1,721,003 research outputs found
Studies of some Operators of Harmonic Analysis in certain Function Spaces with Applications to PDEs
Get PDFThe study in this PhD thesis aims at development of certain mathematical methods used in applications, in particular, in the study of regularity properties of solutions in various mathematical models described by Partial Differential Equations (PDEs). To this end, we study various operators of harmonic analysis in certain function spaces, since solutions to many PDEs may be expressed in terms of such operators.
This PhD thesis consists of four papers (papers A--D) and an Introduction.
In Paper A we introduce a version of weighted anisotropic mixed norm Morrey spaces and anisotropic Hardy operators. We derive conditions for boundedness of these operators in such spaces. We also reveal the role of these operators in the solving of some degenerate hyperbolic PDEs of some class.
In Paper B we prove the boundedness of potential operators in weighted generalised Morrey space in terms of Matuszewska-Orlicz indices of weights and apply this result to the Helmholtz equation in R^3 with a free term in such a space. We also give a short overview of some typical situations when potential type operators arise when solving PDEs.
In Paper C we study the boundedness of some multi-dimensional Hardy type operators in Hölder spaces and derive some new results of interest also in the theory of inequalities.
In Paper D we prove some differentiation formulas for weighted singular integrals, which we suppose to apply in our future studies concerning the solution of some integral equations of the first kind.
These new results are put into a more general frame in an Introduction, where also crucial parts of previous research by the candidate (e.g. published in two Licentiate theses) are briefly described. Note, in particular, that this PhD thesis may be regarded as a more theoretically based continuation of the Licentiate thesis in Wood Technology. This important link is carefully described in the Introduction
Uma abordagem para análise, classificação e resolução de problemas que envolvem trigonometria : exemplos de aplicação
Get PDFComo professora de matemática, com experiência no Ensino Secundário, tenho constatado que os alunos revelam bastantes dificuldades de compreensão, aquisição e aplicação dos conteúdos trigonométricos. Também os conteúdos de trigonometria dos actuais manuais escolares do ensino secundário não são suficientes para aqueles alunos que pretendem seguir estudos superiores nas áreas da Física, da Matemática, da Engenharia, Este trabalho destina-se essencialmente a esse grupo de alunos, mas também pode servir de material de apoio a professores do Ensino Básico/Secundário que queiram enriquecer e aprofundar os seus conhecimentos nesta área. Ao longo deste trabalho, propomos uma forma alternativa de apresentação deste tema, pensamos que deste modo os alunos possam compreender "como, donde e porquê" aparecem as relações trigonométricas. Classificamos e analisamos em profundidade equações trigonométricas, com a finalidade de propor abordagens diferentes de resolução, umas típicas outras originais. Analisamos desigualdades trigonométricas e sistemas de equações trigonométricas utilizando métodos de resolução distintos. Apresentamos versões distintas de demonstrações para as mesmas afirmações, e apresentamos problemas de Geometria, de Topografia e de Física, mostrando desta forma a aplicação prática da Trigonometria. Finalizamos este trabalho com a apresentação de algumas relações trigonométricas na teoria dos Números Complexos. – ABSTRACT: School students, I have noticed that students have many difficulties in understanding trigonometric contents. The contents related to trigonometry that are presented, in modem textbooks adopted by Secondary Schools are not enough for those students who intend to take a degree in areas in field of physics, mathematics and engineering. This study is essentially intended for the above-mentioned students, but it can also be used as a support material for a secondary school teachers who want to enrich and increase their scientific knowledge in the field of trigonometry. This project suggests an alternative way to introduce the topic so that student can understand "how, from, where and why" trigonometric relationships appear. Trigonometric equations are classified and examined deeply in order to suggest different approaches for their solution, typical ones and original others. Trigonometric inequalities and systems of trigonometric equations of special types are also analysed using different solution methods. Different versions of demonstrations for the same statements are presented as well as problems of Geometry, Topography and Physics, with the purpose of showing the practical use of trigonometry. This project ends with the presentation of some trigonometric relationships in the theory of Complex Numbers
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
On research/academic fraudulence, corruption, and violation of publishing ethics. Issue 1: LTU case of academic fraudulence.
Get PDFAbstract: Objective facts regarding five articles of a corrupt team of LTU authors, where false authorship and/or violation of publishing ethics are evident, are provided with evidence in certain documents. All this looks rather as a scenario for Orwellian dystopia; however, it is a sad reality where a model of "rule of law" is based on deceitfulness and shamelessness
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On a Muckenhoupt-type condition for Morrey spaces
No full textAs is known, the class of weights for Morrey type spaces {Mathematical expression} for which the maximal and/or singular operators are bounded, is different from the known Muckenhoupt class A p of such weights for the Lebesgue spaces L p(Ω). For instance, in the case of power weights {Mathematical expression}, {Mathematical expression}, the singular operator (Hilbert transform) is bounded in {Mathematical expression}, if and only if -1 1 we also provide some λ-dependent á priori assumptions on weights and give some estimates of weighted norms {Mathematical expression} of the characteristic functions of balls</p
Weighted Hardy and singular operators in Morrey spaces
Get PDFAbstractWe study the weighted boundedness of the Cauchy singular integral operator SΓ in Morrey spaces Lp,λ(Γ) on curves satisfying the arc-chord condition, for a class of “radial type” almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces Lp,λ(0,ℓ), ℓ>0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy–Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves
Weighted Hardy operators in the local generalized vanishing Morrey spaces
No full textIn this paper we study {Mathematical expression}-boundedness of the multi-dimensional Hardy type operators in the vanishing local generalized Morrey spaces {Mathematical expression} defined by an almost increasing function {Mathematical expression} and radial type weight {Mathematical expression}. We obtain sufficient conditions, in terms of some integral inequalities imposed on {Mathematical expression} and {Mathematical expression}, for such a boundedness. In the case where the function {Mathematical expression} and the weight are power functions, these conditions are also necessary</p
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