartite graph that is not interval colorable. On the other hand, in 1992, Hansen showed that all bipartite graphs with maximum degree at most 3 have an interval coloring. In this article, we give some methods for constructing of interval non‐edge‐colorable bipartite graphs. In particular, by these methods, we construct three bipartite graphs that have no interval coloring, contain 20, 19, 21 vertices and have maximum degree 11, 12, 13, respectively. This partially answers a question that arose in [T.R. Jensen, B. Toft, Graph coloring problems, Wiley Interscience Series in Discrete Mathematics and Optimization, 1995, p. 204]. We also consider similar problems for bipartite multigraphs.     

直觉模糊联盟合作博弈的非线性规划模型

本文研究联盟是直觉模糊集的合作博弈。首先,给出直觉模糊联盟的定义,并根据Choquet积分的直觉模糊形式,得到直觉模糊联盟合作博弈的区间值特征函数,进一步证明直觉模糊联盟合作博弈的区间值特征函数具有超可加性、凸性、弱超可加性. 其次根据区间数的闵可夫斯基距离、区间数的排序及损失函数的定义,建立直觉模糊联盟合作博弈的非线性规划模型,并对其求解得到最优分配. 最后给出一个具体的事例说明本文所建立的模型的合理性和有效性。     

Cluster analysis based on fuzzy equivalence relation

In this paper, a cluster analysis method based on fuzzy equivalence relation is proposed. At first, the distance formula between two trapezoidal fuzzy numbers is used to aggregate subjects' linguistic assessments about attributes ratings to obtain the compatibility relation. Then a fuzzy equivalence relation based on the fuzzy compatibility relation can be constructed. Finally, using a cluster validity index to determine the best number of clusters and taking suitable λ-cut value, the clustering analysis can be effectively implemented. By utilizing this clustering analysis, the subjects' fuzzy assessments with various rating attitudes can be taken into account in the aggregation process to assure more convincing and accurate cluster analysis.