Connected (g,f)‐factors

The vertex set of the reduced Kneser graph KG₂(m,2) consists of all pairs {a,b} such that a, bε{1,2,…,m} and 2≤|a?b|≤m?2. Two vertices are defined to be adjacent if they are disjoint. We prove that, if m≥4 and m≠5, then the circular chromatic number of KG₂(m,2) is equal to m?2, its ordinary chromatic number. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 62–68, 2002     

A New Approach to the Algebraic Structures for Integration Methods

The analysis of compositions of Runge-Kutta methods involves manipulations of functions defined on rooted trees. Existing formulations due to Butcher [1972], Hairer and Wanner [1974], and Murua and Sanz-Serna [1999], while equivalent, differ in details. The subject of the present paper is a new recursive formulation of the composition rules. This both simplifies and extends the existing approaches. Instead of using the order conditions based on trees, we propose the construction of the order conditions using a suitably chosen basis on the tree space. In particular, the linear structure of the tree space gives a representation of the C and D simplifying assumptions on trees which is not restricted to Runge-Kutta methods. A proof of the group structure of the set of elementary weight functions satisfying the D simplifying assumptions is also given is this paper.     

A study of thermal peak splitting in capillary GC

Fluctuating thermal gradients are recognized as a distinct source of peak splitting in capillary column gas chromatography. In this study, the influence of analyte signal level, temperature oscillation amplitude, and oscillation frequency on splitting are quantitatively examined. Stable gradients are also considered. A simple, effective method is proposed for virtually eliminating thermal peak splitting in isothermal capillary GC analysis.     

Computational algorithms for hierarchically structured project networks

A new approach to large size network management based on a structured network representation is proposed. Definitions of arc-structured and vertex-structured networks are given and an extension of topological sorting and time computation algorithms is described. A generalization of the concept of vertex-structured networks is discussed.     

On fuzzy tree definition

The connectedness and acyclicity levels are presented for a fuzzy graph. Several fuzzy tree definitions are given too, and their relations with previous studies on the matter are analyzed.     

Random walks on the Bethe lattice

We obtain random walk statistics for a nearest-neighbor (Pólya) walk on a Bethe lattice (infinite Cayley tree) of coordination numberz, and show how a random walk problem for a particular inhomogeneous Bethe lattice may be solved exactly. We question the common assertion that the Bethe lattice is an infinite-dimensional system.Supported in part by the U.S. Department of Energy.     

The design of branch and bound algorithms for a class of nonlinear integer programs

This paper is concerned with computational experimentation leading to the design of effective branch and bound algorithms for an important class of nonlinear integer programming problems, namely linearly constrained problems, which are used to model several real-world situations. The main contribution here is a study of the effect of node and branching variable selection and storage reduction strategies on overall computational effort for this class of problems, as well as the generation of a set of adequate test problems. Several node and branching variable strategies are compared in the context of a pure breadth-first enumeration, as well as in a special breadth and depth enumeration combination approach presented herein. Also, the effect of using updated pseudocosts is briefly addressed. Computational experience is presented on a set of eighteen suitably-sized nonlinear test problems, as well as on some random linear integer programs. Some of the new rules proposed are demonstrated to be significantly superior to previously suggested strategies; interestingly, even for linear integer programming problems.     

Experimental investigation of circular cantilever beams subjected to impulsive loading

This paper reports the experimental results of quadrantal circular cantilever beam carrying a mass at its tip which is subjected to radial impact. It was observed that after impact a travelling plastic segment moved from the tip towards the root in a very short time, and when specimen reached the largest deformation, the beam whipped out evidently in the reverse direction. The curvature change of the curved beam reaches a peak value near the middle region of the beam and the maximum is at the root. The experimental results are compared with the solutions for the rigid-perfectly plastic model given in [12–13].The authors would like to thank Professor Yang Gui-tong for guidance and help.     

Fuzzy importance in fault tree analysis

In fault tree analysis, system success or failure can be described by the state of the top event, which is usually defined by a so-called structure function. In this paper, we attempt to simplify the calculation process of the structure function and to newly define the state of the top event by the membership function, using fuzzy sets theory. Furthermore, it is shown that the importance of each basic event can be evaluated through fuzzy operations. The method proposed herein is demonstrated by some examples with respect to the failure analysis of structures.