Some notes on Zadeh’s extensions

This paper shows that the Zadeh’s extensions of sendograph-metric-continuous fuzzy-valued functions are sendograph-metric-continuous fuzzy functions.     

品味童装——看图案设计在童装中的应用

图案是所有设计专业的学生在学校学习时所必修的一门专业基础课。纵观中华五千年的文明,哪一朝哪一代都有自己独特的图案风格。那么,在今天的图案设计特别是儿童服装的图案设计与应用中,怎样为孩子营造一个童话的世界,展现孩子的童真与童趣?一名优秀的童装图案设计师,应该充分利用自然环境,社会环境,民族心理和传统文化结构所赋予的条件,来解决这个问题,从而构思出独特完美而富有表现力的童装图案设计作品。     

A compensation cost analysis of service-aggregate transaction for DTNs clients

Clients from Delay Tolerant Networks (DTNs) might encounter overtime exceptions when they aggregate autonomic commercial web service references to form an all-or-nothing transaction. Such exceptions may cause extra overhead—“compensation cost” when aborting transactions. Regarding the delay-related characteristics of DTNs, this paper models the expected compensation cost (ECC) for the schedulings of commit-requests, presents a calculability analysis for quantitative ECC prediction, and explores the limitation of ECC’s probabilistic prediction accordingly. The analysis is based on the timed-2PC plus compensation (t2PC+) protocol and the multi-step price tag pattern, which is verified conditionally by simulation tests through randomly-chosen severely-fluctuant samplings of compensation cost and delays. The ultimate target of this work is to demonstrate the high complexity, and in particular, the uncertainty of ECC predictions due to the randomicity of DTNs’ delays.     

Geometrically non-linear behavior of structural systems with random material property: An asymptotic spectral stochastic approach

An asymptotic spectral stochastic approach is presented for computing the statistics of the equilibrium path in the post-bifurcation regime for structural systems with random material properties. The approach combines numerical implementation of Koiter’s asymptotic theory with a stochastic Galerkin scheme and collocation in stochastic space to quantify uncertainties in the parametric representation of the load–displacement relationship, specifically in the form of uncertain post-buckling slope, post-buckling curvature, and a family of stochastic displacement fields. Using the proposed method, post-buckling response statistics for two plane frames are obtained and shown to be in close agreement with those obtained from Monte Carlo simulation, provided a fine enough spectral representation is used to model the variability in the random dimension.     

Group path covering and distance two labeling of graphs

For a positive integer d, an L(d,1)-labeling f of a graph G is an assignment of integers to the vertices of G such that |f(u)−f(v)|?d if uv∈E(G), and |f(u)−f(v)|?1 if u and u are at distance two. The span of an L(d,1)-labeling f of a graph is the absolute difference between the maximum and minimum integers used by f. The L(d,1)-labeling number of G, denoted by λd,1(G), is the minimum span over all L(d,1)-labelings of G. An L^′(d,1)-labeling of a graph G is an L(d,1)-labeling of G which assigns different labels to different vertices. Denote by the L^′(d,1)-labeling number of G. Georges et al. [Discrete Math. 135 (1994) 103-111] established relationship between the L(2,1)-labeling number of a graph G and the path covering number of Gc, the complement of G. In this paper we first generalize the concept of the path covering of a graph to the t-group path covering. Then we establish the relationship between the L^′(d,1)-labeling number of a graph G and the (d−1)-group path covering number of Gc. Using this result, we prove that and for bipartite graphs G can be computed in polynomial time.     

Necessary optimality conditions for fuzzy variational problems

The main aims of this study are to derive the fuzzy Euler-Lagrange conditions for both fuzzy unconstrained and constrained variational problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its α-level sets.     

Strong stability of the mono-tubular heat exchanger equation with output feedback

We investigate asymptotic behavior of the C₀-semigroup T(t) associated with the mono-tubular heat exchanger equation with output feedback by a perturbation method. It is shown that T(t) is bounded if a constraint is satisfied by the parameters and the spatial distribution function. Further, applying the Arendt-Batty-Lyubich-Vu theorem, a criterion is established to judge strong stability of T(t).     

Computing Green's function of the initial-boundary value problem for the wave equation in a layered cylinder

A new analytical method for the approximate computation of the time-dependent Green's function for the initial-boundary value problem of the three-dimensional wave equation on multi-layered bounded cylinder is suggested in this paper. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients, and an approximate computation of Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. The computational experiment confirms the robustness of the method.