Reconstruction of an unsteady flow from incomplete boundary data:Part I. Theory

Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points

The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to direct sums of regularly solvable operators defined on the separate subintervals, there are other regularly solvable restrications of the maximal operator which involve linking the various intervals together in interface like style.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero

2000 Mathematics Subject Classification: 14B05, 32S25.

A Smooth Four-Dimensional G-Hilbert Scheme

2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.

Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)

2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

On Thom Polynomials for A4(−) via Schur Functions

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.

On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

Weak Langmuir optical turbulence in a fiber cavity

We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied.

A educação básica na região metropolitana de Natal: uma análise da qualidade educativa e sua relação com o contexto familiar dos alunos

This dissertation aimed to investigate the formal learning process of children and teenagers through elementary education and, mainly, the support of family on domestic school activities as a step in the teaching-learning process. The student's family, with its cultural capital, provides an assistance which was the bias of the essay analyzes presented on this paper, using a spatial area of public elementary schools of the municipalities of the Natal metropolitan region. Such frame of Natal metropolis has been justified by the recent review of their basic education, taken by the Brazilian Ministry of Education, diagnosed in 2011, only 1% of students were in a adequate mathematics learning stage. While 62% were considered in a critical stage in this discipline. Given this issue, this dissertation offers a theoretical analysis about inherited and acquired within the family cultural capital, mainly focusing in the distances between the cultural level of the student's family and the defendant by the school. Then, presents the fundamental aspects of the issue on the urban phenomenon, focusing on social hierarchies and structures of city spaces that express differentiation, segmentation and socio-spatial segregation, and social exclusion. The emphasis on inequalities points to the development of an urban ethos, through formal schooling, which develops from social singularities. To theoretically develop the theme of Cultural Capital Family, this study sought to operationalize the concept through the interpretation of the phenomenon studied by a logical validation work hypotheses. The operation concepts systemically transformed into statistical indicators in order to measure the impact of individual, social and cultural characteristics of students elements. Finally, this dissertation found that the components evaluated, family cultural capital and housing conditions, can influence the development of skills and competencies of students in the educational sphere

Acolhimento prescrito x real: uma análise sobre as relações entre trabalhadores e usuários na estratégia saúde da família

User embracement has been proposed as a tool that contributes to humanize the nursing, to increase the users’ access to the services, to ensure the resolvability of claims, to organize the services and promote the strengthening of the links between them and the health professionals. In the city of Recife, this practice has been fomented by the municipal government and its implementation is guided by normative acts, with evaluation matrices and proposition of goals, based on a model created by the public administration. This study intended to analyze the relation between the prescribed user embracement and the real one and their interferences with the relations of reciprocity between workers and users in the health units of basic attention in Recife. Four units of the Family Health Strategy at the Sanitary District IV of the city of Recife – PE were taken as an investigation field. The investigation had a qualitative character, so, Interviews were performed involving professionals and users whose speeches were recorded by the voice digital mode and literally transcript. The obtained speeches were analyzed mostly through the Discourse of the Collective Subject methodological approach, being also used, but on a smaller scale, the technique of thematic analysis, in the dialogic way, with theoretical contributions and official documents related to the theme. The results pointed that in most of the health units the professionals execute the proposed protocols and consider that these have a positive influence for the working process in user embracement, however, factors such as the excessive demand, the physical structure of the units, little resolvability of the reference network, singularities of the units, among others, have appeared, hampering the accomplishment of the prescribed, creating, thus, a negative influence on the working process of the user embracement. The reciprocal relations have also suffered the influences of these factors, which made difficult, therefore, the circulation of gift. Meanwhile, other factors such as access, resolvability, sheltering attitude and responsabilization, potentiated the reciprocal exchange between professionals and users. The findings demand the prescriptive acts and the reciprocal relations of the user embracement to be directly influenced by the singularities present in each community, by the human variabilities and by factors connected to the structure and working process, so it shall be operated with caution in order to provide a real user embracement with quality

Involução criadora: o maior e o menor na obra de Gilles Deleuze

This work is on the political thought of the French philosopher Gilles Deleuze (1925 – 1995) taking the concepts of major/minor as starting point, since by them the deleuzian philosophy produces significant approaches to think politics and its forms. Not only the concepts of major/minor, but also the concept of becoming, in the mode of becoming-minor, marks the proposition, as we could tell, a properly deleuzian political philosophy. Thus, this work attempts to expose the possible form of this politics and of a fight ethic associated to it. To study the Deleuze political thought today is not to abdicate of a political thought that recognizes the singularities and embraces the political fight not as a totalizing revolution, but as resistance. The analyses of the concepts of major/minor, and the becoming shows itself as necessary in the political proposal in the present context