Regularization of time-varying descriptor systems by the asvd

We study linear variable coefficient control problems in descriptor form. Based on a behaviour approach and the general theory for linear differential algebraic systems we give the theoretical analysis and describe numerically stable methods to determine the structural properties of the system.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

A multifractal zeta function for Gibbs measures supported on cookie-cutter sets

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures.

Involvement of Phosphatidylinositol-3 Kinase/AKT/PKC zeta/lambda Pathway in the Effect of Palmitate on Glucose-Induced Insulin Secretion

Objectives: In the present study, a novel pathway by which palmilate potentiates glucose-induced insulin secretion by pancreatic beta cells was investigated. Methods: Groups of freshly isolated islets were incubated in 10 mM glucose with palmitate, LY294002, wortmannin, and fumonism B I for measurement of insulin secretion by radioimmunoassay (RIA). Also, phosphorylation and content of AKT and PKC proteins were evaluated by immunoblotting. Results: Glucose plus palmitate and glucose plus LY294002 or wortmannin (PI3K inhibitors) increased glucose-induced insulin secretion by isolated pancreatic islets. Glucose at 10 mM induced AKT and PKC zeta/lambda phosphorylation. Palmitate (0.1 mM) abolished glucose stimulation of AKT and PKC zeta/lambda phosphorylation possibly through PI3K inhibition because both LY294002 (50 mu M) and wortmannin (100 nM) caused the same effect. The inhibitory effect of palmitate on glucose-induced AKT and PKC zeta/lambda phosphorylation and the stimulatory effect of palmitate on glucose-induced insulin secretion were not observed in the presence of fumonisin B1, all inhibitor of ceramide synthesis. Conclusions: These findings support the proposition that palmilate increases insulin release in the presence of 10 mM glucose by inhibiting PI3K activity through a mechanism that involves ceramide synthesis.

On the Barnes double zeta and Gamma functions

We present a complete description of the analytic properties of the Barnes double zeta and Gamma functions. (C) 2009 Elsevier Inc. All rights reserved.

Comments on regularization of identity based solutions in string field theory

We analyze the consistency of the recently proposed regularization of an identity based solution in open bosonic string field theory. We show that the equation of motion is satisfied when it is contracted with the regularized solution itself. Additionally, we propose a similar regularization of an identity based solution in the modified cubic superstring field theory.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Três métodos para o cálculo da série zeta(2n) de Riemann

Neste trabalho apresentamos três métodos distintos provando que S(n) = +1 X k=−1 (4k + 1)−n é um múltiplo racional de n para todos os inteiros n = 1, 2, 3, . . . O primeiro utiliza a teoria das função analíticas e funções geradoras. No segundo reduzimos o problema, via mudança de variável devida a E. Calabi, ao cálculo do volume de certos politopos em Rn enquanto que no terceiro usamos a teoria dos operadores integrais compactos. Cada um dos métodos tem um interesse intrínsico e está sujeito a generalizações para aplicações em novas situações.

A novel voltage step-down/up ZCS-PWM Zeta converter

This paper presents an analysis of a novel pulse-width-modulated (PWM) voltage step-down/up Zeta converter, featuring zero-current-switching (ZCS) at the active switches. The applications in de to de and ac to de (rectifier) operation modes are used as examples to illustrate the performance of this new ZCS-PWM Zeta converter. Regarding to the new ZCS-PWM Zeta rectifier proposed, it should be noticed that the average-current mode control is used in order to obtain a structure with high power-factor (HPF) and low total harmonic distortion (THD) at the input current.Two active switches (main and auxiliary transistors), two diodes, two small resonant inductors and one small resonant capacitor compose the novel ZCS-PWM soft-commutation cell, used in these new ZCS-PWM Zeta converters. In this cell, the turn-on of the active switches occurs in zero-current (ZC) and their turn-off in zero-current and zero-voltage (ZCZV). For the diodes, their turn-on process occurs in zero-voltage (ZV) and their reverse-recovery effects over the active switches are negligible. These characteristics make this cell suitable for Insulated-Gate Bipolar Transistors (IGBTs) applications.The main advantages of these new Zeta converters, generated from the new soft-commutation cell proposed, are possibility of obtaining isolation (through their accumulation inductors), and high efficiency, at wide load range. In addition, for the rectifier application, a high power factor and low THD in the input current ran be obtained, in agreement with LEC 1000-3-2 standards.The principle of operation, the theoretical analysis and a design example for the new de to de Zeta converter operating in voltage step-down mode are presented. Experimental results are obtained from a test unit with 500W output power, 110V(dc) output voltage, 220V(dc) input voltage, operating at 50kHz switching frequency. The efficiency measured at rated toad is equal to 97.3%for this new Zeta converter.Finally, the new Zeta rectifier is analyzed, and experimental results from a test unit rated at 500W output power, 110V(dc) output voltage, 220V(rms) input voltage, and operating at 50kHz switching frequency, are presented. The measured efficiency is equal to 96.95%, the power-factor is equal to 0.98, and the input current THD is equal to 19.07%, for this new rectifier operating at rated load.

Regularization and singular perturbation techniques for non-smooth systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)