Polynomials generated by a three term recurrence relation: bounds for complex zeros

This paper deals with the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to find bounds, in terms of the coefficients of the recurrence relation, for the regions where the zeros are located. In most part, the zeros are explored through an Eigenvalue representation associated with a corresponding Hessenberg rnatrix. Applications to Szego polynomials, para-orthogonal polynomials and polynomials with non-zero complex coefficients are considered. (C) 2004 Elsevier B.V. All rights reserved.

Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity of zeros of Laguerre polynomials

Denote by X(nk)(alpha), k = 1, ..., n, the zeros of the Laguerre polynomial L(n)((alpha))(X). We establish monotonicity with respect to the parameter at of certain functions involving X(nk)(alpha). As a consequence we obtain sharp upper bounds for the largest zero of L(n)((alpha))(X). (C) 2009 Elsevier B.V. All rights reserved.

Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sharp bounds for the extreme zeros of classical orthogonal polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Convolutions and zeros of orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Distances between critical points and midpoints of zeros of hyperbolic polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

External Hexagon and Internal Hexagon in Straight and Offset Implant Placement: Strain Gauge Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Straight and Offset Implant Placement under Axial and Nonaxial Loads in Implant-Supported Prostheses: Strain Gauge Analysis

Purpose: The aim of this in vitro study was to quantify strain development during axial and nonaxial loading using strain gauge analysis for three-element implant-supported FPDs, varying the arrangement of implants: straight line (L) and offset (O). Materials and Methods: Three Morse taper implants arranged in a straight line and three implants arranged in an offset configuration were inserted into two polyurethane blocks. Microunit abutments were screwed onto the implants, applying a 20 Ncm torque. Plastic copings were screwed onto the abutments, which received standard wax patterns cast in Co-Cr alloy (n = 10). Four strain gauges were bonded onto the surface of each block tangential to the implants. The occlusal screws of the superstructure were tightened onto microunit abutments using 10 Ncm and then axial and nonaxial loading of 30 Kg was applied for 10 seconds on the center of each implant and at 1 and 2 mm from the implants, totaling nine load application points. The microdeformations determined at the nine points were recorded by four strain gauges, and the same procedure was performed for all of the frameworks. Three loadings were made per load application point. The magnitude of microstrain on each strain gauge was recorded in units of microstrain (mu). The data were analyzed statistically by two-way ANOVA and Tukey's test (p < 0.05). Results: The configuration factor was statistically significant (p= 0.0004), but the load factor (p= 0.2420) and the interaction between the two factors were not significant (p= 0.5494). Tukey's test revealed differences between axial offset (mu) (183.2 +/- 93.64) and axial straight line (285.3 +/- 61.04) and differences between nonaxial 1 mm offset (201.0 +/- 50.24) and nonaxial 1 mm straight line (315.8 +/- 59.28). Conclusion: There was evidence that offset placement is capable of reducing the strain around an implant. In addition, the type of loading, axial force or nonaxial, did not have an influence until 2 mm.

Monotonicity of the zeros of orthogonal polynomials through related measures

Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered. (c) 2005 Elsevier B.V. All rights reserved.

Optimal capacitor placement in radial distribution networks

The capacitor placement (replacement) problem for radial distribution networks determines capacitor types, sizes, locations and control schemes. Optimal capacitor placement is a hard combinatorial problem that can be formulated as a mixed integer nonlinear program. Since this is a NP complete problem (Non Polynomial time) the solution approach uses a combinatorial search algorithm. The paper proposes a hybrid method drawn upon the Tabu Search approach, extended with features taken from other combinatorial approaches such as genetic algorithms and simulated annealing, and from practical heuristic approaches. The proposed method has been tested in a range of networks available in the literature with superior results regarding both quality and cost of solutions.

The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings

We carry out a numerical and analytic analysis of the Yang-Lee zeros of the ID Blume-Capel model with periodic boundary conditions and its generalization on Feynman diagrams for which we include sums over all connected and nonconnected rings for a given number of spins. In both cases, for a specific range of the parameters, the zeros originally on the unit circle are shown to depart from it as we increase the temperature beyond some limit. The curve of zeros can bifurcate- and become two disjoint arcs as in the 2D case. We also show that in the thermodynamic limit the zeros of both Blume-Capel models on the static (connected ring) and on the dynamical (Feynman diagrams) lattice tend to overlap. In the special case of the 1D Ising model on Feynman diagrams we can prove for arbitrary number of spins that the Yang-Lee zeros must be on the unit circle. The proof is based on a property of the zeros of Legendre polynomials.