Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Divisibility of Trinomials by Irreducible Polynomials over F_2

Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials x^m + x^s + 1 to the trinomials x^am + x^bs + 1.

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

Moments of classical orthogonal polynomials

The aim of this work is to find simple formulas for the moments mu_n for all families of classical orthogonal polynomials listed in the book by Koekoek, Lesky and Swarttouw. The generating functions or exponential generating functions for those moments are given.

On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

Multisensor Modeling Underwater with Uncertain Information

This thesis develops an approach to the construction of multidimensional stochastic models for intelligent systems exploring an underwater environment. It describes methods for building models by a three- dimensional spatial decomposition of stochastic, multisensor feature vectors. New sensor information is incrementally incorporated into the model by stochastic backprojection. Error and ambiguity are explicitly accounted for by blurring a spatial projection of remote sensor data before incorporation. The stochastic models can be used to derive surface maps or other representations of the environment. The methods are demonstrated on data sets from multibeam bathymetric surveying, towed sidescan bathymetry, towed sidescan acoustic imagery, and high-resolution scanning sonar aboard a remotely operated vehicle.

Prediction of glucose excursions under uncertain parameters and food intake in intensive insulin therapy for type 1 diabetes mellitus

Considering the difficulty in the insulin dosage selection and the problem of hyper- and hypoglycaemia episodes in type 1 diabetes, dosage-aid systems appear as tremendously helpful for these patients. A model-based approach to this problem must unavoidably consider uncertainty sources such as the large intra-patient variability and food intake. This work addresses the prediction of glycaemia for a given insulin therapy face to parametric and input uncertainty, by means of modal interval analysis. As result, a band containing all possible glucose excursions suffered by the patient for the given uncertainty is obtained. From it, a safer prediction of possible hyper- and hypoglycaemia episodes can be calculated

Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

Active control of structures with uncertain coupled subsystems and actuator dynamics

This paper deals with the problem of stabilizing a class of structures subject to an uncertain excitation due to the temporary coupling of the main system with another uncertain dynamical subsystem. A Lyapunov function based control scheme is proposed to attenuate the structural vibration. In the control design, the actuator dynamics is taken into account. The control scheme is implemented by using only feedback information of the main system. The effectiveness of the control scheme is shown for a bridge platform with crossing vehicle

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

A proposal for the diagnosis of uncertain dynamic systems based on interval models

The performance of a model-based diagnosis system could be affected by several uncertainty sources, such as,model errors,uncertainty in measurements, and disturbances. This uncertainty can be handled by mean of interval models.The aim of this thesis is to propose a methodology for fault detection, isolation and identification based on interval models. The methodology includes some algorithms to obtain in an automatic way the symbolic expression of the residual generators enhancing the structural isolability of the faults, in order to design the fault detection tests. These algorithms are based on the structural model of the system. The stages of fault detection, isolation, and identification are stated as constraint satisfaction problems in continuous domains and solved by means of interval based consistency techniques. The qualitative fault isolation is enhanced by a reasoning in which the signs of the symptoms are derived from analytical redundancy relations or bond graph models of the system. An initial and empirical analysis regarding the differences between interval-based and statistical-based techniques is presented in this thesis. The performance and efficiency of the contributions are illustrated through several application examples, covering different levels of complexity.

Application of modal interval analysis to the simulation of the behaviour of dynamic systems with uncertain parameters

Els models matemàtics quantitatius són simplificacions de la realitat i per tant el comportament obtingut per simulació d'aquests models difereix dels reals. L'ús de models quantitatius complexes no és una solució perquè en la majoria dels casos hi ha alguna incertesa en el sistema real que no pot ser representada amb aquests models. Una forma de representar aquesta incertesa és mitjançant models qualitatius o semiqualitatius. Un model d'aquest tipus de fet representa un conjunt de models. La simulació del comportament de models quantitatius genera una trajectòria en el temps per a cada variable de sortida. Aquest no pot ser el resultat de la simulació d'un conjunt de models. Una forma de representar el comportament en aquest cas és mitjançant envolupants. L'envolupant exacta és complete, és a dir, inclou tots els possibles comportaments del model, i correcta, és a dir, tots els punts dins de l'envolupant pertanyen a la sortida de, com a mínim, una instància del model. La generació d'una envolupant així normalment és una tasca molt dura que es pot abordar, per exemple, mitjançant algorismes d'optimització global o comprovació de consistència. Per aquesta raó, en molts casos s'obtenen aproximacions a l'envolupant exacta. Una aproximació completa però no correcta a l'envolupant exacta és una envolupant sobredimensionada, mentre que una envolupant correcta però no completa és subdimensionada. Aquestes propietats s'han estudiat per diferents simuladors per a sistemes incerts.

Robust Control of Systems Subjected to Uncertain Disturbances and Actuator Dynamics

Esta tesis está enfocada al diseño y validación de controladores robustos que pueden reducir de una manera efectiva las vibraciones structurales producidas por perturbaciones externas tales como terremotos, fuertes vientos o cargas pesadas. Los controladores están diseñados basados en teorías de control tradicionalamente usadas en esta area: Teoría de estabilidad de Lyapunov, control en modo deslizante y control clipped-optimal, una técnica reciente mente introducida : Control Backstepping y una que no había sido usada antes: Quantitative Feedback Theory. La principal contribución al usar las anteriores técnicas, es la solución de problemas de control estructural abiertos tales como dinámicas de actuador, perturbaciones desconocidas, parametros inciertos y acoplamientos dinámicos. Se utilizan estructuras típicas para validar numéricamente los controladores propuestos. Especificamente las estructuras son un edificio de base aislada, una plataforma estructural puente-camión y un puente de 2 tramos, cuya configuración de control es tal que uno o mas problemas abiertos están presentes. Se utilizan tres prototipos experimentales para implementar los controladores robustos propuestos, con el fin de validar experimentalmente su efectividad y viabilidad. El principal resultado obtenido con la presente tesis es el diseño e implementación de controladores estructurales robustos que resultan efectivos para resolver problemas abiertos en control estructural tales como dinámicas de actuador, parámetros inciertos, acoplamientos dinámicos, limitación de medidas y perturbaciones desconocidas.

Private long-term investment in uncertain times. Bruegel Policy Contribution 2012/23, December 2012

The economic and financial crisis in Europe is affecting the financing of long-term infrastructure investment. There are multiple clearly identifiable channels: reduced demand for long-term investment, a tightening prudential framework for lending, upward adjustment of risk perception, complex transition of the financial system, and increasing macroeconomic, sovereign and regulatory risk. Some of the identified channels are potentially dangerous spillovers from the crisis that entail the risk of a downward spiral (eg increasing regulatory risk), while others are efficient market responses (eg reduced investment demand, correction of pricing of risk). Consequently, public policy instruments should not address the accessibility of long-term finance per se, but should explicitly target the critical channels.