{X,Y}-Cyclacene Graphs with Next Nearest Neighbor Interactions

Eigensolutions of {X( = C,B,N),Y( = C,B,N)}-cyclacene graphs with next nearest neighbor (nnn) interactions have been obtained in analytical forms by adapting n-fold rotational symmetry followed by two-fold rotational symmetry (or a plane of symmetry). Expressions of eigensolution indicate the subspectral relationship among such cyclacenes with an even number of hexagonal rings e.g., eigenvalues of {X,Y}-di-cyclacene are found in the eigenspectra of all such even cyclacenes. Total π-electron energies and highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gaps are calculated using the analytical expressions obtained and are found to vary negligibly with the variation of nnn interactions in such cyclacenes. Total π-electron energy is found to increase due to increase in restriction intensity of nnn interactions, whereas the HOMO–LUMO gap of polyacenecs having the even number of hexagonal rings and with one electron at each site (atom) decreases with increase in the restriction intensity since such systems contain degenerate half-filled HOMO (bonding or nonbonding) that are much more vulnerable for perturbations imposed through nnn interactions.     

Wavefront reduction using graphs,neural networks and genetic algorithm

This paper presents an algorithm for nodal numbering in order to obtain a small wavefront. Element clique graphs are employed as the mathematical models of finite element meshes. A priority function containing five vectors is used, which can be viewed as a generalization of Sloan's function. These vectors represent different connectivity properties of the graph models. Unlike Sloan's algorithm, which uses two fixed coefficients, here, five coefficients are employed, based on an evaluation by artificial neural networks. The networks weights are obtained using a simple genetic algorithm. Examples are included to illustrate the performance of the present hybrid method. Copyright © 2004 John Wiley & Sons, Ltd.     

Maximum Cardinality Search for Computing Minimal Triangulations of Graphs

We present a new algorithm, called MCS-M, for computing minimal triangulations of graphs. Lex-BFS, a seminal algorithm for recognizing chordal graphs, was the genesis for two other classical algorithms: LEX M and MCS. LEX M extends the fundamental concept used in Lex-BFS, resulting in an algorithm that not only recognizes chordality, but also computes a minimal triangulation of an arbitrary graph. MCS simplifies the fundamental concept used in Lex-BFS, resulting in a simpler algorithm for recognizing chordal graphs. The new algorithm MCS-M combines the extension of LEX M with the simplification of MCS, achieving all the results of LEX M in the same time complexity.     

Reduced modified quadratures for quadratic membrane finite elements

Reduced integration is frequently used in evaluating the element stiffness matrix of quadratically interpolated finite elements. Typical examples are the serendipity (Q8) and Lagrangian (Q9) membrane finite elements, for which a reduced 2 × 2 Gauss–Legendre integration rule is frequently used, as opposed to full 3 × 3 Gauss–Legendre integration. This ‘softens’ these element, thereby increasing accuracy, albeit at the introduction of spurious zero energy modes on the element level. This is in general not considered problematic for the ‘hourglass’ mode common to Q8 and Q9 elements, since this spurious mode is non‐communicable. The remaining two zero energy modes occurring in the Q9 element are indeed communicable. However, in topology optimization for instance, conditions may arise where the non‐communicable spurious mode associated with the elements becomes activated. To effectively suppress these modes altogether in elements employing quadratic interpolation fields, two modified quadratures are employed herein. For the Q8 and Q9 membrane elements, the respective rules are a five and an eight point rule. As compared to fully integrated elements, the new rules enhance element accuracy due to the introduction of soft, higher‐order deformation modes. A number of standard test problems reveal that element accuracy remains comparable to that of the under‐integrated counterparts. Copyright © 2004 John Wiley & Sons, Ltd.     

应用图论及广义简约梯度法进行压力管网优化设计

广义简约梯度法(GRG)是非线性规划算法中最有效的算法之一，本文把图论应用于广义简约梯度法优化的过程中，使输入简便，计算简化，应用GRG算法对武汉市的汉阳管网进行了模拟优化设计，并对管段的计算管径用线性规划法进行标准化，取得了满意的结果     

OSCILLATION AMPLITUDE OF THE FREE END OF A FLEXIBLY MOUNTED RIGID CYLINDER IN TRIANGLE ARRANGEMENT

In this paper,the oscillation amplitude of the free end of a group of threecylinders are studied.The three cylinders are erected at the vertices of an equilateral trian-gle,and three arrangements are made in this study.One of the three cylinders is served asa working cylinder which is mounted by a flexible cantilever and two accelerometers areattached on the free end in two directions.The results of the three-cylinder arrangementare compared with those of two cylinders in tandem/side-by-side arrangement in the samecondition.The experimental results show that the rear cylinder of a group of three cylin-ders is affected more seriously than that of the corresponding two cylinders in the contrastarrangement.The main direction of oscillation is changed.The transversal oscillation isstronger than the longitudinal oscillation in the three-cylinder arrangement.On the con-trary,the transversal oscillation is much weaker than the longitudinal oscillation in two-cylinder arrangement.The largest transversal oscillat     

Pancyclicity of recursive circulant graphs

In this paper, we study the existence of cycles of all lengths in the recursive circulant graphs, and we show a necessary and sufficient condition for the graph being pancyclic and bipancyclic.     

Tight upper bound on the number of edges in a bipartite K3,3-free or K5-free graph with an application

We show that an n-vertex bipartite K_3,3-free graph with n?3 has at most 2n−4 edges and that an n-vertex bipartite K₅-free graph with n?5 has at most 3n−9 edges. These bounds are also tight. We then use the bound on the number of edges in a K_3,3-free graph to extend two known NC algorithms for planar graphs to K_3,3-free graphs.     

Reliability models for computer systems: An overview including dataflow graphs

The reliability of a system is the probability that the system will perform its intended mission under given conditions. This paper provides an overview of the approaches to reliability modelling and identifies their strengths and weaknesses. The models discussed include structure models, simple stochastic models and decomposable stochastic models. Ignoring time-dependence, structure models give reliability as a function of the topological structure of the system. Simple stochastic models make direct use of the properties of underlying stochastic processes, while decomposable models consider more complex systems and analyse them through subsystems. Petri nets and dataflow graphs facilitate the analysis of complex systems by providing a convenient framework for reliability analysis.     

Parallelization of WHILE loops on pipelined architectures

Modulo scheduling theory can be applied successfully to overlap Fortran DO loops on pipelined computers issuing multiple operations per cycle both with and without special loop architectural support. This paper shows that a broader class of loops—REPEAT-UNTIL, WHILE, and loops with more than one exit, in which the trip count is not known beforehand—can also be overlapped efficiently on multiple-issue pipelined machines. The approach is described with respect to a specific machine model, but it can be extended to other models. Special features in the architecture, as well as compiler representations for accelerating these loop constructs, are discussed. Performance results are presented for a few select examples.An earlier version of this paper was presented at Supercomputing '90.