Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Generalized correlation functions for conductance fluctuations and the mesoscopic spin Hall effect

We study the spin Hall conductance fluctuations in ballistic mesoscopic systems. We obtain universal expressions for the spin and charge current fluctuations, cast in terms of current-current autocorrelation functions. We show that the latter are conveniently parametrized as deformed Lorentzian shape lines, functions of an external applied magnetic field and the Fermi energy. We find that the charge current fluctuations show quite unique statistical features at the symplectic-unitary crossover regime. Our findings are based on an evaluation of the generalized transmission coefficients correlation functions within the stub model and are amenable to experimental test. DOI: 10.1103/PhysRevB.86.235112

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Metrizability of spaces of holomorphic functions

In this paper we prove that if U is an open subset of a metrizable locally convex space E of infinite dimension, the space H(U) of all holomorphic functions on U, endowed with the Nachbin–Coeuré topology τδ, is not metrizable. Our result can be applied to get that, for all usual topologies, H(U) is metrizable if and only if E has finite dimension. RESUMEN. En este artículo se demuestra que si U es un abierto en un espacio E localmente convexo metrizable de dimensión infinita y H(U) es el espacio de funciones holomorfas en U, entonces la topología de Nachbin-Coeuré en H(U) no es metrizable. Este resultado se utiliza para demostrar que las topologías habituales en H(U) son metrizables si y sólo si E tiene dimensión finita.

Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions

∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33

On the Generalized Associated Legendre Functions

Mathematics Subject Classification: 33C60, 33C20, 44A15

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.