Existence results for partial neutral functional differential equations with state-dependent delay

In this paper we study the existence of mild solutions for a class of first order abstract partial neutral differential equations with state-dependent delay. (C) 2008 Elsevier Ltd. All rights reserved.

The influence of oscillations on global existence for a class of semi-linear wave equations

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u(tt) - a(t)(2) Delta u = u(t)(2) - a(t)(2)vertical bar del u vertical bar(2). In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions. Copyright c 2011 John Wiley & Sons, Ltd.

Existence of solutions for a class of abstract differential equations with nonlocal conditions

We discuss the existence of mild, classical and strict solutions for a class of abstract differential equations with nonlocal conditions. Our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution. Some concrete applications to partial differential equations are considered. (C) 2010 Elsevier Ltd. All rights reserved.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

On the fractional central differences and derivatives

Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivatives are presented and particular cases studied.

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Generating highly balanced sudoku problems as hard problems

Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in [8, 44, 39, 9]. On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m = n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables – variables with the same value in all the solutions of an instance– and hardness of GSP.

On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system With impulses is considered. (c) 2008 Elsevier Ltd. All rights reserved.

HQET at order 1/m: II. Spectroscopy in the quenched approximation

Using Heavy Quark Effective Theory with non-perturbatively determined parameters in a quenched lattice calculation, we evaluate the splittings between the ground state and the first two radially excited states of the B(s) system at static order. We also determine the splitting between first excited and ground state, and between the B(s)* and B(s) ground states to order 1/m(b). The Generalized Eigenvalue Problem and the use of all-to-all propagators are important ingredients of our approach.

Task assignment optimization in SAP Extended WarehouseManagement

Nowadays in the world of mass consumption there is big demand for distributioncenters of bigger size. Managing such a center is a very complex and difficult taskregarding to the different processes and factors in a usual warehouse when we want tominimize the labor costs. Most of the workers’ working time is spent with travelingbetween source and destination points which cause deadheading. Even if a worker knowsthe structure of a warehouse well and because of that he or she can find the shortest pathbetween two points, it is still not guaranteed that there won’t be long traveling timebetween the locations of two consecutive tasks. We need optimal assignments betweentasks and workers.In the scientific literature Generalized Assignment Problem (GAP) is a wellknownproblem which deals with the assignment of m workers to n tasks consideringseveral constraints. The primary purpose of my thesis project was to choose a heuristics(genetic algorithm, tabu search or ant colony optimization) to be implemented into SAPExtended Warehouse Management (SAP EWM) by with task assignment will be moreeffective between tasks and resources.After system analysis I had to realize that due different constraints and businessdemands only 1:1 assingments are allowed in SAP EWM. Because of that I had to use adifferent and simpler approach – instead of the introduced heuristics – which could gainbetter assignments during the test phase in several cases. In the thesis I described indetails what ware the most important questions and problems which emerged during theplanning of my optimized assignment method.

Métodos de geração de colunas para problemas de atribuição

Este trabalho apresenta métodos de geração de colunas para dois importantes problemas de atribuição: o Problema Generalizado de Atribuição (PGA) e o Problema de Atribuição de Antenas a Comutadores (PAAC). O PGA é um dos mais representativos problemas de Otimização Combinatória e consiste em otimizar a atribuição de n tarefas a m agentes, de forma que cada tarefa seja atribuída a exatamente um agente e a capacidade de cada agente seja respeitada. O PAAC consiste em atribuir n antenas a m comutadores em uma rede de telefonia celular, de forma a minimizar os custos de cabeamento entre antenas e comutadores e os custos de transferência de chamadas entre comutadores. A abordagem tradicional de geração de colunas é comparada com as propostas neste trabalho, que utilizam a relaxação lagrangeana/surrogate. São apresentados testes computacionais que demonstram a efetividade dos algoritmos propostos.