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Articles 181 - 190 of 190
Full-Text Articles in Education
Vertices Of Self-Similar Tiles, Da-Wen Deng, Sze-Man Ngai
Vertices Of Self-Similar Tiles, Da-Wen Deng, Sze-Man Ngai
Department of Mathematical Sciences Faculty Publications
The set Vn of n-vertices of a tile T in \Rd is the common intersection of T with at least n of its neighbors in a tiling determined by T. Motivated by the recent interest in the topological structure as well as the associated canonical number systems of self-similar tiles, we study the structure of Vn for general and strictly self-similar tiles. We show that if T is a general self-similar tile in \R2 whose interior consists of finitely many components, then any tile in any self-similar tiling generated by T has a finite …
Self-Similar Measures Associated To {Ifs} With Non-Uniform Contraction Ratios, Sze-Man Ngai, Yang Wang
Self-Similar Measures Associated To {Ifs} With Non-Uniform Contraction Ratios, Sze-Man Ngai, Yang Wang
Department of Mathematical Sciences Faculty Publications
In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, Peres, et al.
Long-Step Homogeneous Interior-Point Method For P*-Nonlinear Complementarity Problem, Goran Lesaja
Long-Step Homogeneous Interior-Point Method For P*-Nonlinear Complementarity Problem, Goran Lesaja
Department of Mathematical Sciences Faculty Publications
A P*-Nonlinear Complementarity Problem as a generalization of the P*Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.
A Note On Computing The Generalized Inverse A^(2)_{T,S} Of A Matrix A, Xiezhang Li, Yimin Wei
A Note On Computing The Generalized Inverse A^(2)_{T,S} Of A Matrix A, Xiezhang Li, Yimin Wei
Department of Mathematical Sciences Faculty Publications
The generalized inverse A T,S (2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T,S (2) has been recently developed with the condition σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose …
On Inequalities And Partial Orderings For Weighted Reliability Measures, Broderick O. Oluyede
On Inequalities And Partial Orderings For Weighted Reliability Measures, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
Inequalities, relations and partial ordering for weighted reliability measures are presented. Inequalities for Lévy distance measure for weighted distributions are obtained in terms of the parent distributions. Reliability inequalities and stability results are established for weighted distributions with monotone hazard and mean residual life functions.
On Stochastic Inequalities And Comparisons Of Reliability Measures For Weighted Distributions, Broderick O. Oluyede, E. Olusegun George
On Stochastic Inequalities And Comparisons Of Reliability Measures For Weighted Distributions, Broderick O. Oluyede, E. Olusegun George
Department of Mathematical Sciences Faculty Publications
Inequalities, relations and stochastic orderings, as well as useful ageing notions for weighted distributions are established. Also presented are preservation and stability results and comparisons for weighted and length-biased distributions. Relations for length-biased and equilibrium distributions as examples of weighted distributions are also presented.
On Moment Inequalities And Stochastic Ordering For Weighted Reliability Measures, Broderick O. Oluyede, Mekki Terbeche
On Moment Inequalities And Stochastic Ordering For Weighted Reliability Measures, Broderick O. Oluyede, Mekki Terbeche
Department of Mathematical Sciences Faculty Publications
We obtain stochastic inequalities, error bounds, and classification probability for a general class of distributions. We introduce the notion of variability ordering via the probability functional and comparisons made for the weighted and the original distributions. We present moment inequalities, comparisons, and applications.
On Stochastic Comparisons Of Energy Functions With Applications, Broderick O. Oluyede
On Stochastic Comparisons Of Energy Functions With Applications, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
We develop simple methods for the stochastic comparisons of informational energy functions. We introduce modified informational energy functions and uncertainty of parameter functions are introduced for models with realistic parameter spaces. We present inequalities, comparisons, and applications including test procedures for testing the equality of informational energy functions. Some illustrative examples are also presented.
On Some Length Biased Inequalities For Reliability Measures, Broderick O. Oluyede
On Some Length Biased Inequalities For Reliability Measures, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
In this note, inequalities for length biased and the original residual life function and equilibrium distribution function with monotone hazard rate and mean residual life functions are derived. We also obtain estimates of the length biased probability density function and hazard function under random censoring. Finally, the Bayesian exponential reliability estimate under length biased sampling using a conjugate prior for the scale parameter is given.
Interior-Point Methods And Modern Optimization Codes, Goran Lesaja
Interior-Point Methods And Modern Optimization Codes, Goran Lesaja
Department of Mathematical Sciences Faculty Publications
During the last fifteen years we have witnessed an explosive development in the area of optimization theory due to the introduction and development of interior-point methods. This development has quickly led to the development of new and more efficient optimization codes. In this paper, the basic elements of interior-point methods for linear programming will be discussed as well as extensions to convex programming, complementary problems, and semidefinite programming. Interior-point methods are polynomial and effective algorithms based on Newton 's method. Since they have been introduced, the classical distinction between linear programming methods, based on the simplex algorithm, and those methods …