A CLASS OF SPECTRALLY ARBITRARY RAY PATTERNS

An n × n ray pattern A is said to be spectrally arbitrary if for every monic nth degree polynomial f(x) with coefficients from C, there is a complex matrix in the ray pattern class of A such that its characteristic polynomial is f(x). In this paper, a family ray patterns is proved to be spectrally arbitrary by using Nilpotent-Jacobian method.     

A NEW STEPSIZE FOR THE STEEPEST DESCENT METHOD

The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize αk for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems.     

Vertex-distinguishing IE-total Colorings of Complete Bipartite Graphs K8,n

Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C(x) be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C(u) 6= C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χievt(G) and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K8,n are discussed in this paper. Particularly, the VDIET chromatic number of K8,n are obtained.     

A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS

Based on the work of paper,we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x)=0,where F(x):R^n→R^n is continuously differentiable and F‘(x)is Lipschitz continuous.The algorithm is equivalent to a trust region algorithm in some sense,and the global convergence result is given.The sequence generated by the algorithm converges to the solution quadratically,if ||F(x)||2 provides a local error bound for the system of nonlinear equations.Numerical results show that the algorithm performs well.     

A GENERAL DETERMINISTIC PIVOT METHOD FOR ORIENTED MATROID PROGRAMMING

A new pivot method for oriented matroid progiamming is given out. This mathod is deterministic by nature and is general in the sense that its flexible pivot selection rule allows a family of possible algorithms to be its special cases, including the so called criss-cross algorithm and the Edmonds-Fukuda algorithm as well. As an example of a special implementation of our general method, an extended version of the Edmonds-Fukuda algorithm is presented.     

完全二部图K_(8,n)的点可区别IE-全染色（英文）

Let G be a simple graph. An IE-total coloring f of G is a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. For each vertex x of G, let C(x) be the set of colors of vertex x and edges incident to x under f. For an IE-total coloring f of G using k colors, if C(u) ≠ C(v) for any two different vertices u and v of G, then f is called a k-vertex-distinguishing IE-total-coloring of G or a k-VDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χ_(vt)~(ie) (G) and is called vertex-distinguishing IE-total chromatic number or the VDIET chromatic number of G for short. The VDIET colorings of complete bipartite graphs K_(8,n)are discussed in this paper. Particularly, the VDIET chromatic number of K_(8,n) are obtained.     

A SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHM FOR SDP RELAXATION OF MAX-BISECTION

A successive quadratic programming algorithm for solving SDP relaxation of Max- Bisection is provided and its convergence result is given.The step-size in the algorithm is obtained by solving n easy quadratic equations without using the linear search technique.The numerical experiments show that this algorithm is rather faster than the interior-point method.     

A polynomial algorithm for finding (g,f)-colorings orthogonal to stars in bipartite graphs

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two nonnegative integer-valued functions defined on V(G) such that g(x)≤ f(x) for every vertex x of V(G). A (g. f)-coloring of G is a generalized edge-coloring in which each color appears at each vertex x at least g(x) and at most f(x) times. In this paper a polynomial algorithm to find a (g. f)-coloring of a bipartite graph with some constraints using the minimum number of colors is given. Furthermore, we show that the results in this paper are best possible.     

THE SPACES OF CESARO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMB

As known,the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces.However,the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new(see [15]).The purpose of this paper is to introduce the new spaces f and f0 consisting of all sequences whose Cesa`ro transforms of order one are in the spaces f and f0,respectively.Also,in this paper,we show that f and f0 are linearly isomorphic to the spaces f and f0,respectively.The β-and γ-duals of the spaces f and f0 are computed.Furthermore,the classes(f:) and(:f) of infinite matrices are characterized for any given sequence space,and determined the necessary and sufficient conditions on a matrix A to satisfy BC-core(Ax) K-core(x),K-core(Ax) BC-core(x),BC-core(Ax) BC-core(x),BC-core(Ax) st-core(x) for all x ∈∞.     

Optimal Delaunay Triangulations

The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function ‖x‖^2 among all the triangulations with a given set of vertices. For a more general function, a functiondependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-depend entoptimal Delaunay triangulation is proved to exist for any given convex continuous function.On an optimal Delaunay triangulation associated with f, it is proved that △↓f at the interior vertices can be exactly recovered by the function values on its neighboring vertices.Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.