Sparse graph certificates for mixed connectivity

We give a short proof for the Mixed Connectivity Certificate Theorem of Even, Itkis and Rajsbaum and provide an upper bound on the edge number of a certificate of local T-mixed connectivity up to k.     

神经网络在大型复杂武器装备质量综合评价排序中的应用

从大型复杂武器装备系统的具体特点出发,运用基于神经网络的评价方法,构建了大型复杂武器装备质量综合评价模型。实证分析的结果表明该方法得出的结果与实际情况相符。     

Phase Separation Driven by a Fluctuating Two-Dimensional Self-Affine Potential Field

We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar–Parisi–Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetry of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features.     

Memory management optimization problems for integrated circuit simulators

In hardware design, it is necessary to simulate the anticipated behavior of the integrated circuit before it is actually cast in silicon. As simulation procedures are long due to the great number of tests to be performed, optimization of the simulation code is of prime importance. This paper describes two mathematical models for the minimization of the memory access times for a cycle-based simulator.An integrated circuit being viewed as a directed acyclic graph, the problem consists in building a graph order on the vertices, compatible with the relation order induced by the graph, in order to minimize a cost function that represents the memory access time. For both proposed cost functions, we show that the corresponding problems are NP-complete. However, we show that the special cases where the graphs are in-trees or out-trees can be solved in polynomial time.     

Numerical study of charge ordering in NaxCoO2

A simple microscopic model of charge ordering in the Na_xCoO₂ system is presented. The model takes into account the interplane interactions between the ordered Na ions and d electrons from the CoO₂ layers as well as the nearest-neighbor intraplane Coulomb interactions between d electrons. It is shown that a driving force of charge ordering in the CoO₂ layers is the interplane interaction that alone is able to describe various types of inhomogeneous charge ordering (e.g., the striped phases) as well as to predict correctly the conducting properties of the system.     

On disjoint configurations in infinite graphs

For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?₀ disjoint copies of A is referred to as ?₀A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?₀A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G₁, G₂,… such that G_i is not a minor of G_j for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?₀A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016     

Nanostructural Approach to Proton Ordering in Gas Hydrate Cages

A nanostructural approach to analysis of proton ordering in gas hydrate cages has been worked out within the framework of the topological model of strong and weak H-bonds. The approach involves rejection of the periodic boundary conditions, decomposition of the H-bond net into spherical layers, and two-dimensional drawing of the structure of spherical (spheroidal) fragments in the form of conjugate Schlegel diagrams. To analyze proton ordering in the spherical fragments composed of gas hydrate voids, we used the simulated annealing procedure and the correlation extension method proposed earlier.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

A reinvestigation of quaternary layered bismuth oxyhalides of the Sillén X1 type

A family of layered bismuth oxyhalides, L^I_0.5Bi_1.5O₂X and L^IIBiO₂X has been reinvestigated. Formation of X1-type Sillén compounds has been established for L^I=Li, Na, L^II=Ca, Sr, Ba, and X=Cl, Br, I, but the details of their crystal structures are different. While all L^I_0.5Bi_1.5O₂X, CaBiO₂Br, and CaBiO₂I adopt the disordered tetragonal Nd₂O₂Te structure, all compounds of L^II=Sr and Ba are orthorhombic and isostructural to PbSbO₂Cl, due to L/Bi cation ordering. Crystal structures have been determined for CaBiO₂I, SrBiO₂Br, SrBiO₂I, and BaBiO₂I. We discuss the factors which determine the occurrence and type of cation ordering in the quaternary bismuth and antimony X1-type oxyhalides. We also predict that more isostructural compounds can be prepared with antimony.