1,720,962 research outputs found
HARDY TYPE INEQUALITIES INVOLVING GRADIENT OF DISTANCE FUNCTION
No full textWe prove several new Hardy type inequalities in Euclidean domains; these inequalities involve the gradient of the distance function from a point to the boundary of the domain. For test functions we consider improved inequalities in form proposed by Balinskv and Evans for convex domains. Namely, in Hardy type inequalities, instead of the gradient of the test function, one takes the scalar product of the gradients of the test function and of the distance from a point to the boundary of a given domain. In the present paper, integral Hardy type inequalities are studied in non-convex n-dimensional domains having a finite inradius. We prove three new Hardy type Lp-inequalities in an improved form with explicit estimates for the constants depending on the dimension of the Euclidean space n> 2, the inradius of the domain and two parameters p> 1, s >n. Our proofs are based on three key ingredients. The first of them is related with an approximation and a special partition of the domain, in particular, we employ the approximation of the domain by subsets formed by finitely many cubes with sides parallel to the coordinate planes. The second ingredient is the representation of the domain as a countable union of subdomains with piece-wise smooth boundaries and applying a new theorem by the author on convergence of the gradients of the distance functions for these subdomains. Moreover, we prove three new Hardy type inequalities on a finite interval, which are employed in justifying the inequalities in multi-dimensional domains
Conformal mappings of circular domains on finitely-connected non-smirnov type domains
Get PDF© Avkhadiev F.G., Shabalin P.L. 2017.We consider a canonical factorization and integral representation for the derivatives of the conformal mappings of circular domains on finitely-connected non-Smirnov type domains. By means of the functions in the Zygmund class, we obtain the conditions for the global univalence. Earlier similar results were obtained by a series of authors just for simply-connected domains
Conformal mappings of circular domains on finitely-connected non-smirnov type domains
No full text© Avkhadiev F.G., Shabalin P.L. 2017.We consider a canonical factorization and integral representation for the derivatives of the conformal mappings of circular domains on finitely-connected non-Smirnov type domains. By means of the functions in the Zygmund class, we obtain the conditions for the global univalence. Earlier similar results were obtained by a series of authors just for simply-connected domains
Brezis–Marcus Problem and its Generalizations
No full textCertain Hardy inequalities in domains of Euclidean space contain sharp but unreachable constants. V. G. Maz’ya and other authors used this fact to improve the corresponding inequalities by adding new integral terms. In this paper, a survey of results in this direction initiated by H. Brezis and M. Marcus is presented. Also, we give some generalizations of Brezis–Marcus-type inequalities to the case of Rellich-type inequalities with weights that are powers of the distance from a point to the boundary of the domain. Generalizations to the case of conformally invariant integral inequalities in simply connected and doubly connected planar hyperbolic domains are discussed
Properties and Applications of the Distance Functions on Open Sets of the Euclidean Space
No full text© 2020, Allerton Press, Inc. For an open subset of the Euclidean space of dimension n we consider interior and exterior approximations by sequences of open sets. We prove convergence everywhere of the corresponding sequences of distance functions from boundary as well as convergence almost everywhere for their gradients. As applications we obtain several new Hardy-type inequalities that contain the scalar product of gradients of test functions and the gradient of the distance function from the boundary of an open subset of the Euclidean space
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
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
A strong form of Hardy Type Inequalities on Domains of the Euclidean Space
No full textWe prove new integral inequalities for real-valued test functions defined on subdomainsof the Euclidean space. Namely, we obtain several new Hardy-type inequalities that contain thescalar product of gradients of test functions and of the gradient of the distance function from theboundary of an open subset of the Euclidean space.Our method of proof is based on interior and exterior approximations of a given domain bysequences of simplest domains and has two important ingredients. The first one is approximations ofa given domain by elementary domains that admit a special partition. The second ingredient is pre-sented in this paper by theorems 1 and 2 about convergence everywhere of the sequences of distancefunctions from boundary of approximating elementary domains as well as about convergence almosteverywhere for their gradients. In the proofs we also use some basic theorems due to Rademacher,Hardy, Motzkin and Hadwiger
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