Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Nonexistence of global solutions for a class of complex vector fields on two-torus

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon C(infinity) (S(1) ; R), defined on two-torus T(2) congruent to R(2)/2 pi Z(2). The kernel of transpose operator L is described and the solvability near the characteristic set is also studied. (c) 2008 Elsevier Inc. All rights reserved.

Acompanhando o crescimento e o desenvolvimento da criança : uma intervenção integrada entre enfermagem e família

The accompanying the growth and development of the child is the guiding line of basic health measures directed at this public, acting within the scope of health monitoring and inferring positively in the rate of infant morbidity and mortality, which are still a preoccupation worldwide and in Brazil. However, mostly, this practice is based on the biomedical model of care, individualized, with emphasis on the medicalization and complaints, favoring the passivity of users. Given this issue, aim to develop accompanying the growth and development of the child in a Basic Unit Family Health, through a collective approach of medical care next to a health team, especially nurses and caregivers. This is a qualitative study, with the research-action method. Involved the four nurses and twenty-six of children's caregivers of the area of Basic Unit Family Health of Cidade Nova, in Natal, in the period from February to July 2010. The results were analyzed following the direction of the thematic analysis of Freire. In the situation analysis of the current reality of the accompanying the growth and development the children in the Basic Unit Family Health, through participant observation and applying a questionnaire to the nurses, we realize that despite these professionals have a knowledge tied to the paradigm of health promotion, in practice the monitoring of child is done through individual consultations in outpatient room, based on complaints brought by caregivers, with little solvability in actions employed. Given the need for change in medical care model, we decided jointly, in the focal group, for the collective monitoring of children's the growth and development, featuring then this proposal to the multidisciplinary team, discussing the participation of professional categories and planned collectively the actions. In the implementation stage of collective action, we contemplate the execution by the caregivers of anamnesis and physical examination, recording data in the Child Health Handbook and discussion of clinical findings, under the supervision of nurses and facilitators. In the evaluation, we found that this collective accompanying strategy allowed to caregivers learn new knowledge, exchange experiences, assistance in home care, beyond reduce the waiting time for medical care and creating opportunity of more time for debate about the children‟s health situation, differing of ambulatory care. As difficulties, we face with a high rate of defaulters (53.8%), lack of motivation and passivity of the users, little participation of other health professionals and nurses' involvement in other activities, technical and bureaucratic in the moment of care. Thus, we note also a strong rooting of individual clinical model on the way of thinking and acting of nurses and caregivers

General structures of Hamiltonian hierarchies

Three dimensional exactly solvable quantum potentials for which an extra term of form 1/r(2) has been added are shown to maintain their functional form which allows the construction of the Hamiltonian hierarchy and the determination of the spectra of eigenvalues and eigenfunctions within the Supersymmetric Quantum Mechanics formalism. For the specific cases of the harmonic oscillator and the Coulomb potentials, known as pseudo-harmonic oscillator and pseudo-Coulomb potentials, it is shown here that the inclusion of the new term corresponds to rescaling the angular momentum and it is responsible for maintaining their exact solvability.

Multistable behavior above synchronization in a locally coupled Kuramoto model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Approximate expression for the energy of a D-dimensional anharmonic oscillator

An approximate expression is constructed for the energy of an anharmonic potential with centrifugal barrier. In order to obtain such an analytical expression, the quasi-exact solvability is used and then a fitting of these exact solutions is done.

Hamiltonian hierarchy of pseudo-potentials

The general structure of the Hamiltonian hierarchy of the pseudo-Coulomb and pseudo-Harmonic potentials is constructed by the factorization method within the supersymmetric quantum mechanics (SQMS) formalism. The excited states and spectra of eigenfunctions of the potentials are obtained through the generation of the members of the hierarchy. It is shown that the extra centrifugal term added to the Coulomb and Harmonic potentials maintain their exact solvability.

So(2,1) Lie algebra and the Green's functions for the conditionally exactly solvable potentials

The Green's functions of the recently discovered conditionally exactly solvable potentials are computed. This is done through the use of a second-order differential realization of the so(2,1) Lie algebra. So we present the dynamical symmetry underlying the solvability of such potentials and show that they belong to a general class of solvable and partially solvable potentials. © 1994 The American Physical Society.

Problemas de valor de contorno não clássicos: uma abordagem usando funções de Green

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Measure Functional Differential Equations in the Space of Functions of Bounded Variation

We establish general conditions for the unique solvability of nonlinear measure functional differential equations in terms of properties of suitable linear majorants.

Dynamical algebra of quasi-exactly-solvable potentials

We show that by using second-order differential operators as a realization of the so(2,1) Lie algebra, we can extend the class of quasi-exactly-solvable potentials with dynamical symmetries. As an example, we dynamically generate a potential of tenth power, which has been treated in the literature using other approaches, and discuss its relation with other potentials of lowest orders. The question of solvability is also studied. © 1991 The American Physical Society.

Organização da demanda de um Centro de Especialidades Odontológicas

Introduction: Secondary care in oral health in Brazil is still a little researched topic. Objective: The aim of this study was to analyze the resolution of dental services in SUS based on the referral to secondary attention and backreferral to primary attention. Methodology: It’s a descriptive, quantitative study that used secondary data collected from dental records of patients seen at Centre of Dental Specialties (Ceo) in a city of São Paulo State. Result: It was analyzed 1030 dental records. Just 1236 proceedings received referral to Ceo and among then, 86.4% showed the first attendance on Basic Health Unity (UBS) through spontaneous demand and 50.4% (n=623) received referral to endodontic treatment. There was evasion of 2.27% of studied population (n=28) on the first specialized consultation. Among 1208 proceedings that started the treatment in Ceo, 62.6% (n=757) were finalized and received back-referral to primary attention, that finalized 61.1% (n=463) of proceedings. To conclude the treatment, considering the time spent in Ceo and primary attention, there was variation according to specialty: periodontics – 62 days (sd ±68) and endodontics – 71 days (sd ±51.8), requiring 3 consultations in average, regardless specialty. Conclusion: The Centre of Dental Specialties gave referral and attention to the majority of demand, regardless specialty. However, there are many cases of evasion during dental treatment, alerting managers to develop methods to entice these patients, reducing service expenses and raising solvability of dental procedures previously initiated.

Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.