We find an adequate interpretation of the Lamé operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lamé system.

In the thesis we investigate the connections between arbitrary functions and their realizing polynomials over finite algebras. We study functionally complete algebras, i.e. algebras over which every function can be realized by a polynomial expression. We characterize functional completeness by the so called Stone-Weierstrass property, and we determine the functionally complete semigroups and semirings. Then we investigate the computational perspective of the function-polynomial relationships over finite groups. We consider the efficient representability, the equivalence, and the equation solvability problems. We approach the efficient representability problem from three directions. We consider the length of functions, we investigate the circuit complexity of functions, and we analyse the finite-state sequential machine representation of Boolean functions. From each of these viewpoints we give bounds on the potential efficiency of computations based on functionally complete groups compared to computations based on the two-element Boolean algebra. Neither the equivalence problem nor the equation solvability problem has been completely characterized for finite groups. The complexity of the equivalence problem was only known for nilpotent groups. In the thesis we determine the complexity of the equivalence problem for certain meta-Abelian groups and for all non-solvable groups. The complexity of the equation solvability problem is known for nilpotent groups and for non-solvable groups. There are no results about the complexity of the equation solvability problem for solvable non-nilpotent groups apart from the case of certain meta-cyclic groups that we present in the thesis. Moreover, we determine the complexity of the equation solvability problem for all functionally complete algebra. The idea of the extended equivalence problem emerges from the observation that the commutator might significantly change the length of group-polynomials. We characterize the complexity of the extended equivalence problem for finite groups. For many finite groups we determine the complexity of the equivalence problem if the commutator is considered as the basic operation of the group.

The Neutron-star Interior Composition Explorer is an X-ray astrophysics payload that will be placed on the International Space Station. Its primary science goal is to measure with high accuracy the pulse profiles that arise from the non-uniform thermal surface emission of rotation-powered pulsars. Modeling general relativistic effects on the profiles will lead to measuring the radii of these neutron stars and to constraining their equation of state. Achieving this goal will depend, among other things, on accurate knowledge of the source, sky, and instrument backgrounds. We use here simple analytic estimates to quantify the level at which these backgrounds need to be known in order for the upcoming measurements to provide significant constraints on the properties of neutron stars. We show that, even in the minimal-information scenario, knowledge of the background at a few percent level for a background-to-source countrate ratio of 0.2 allows for a measurement of the neutron star compactness to better than 10% uncertainty for most of the parameter space. These constraints improve further when more realistic assumptions are made about the neutron star emission and spin, and when additional information about the source itself, such as its mass or distance, are incorporated.

On s'intéresse à la modélisation numérique des structures sandwichs trois couches à âme viscoélastique utilisées pour l'amortissement passif et le contrôle des vibrations dans divers domaines d’application tels que l’aéronautique, l’aérospatial, l’automobile et l’électroménager. La complexité de la modélisation en dynamique de ces structures est liée d'une part aux non linéarités matérielles dues à la dépendance en fréquence et en température de la rigidité et d'autre part aux non linéarités géométriques dues aux grands déplacements. Nous proposons dans ce travail un cadre de modélisation des vibrations linéaires et non linéaires des poutres et des plaques sandwichs avec la dépendance en fréquence du comportement viscoélastique. En couplant la méthode asymptotique numérique et les techniques de différentiation automatique, nous avons développé un algorithme générique de résolution du problème numérique de valeur propre complexe gouvernant les vibrations libres linéaires des structures sandwichs viscoélastiques. L'algorithme est implémenté sous un solveur numérique en langage Matlab et permet pour une structure sandwich donnée, de déterminer de façon directe et exacte les propriétés amortissantes et les modes propres de vibration, quelle que soit la non linéarité en fréquence de la loi viscoélastique. L'efficacité de l'algorithme est illustrée sur trois modèles viscoélastiques différents: le modèle à module constant, le modèle de Maxwell généralisé et le modèle à dérivées fractionnaires. Puis, nous avons présenté une théorie basée sur la méthode des éléments finis pour la modélisation des vibrations non linéaires des poutres sandwichs. Cette théorie combine la technique d'équilibrage harmonique à la méthode de Galerkin à un mode et permet de réduire le problème de vibration non linéaire à une équation d'amplitude complexe. La résolution de l'équation d'amplitude permet de caractériser les propriétés modales et les réponses en amplitude. L'évaluation du choix de la base de Galerkin pour différentes approximations des modes a permis de montrer l'inadéquation des modes réels classiquement utilisés dans l'analyse des vibrations linéaires et non linéaires. Enfin, la théorie est appliquée pour modéliser les vibrations non linéaires des plaques sandwichs. Les coefficients de l'équation d'amplitude gouvernant les vibrations non linéaires sont formulés dans le cadre élément fini et nécessitent la résolution numérique de trois problèmes: un problème de valeur propre complexe non linéaire et deux problèmes linéaires. Pour l'efficacité de la méthode numérique ainsi proposée, la base de Galerkin est améliorée en utilisant des modes complexes afin de prendre en compte l'amortissement dans les modes de vibration. Les résultats obtenus montrent l'effet des non linéarités géométriques, des conditions aux limites et de la température sur les propriétés modales et les réponses en amplitude / The problem of interest is the numerical modeling of three layered viscoelastic sandwich structures used for passive damping and vibration control. The complexity in the dynamic modeling of these structures lies in the presence on the one hand of the material nonlinearities due to the frequency and temperature dependence of the stiffness and on the other hand of the geometrical nonlinearities due to large amplitude vibrations. We propose in this work a modeling framework of linear and nonlinear vibrations of viscoelastic sandwich beams and plates that takes into account the frequency dependent behaviour. Coupling the asymptotic numerical method to automatic differentiation techniques, we developed a generic algorithm for the solution of the complex eigenvalue problem governing the linear free vibrations of viscoelastic sandwich structures. The algorithm is implemented using Matlab language and a numerical solver has been designed for direct and exact computation of damping properties and vibration modes, whatever the dependence on frequency of the viscoelastic law. The efficiency of the algorithm is illustrated on three different viscoelastic models: the constant modulus model, the generalized Maxwell model and the fractional derivative model. Then, we presented a finite element based theory for nonlinear vibration analysis of viscoelastic sandwich beams. This theory combines the harmonic balance technique to one mode Galerkin's procedure and allows to reduce the nonlinear vibration problem in a complex amplitude equation. Solving the amplitude equation yields the modal properties and the amplitude responses. An assessment of the Galerkin's basis choice for various eigenmodes approaches shows the inaccuracy of the classical real eigenmodes used for linear and nonlinear vibration analysis. The theory is applied to model the nonlinear vibrations of viscoelastic sandwich plates. The amplitude equation coefficients are established in the finite element framework by numerically solving three problems: a nonlinear complex eigenvalue problem and two linear problems. For the efficiency of the proposed method, the Galerkin's basis has been improved using complex eigenmodes in order to take account the damping in the vibration modes. The obtained results show the effects of geometrical nonlinearities, boundary conditions and temperature on the modal properties and amplitude responses

We consider two one-dimensional harmonic chains coupled along their length via linear springs. Casting the elastic wave equation for this system in a Dirac-like form reveals a directional representation. The elastic band structure, in a spectral representation, is constituted of two branches corresponding to symmetric and antisymmetric modes. In the directional representation, the antisymmetric states of the elastic waves possess a plane wave orbital part and a 4x1 spinor part. Two of the components of the spinor part of the wave function relate to the amplitude of the forward component of waves propagating in both chains. The other two components relate to the amplitude of the backward component of waves. The 4x1 spinorial state of the two coupled chains is supported by the tensor product Hilbert space of two identical subsystems composed of a non-interacting chain with linear springs coupled to a rigid substrate. The 4x1 spinor of the coupled system is shown to be in general not separable into the tensor product of the two 2x1 spinors of the uncoupled subsystems in the directional representation. (C) 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

A fairly general method for studying electromagnetic induction in cases where any lateral variations in conductivity are confined to the near-surface region is developed using the thin-sheet technique. The significant feature is that extended anomalies, subject only to the restriction that well-defined two-dimensional problems are approached at infinity, can be handled. The approximate boundary condition is that gradients parallel to the coordinate axes vanish at infinity. / Graduate

The object of this paper is to derive Landau's theory of quantized hydrodynamics from the many-particle Schroedinger equation. Landau's results are obtained, together with an additional term in the Hamiltonian.

In mathematical physics, Laplace's equation plays an especially significant role. It is fundamental to the solution of problems in electrostatics, thermodynamics, potential theory and other branches of mathematical physics. It is for this reason that this investigation concerns the development of some general properties of continuous solutions of this equation.

Perceived quality in the context of e-commerce was defined and examined in numerous studies, but, to date, there are no consistent definitions and measurement scales. Instruments that measure quality in e-commerce industries primarily focus on website quality or service quality during the transaction and delivery phases. Even though some scholars have proposed instruments from different perspectives, these scales do not fully evaluate the level of quality perceived by customers during the entire decision-making process. This dissertation purports to provide five main contributions for the e-commerce, service quality, and decision science literature: (1) development of a comprehensive instrument to measure how online customers perceive the quality of the shopping channel, website, transaction and recovery based on the customer decision making process; (2) identification of the determinants of customer satisfaction and the key dimensions of customer behavioral intentions in e-commerce; (3) examination of the relationships among perceived quality, customer satisfaction and loyalty intention using empirical data; (4) application of different statistical packages (LISREL and PLS-Graph) for data analysis and comparison of how these methods impact the results; and (5) examination of the moderating effects of control variables. A survey was designed and distributed to a total of 1126 college students in a large southwestern university in the U.S. Exploratory factor analysis, confirmatory factor analysis, and structural equation modeling with both LISREL and PLS-Graph are used to validate the comprehensive instrument and test the research hypotheses. The results provide theoretical and normative guidelines for researchers and practitioners in the e-commerce domain. The research results will also help e-commerce platform providers or e-retailers to improve their business and marketing strategies by providing a better understanding of the most important factors influencing customer behavioral intentions.

In this paper we consider an existence of a solution for a nonlinear nonmonotone wave equation in [0,π]xR and an existence of a positive solution for a non-positone Dirichlet problem in a bounded subset of R^n.