Algorithm for recognizing Cartesian graph bundles

Graph bundles generalize the notion of covering graphs and graph products. In [8], authors constructed an algorithm that finds a presentation as a nontrivial Cartesian graph bundle for all graphs that are Cartesian graph bundles over triangle-free simple base. In [21], the unique square property is defined and it is shown that any equivalence relation possessing the unique square property determines the fundamental factorization of a graph as a nontrivial Cartesian graph bundle over arbitrary base graph. In this paper we define a relation Δ having a unique square property on Cartesian graph bundles over K₄e-free simple base. We also give a polynomial algorithm for recognizing Cartesian graph bundles over K₄e-free simple base.     

Domination graphs: examples and counterexamples

We give a counterexample to a conjecture of Dahlhaus et al. [3] claiming that the Special Quadratic Consensus Method yields a polynomial-time recognition for domination graphs, and discuss several new properties of domination graphs.     

Environment system and dynamic management decision

Dynamic management decision means a new technology which is designed for improving the environment of the region. If resources such as plenty of sunshine, water, greenery and highly educated people in a district are used appropriately, the quality of life of the people will be greatly enhanced. In Section 1, we discuss the ecology. In Section 2, we consider an urban system that understands the timing of expansions of system capacity, a dynamic fuzzy criterion model for reservoir operations and assigning priorities to welfare policies. In Section 3, we discuss the energies and the resources. In conclusion we discuss further research.     

Invariant variational principles and conservation laws for some nonlinear partial differential equations with constant coefficients – I

The invariance under a one-parameter infinitesimal transformation groups [1] has been proven for a number of nonlinear partial differential equations (NLPDEs) with constant coefficients, which appear in a wide variety of modelling physical phenomena/applications. The invariance identities of Rund [2] involving the Lagrangian and the generators of the infinitesimal Lie groups are utilized, for writing down the conservation laws via Noether's theorem. In order that the study becomes more exhaustive, we have applied the above technique to the cases arising from the generalized Klein–Gordon equation by transforming it to ordinary differential equation (ODE), to get on exact solution for it.     

The application of automated reasoning to formal models of combinatorial optimization

Many formalisms have been proposed over the years to capture combinatorial optimization algorithms such as dynamic programming, branch and bound, and greedy. In 1989 Helman [9] presented a common formalism that captures dynamic programming and branch and bound type algorithms. The formalism was later extended to include greedy algorithms. In this paper, we describe the application of automated reasoning techniques to the domain of our model, in particular considering some representational issues and demonstrating that proofs about the model can be obtained by an automated reasoning program. The long-term objective of this research is to develop a methodology for using automated reasoning to establish new results within the theory, including the derivation of new lower bounds and the discovery (and verification) of new combinatorial search strategies.     

A parameter-uniform implicit difference scheme for solving time-dependent Burgers’ equations

A numerical study is made for solving one dimensional time dependent Burgers’ equation with small coefficient of viscosity. Burgers’ equation is one of the fundamental model equations in the fluid dynamics to describe the shock waves and traffic flows. For high coefficient of viscosity a number of solution methodology exist in the literature [6], [7], [8] and [9] and [14] but for the sufficiently low coefficient of viscosity, the exist solution methodology fail and a discrepancy occurs in the literature. In this paper, we present a numerical method based on finite difference which works nicely for both the cases, i.e., low as well as high viscosity coefficient. The method comprises a standard implicit finite difference scheme to discretize in temporal direction on uniform mesh and a standard upwind finite difference scheme to discretize in spacial direction on piecewise uniform mesh. The quasilinearzation process is used to tackle the non-linearity. An extensive amount of analysis has been carried out to obtain the parameter uniform error estimates which show that the resulting method is uniformly convergent with respect to the parameter. To illustrate the method, numerical examples are solved using the presented method and compare with exact solution for high value of coefficient of viscosity.     

A ternary 4-point approximating subdivision scheme

In the implementation of subdivision scheme, three of the most important issues are smoothness, size of support, and approximation order. Our objective is to introduce an improved ternary 4-point approximating subdivision scheme derived from cubic polynomial interpolation, which has smaller support and higher smoothness, comparing to binary 4-point and 6-point schemes, ternary 3-point and 4-point schemes (see Table 2). The method is easily generalized to ternary (2n + 2)-point approximating subdivision schemes. We choose a ternary scheme because a way to get smaller support is to raise arity. And we use polynomial reproduction to get higher approximation order easily.     

On the stability and boundedness of solutions of a kind of third order delay differential equations

In this paper, we study Eq. (1.1) for asymptotic stability of the zero solution when and uniformly bounded and uniformly ultimate bounded of all solutions when      

Smooth particle hydrodynamics simulation of surface coating

The simulation of plane impinging jets using the Lagrangian technique of smooth particle hydrodynamics is presented. In Section 1 the impingement of a plane jet onto a stationary surface is considered for Reynolds numbers 800, 4000, 8000 and Froude number 4. For each case, the height of the associated streams is measured and compared with both experimental and theoretical results. The agreement between these results is found to be close for most impingement angles. In the second section, impingement onto a moving surface is considered for Reynolds numbers of 50 and 800 and Froude numbers of 1 and 4. The preliminary results show that the moving surface can lead to some spatial height variation in at least one of the streams.     

Inequalities and solution of an operator equation

In this work, we prove several important inequalities, and investigate the solution of an operator equation by means of the fixed point index in the theory of topological degree. For operator equations with different boundary conditions, the same conclusion is obtained. Meanwhile, the famous Rothe’s Theorem is generalized. Finally, an example is given to show the application of Theorem 3.     

Chromatic-index-critical graphs of orders 13 and 14

A graph is chromatic-index-critical if it cannot be edge-coloured with Δ colours (with Δ the maximal degree of the graph), and if the removal of any edge decreases its chromatic index. The Critical Graph Conjecture stated that any such graph has odd order. It has been proved false and the smallest known counterexample has order [[18] A.J.W. Hilton, R.J. Wilson, Edge-colorings of graphs: a progress report, in: M.F. Cabobianco, et al. (Eds.), Graph Theory and its Applications: East and West, New York, 1989, pp. 241–249; [31] H.P. Yap, Some topics in graph theory, London Mathematical Society, Lecture Note Series, vol. 108, Cambridge University Press, Cambridge, 1986].

In this paper we show that there are no chromatic-index-critical graphs of order 14. Our result extends that of [[5] G. Brinkmann, E. Steffen, Chromatic-index-critical graphs of orders 11 and 12, European J. Combin. 19 (1998) 889–900] and leaves order 16 as the only case to be checked in order to decide on the minimality of the counterexamples given by Chetwynd and Fiol. In addition we list all nontrivial critical graphs of order 13.     

On AR(1) models with periodic and almost periodic coefficients

This paper is concerned with the existence of bounded solutions to the system of equations X_n=a_nX_n−1+ξ_n, nZ, where ξ_n are uncorrelated constant variance zero mean random variables. We give necessary and sufficient conditions for boundedness in the general case and then specifically for periodic and almost periodic (a_n). This provides the first step in extending the periodic autoregressive models, for which boundedness is equivalent to the stationarity of the blocked vector sequence

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to the almost periodic case.     

A note on unsolvable systems of max–min (fuzzy) equations

For unsolvable systems of linear equations of the form Ax=b over the max–min (fuzzy) algebra

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we propose an efficient method for finding a Chebychev-best approximation of the matrix in the set

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.     

Longest cycles in 3-connected graphs

In this paper, we get the following result: Let G be a 3-connected graph with n vertices. Then , where

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. This is a new lower bound for the circumference c(G) of a 3-connected graph G.     

Directed triangles in directed graphs

We show that each directed graph on n vertices, each with indegree and outdegree at least n/t, where

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, contains a directed circuit of length at most 3.     

First inverse moment of a generalized quadratic form

In this paper an approximate expression for the first inverse moment of

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where _k is a Gaussian stationary vector process is derived. This generalized quadratic form is the estimate of the information matrix when using the Recursive Least Squares (RLS) algorithm with forgetting factor. This estimator is commonly used when estimating parameters in time-varying linear stochastic systems.     

Another view on martingale central limit theorems

Based on the martingale version of the Skorokhod embedding Heyde and Brown (1970) established a bound on the rate of convergence in the central limit theorem (CLT) for discrete time martingales having finite moments of order 2+2δ with 0<δ1. An extension for all δ>0 was proved in Haeusler (1988). This paper presents a rather quick access based solely on truncation, optional stopping, and prolongation techniques for martingale difference arrays to obtain other upper bounds for sup

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(φbeing the standard normal d.f.) yielding weak sufficient conditions for the asymptotic normality of . It is shown that our approach also yields two types of martingale central limit theorems with random norming.     

On approximation of solutions of multidimensional SDE's with reflecting boundary conditions

Let D be either a convex domain in ^d or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman [7] and Saisho [11]. We estimate the rate of L^p convergence for Euler and Euler–Peano schemes for stochastic differential equations in D with normal reflection at the boundary of the form

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, where W is a d-dimensional Wiener process. As a consequence we give the rate of almost sure convergence for these schemes.     

Strong continuity of the relative rearrangement maps and application to a Galerkin approach for nonlocal problems

We study the strong continuity of the map u   (b_*u, b_*u(| > u(·)|)). Here,

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for σ]0 means Ω[, u_* (respectively, (b|_{u=u*(σ)})*) denotes the decreasing rearrangement of u (respectively b restricted to the set {u = u_*(σ)}) and |E| denotes the Lebesgue measure of a set E included in a domain Ω. The results are useful for solving plasmas physics equations or any nonlocal problems involving the monotone rearrangement, its inverse or its derivatives.     

Comparison of two norms of matrices

Any complex n × n matrix A satisfies the inequality

A ₁ ≤ n 1/2 A _d

where .₁ is the trace norm and ._d is the norm defined by

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,

where B is the set of orthonormal bases in the space of n × 1 matrices. The present work is devoted to the study of matrices A satisfying the identity:

A₁ = n1/2 A _d

This paper is a first step towards a characterization of matrices satisfying this identity. Actually, a workable characterization of matrices subject to this condition is obtained only for n = 2. For n = 3, a partial result on nilpotent matrices is presented. Like our previous study (J. Dazord, Linear Algebra Appl. 254 (1997) 67), this study is a continuation of the work of M. Marcus and M. Sandy (M. Marcus and M. Sandy, Linear and Multilinear Algebra 29 (1991) 283). Also this study is related to the work of R. Gabriel on classification of matrices with respect to unitary similarity (see R. Gabriel, J. Riene Angew, Math. 307/308 (1979) 31; R. Gabriel, Math. Z. 200 (1989) 591).