125,493 research outputs found
Some Grüss Type Inequalities for Vector-Valued Functions in Banach Spaces and Applications
No full textSome Grüss type inequalities for the Bochner integral of vectorvalued
functions in real or complex Banach spaces are given. Applications in
connection to the Heisenberg inequality for functions with values in Hilbert
spaces are also pointed out
On Bochner Flat Kähler B-Manifolds
No full textWe obtain on a Kähler B-manifold (i.e., a Kähler manifold with a Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning the Bochner curvature. We prove that such a manifold is of constant totally real sectional curvatures if and only if it is a holomorphic Einstein, Bochner flat manifold. Moreover, we provide the necessary and sufficient conditions for a gradient Ricci soliton or a holomorphic η-Einstein Kähler manifold with a Norden metric to be Bochner flat. Finally, we show that a Kähler B-manifold is of quasi-constant totally real sectional curvatures if and only if it is a holomorphic η-Einstein, Bochner flat manifold
Hermite-Hadamard's Inequality and the p-HH-Norm on the Cartesian Product of Two Copies of a Normed Space
No full textThe Cartesian product of two copies of a normed space is naturally equipped with
the well-known p-norm. In this paper, another notion of norm is introduced, and will be
called the p-HH-norm. This norm is an extension of the generalised logarithmic mean and is
connected to the p-norm by the Hermite-Hadamard's inequality. The Cartesian product space
(with respect to both norms) is complete, when the (original) normed space is. A proof for the
completeness of the p-HH-norm via Ostrowski's inequality is provided. This space is embedded
as a subspace of the well-known Lebesgue-Bochner function space (as a closed subspace, when
the norm is a Banach norm). Consequently, its geometrical properties are inherited from those
of Lebesgue-Bochner space. An explicit expression of the superior (inferior) semi-inner product
associated to both norms is considered and used to provide alternative proofs for the smoothness
and reflexivity of this space
On Bochner-Krall orthogonal polynomial systems
No full textIn this paper we address the classical question going back to S. Bochner and H. L. Krall to describe all systems of orthogonal polynomials (OPS) which are the eigenfunctions of some finite order differential operator. Such systems of orthogonal polynomials are called Bochner-Krall OPS (or BKS for short) and their spectral differential operators are accordingly called Bochner-Krall operators (or BK-operators for short). We show that the leading coefficient of a Nevai type BK-operator is of the form . This settles the special case of the general conjecture 7.3. of [4] describing the leading terms of all BK-operators
Human Mast-cells Adhere To Extracellular-matrix Proteins Through Their Selective Expression of Beta-1 Integrins
No full textGoing Beyond Counting First Authors in Author Co-citation Analysis
No full textThe 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
Human Skin Mast-cells Express Functional Beta(1) Integrins That Mediate Adhesion To Extracellular-matrix Proteins
No full textLos Espacios de Sobolev-Bochner
No full textTraballo Fin de Grao en Matemáticas. Curso 2020-2021[ES] En este trabajo hablaremos sobre los espacios de Sobolev-Bochner Wᵐ,ᵖ(B). Estos
espacios son una generalización de los espacios de Sobolev Wᵐ,ᵖ(I), cuya construcción
se debe al matemático ruso Serguéi Sobolev. No obstante, para poder definir los espacios
de Sobolev-Bochner a partir de estos últimos será necesario debilitar la noción clásica de
derivada y definir un nuevo tipo de integral, además de dejar atrás el uso de funciones con
valores en un espacio vectorial de dimensión finita para emplear funciones cuya imagen es té contenida en un espacio de Banach genérico. Además, los espacios de Sobolev-Bochner
Wᵐ,ᵖ(B) tienen especial interés, sobre todo, en el estudio de la existencia de soluciones
de ciertas ecuaciones en derivadas parciales como, por ejemplo, las ecuaciones de evolución parabólicas. Entre dichas ecuaciones se encuentra la ecuación del calor, cuyo análisis
matemático está entre los objetivos de este trabajo.[EN] In this document we will talk about the Sobolev-Bochner spaces Wᵐ,ᵖ(B). These spaces are a generalisation of the Sobolev spaces Wᵐ,ᵖ(I), whose construction is due to the
Russian mathematician Serguéi Sobolev. However, in order to define the Sobolev-Bochner
spaces from the latter, it will be necessary to weaken the classical notion of derivative and
to define a new type of integral, as well as to leave behind the use of functions with values
in a finite-dimensional vector space in order to use functions whose image is contained in
a generic Banach space. Furthermore, the Sobolev-Bochner spaces Wᵐ,ᵖ(B) are of special
interest, above all, in the study of the existence of solutions of certain equations in partial
derivatives such as, for example, the parabolic evolution equations. Among these equations
is the heat equation, whose mathematical analysis is among the objectives of this wor
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Bochner vs. Pettis norm: examples and results
No full text. Our basic example shows that for an arbitrary infinite-dimensional Banach space X, the Bochner norm and the Pettis norm on L 1 (X) are not equivalent. Refinements of this example are then used to investigate various modes of sequential convergence in L 1 (X). 1. INTRODUCTION Over the years, the Pettis integral along with the Pettis norm have grabbed the interest of many. In this note, we wish to clarify the differences between the Bochner and the Pettis norms. We begin our investigation by using Dvoretzky's Theorem to construct, for an arbitrary infinite-dimensional Banach space, a sequence of Bochner integrable functions whose Bochner norms tend to infinity but whose Pettis norms tend to zero. By refining this example (again working with an arbitrary infinite-dimensional Banach space), we produce a Pettis integrable function that is not Bochner integrable and we show that the space of Pettis integrable functions is not complete. Thus our basic example provides a unified constructive..
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