Search results for "Functions"

Integral holomorphic functions

2004

We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Frechet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity. In this paper we define and study a class of holomorphic functions over infinite- dimensional Banach spaces admitting integral representation. Our purpose, and the motivation for our definition, are two-fold: we wish to obtain an integral repre- sentation formula …

Mapping properties for the Bargmann transform on modulation spaces

2010

We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.

Critical points for nondifferentiable functions in presence of splitting

2006

A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.

Indefinite integrals of special functions from inhomogeneous differential equations

2018

A method is presented for deriving integrals of special functions which obey inhomogeneous second-order linear differential equations. Inhomogeneous equations are readily derived for functions sati...

Matrix-based complexity functions and recognizable picture languages

2008

BMaD – A Boolean Matrix Decomposition Framework

2014

Boolean matrix decomposition is a method to obtain a compressed representation of a matrix with Boolean entries. We present a modular framework that unifies several Boolean matrix decomposition algorithms, and provide methods to evaluate their performance. The main advantages of the framework are its modular approach and hence the flexible combination of the steps of a Boolean matrix decomposition and the capability of handling missing values. The framework is licensed under the GPLv3 and can be downloaded freely at http://projects.informatik.uni-mainz.de/bmad.

Temporal and spatial diversification of the African disjunct genus Androcymbium (Colchicaceae)

2009

Abstract The genus Androcymbium (Colchicaceae) includes 57 species that are distributed in the extreme northern and southern portions of Africa, mainly in regions with a Mediterranean climate. We present the first phylogeographic analysis of the genus with species from all five of its distribution areas (North Africa, Horn of Africa, Namibia, western South Africa, and eastern South Africa). We used sequence data from six chloroplast regions and one nuclear region. Phylogeographic reconstructions were conducted using both parsimony and Bayesian inference methods. Molecular dating estimates using a Bayesian approach suggest a middle Miocene (13.4 ± 1.5 mya) origin of the genus; this approach …

Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables

2012

Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…

Approximation of fixed points of multifunctions in partial metric spaces

2013

Recently, Reich and Zaslavski [S. Reich and A.J. Zaslavski, Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings, Fixed Point Theory Appl. 2010 (2010), Article ID 518243, 10pages] have studied a new inexact iterative scheme for fixed points ofcontractive multifunctions. In this paper, using the partial Hausdorffmetric introduced by Aydi et al., we prove an analogous to a resultof Reich and Zaslavski for contractive multifunctions in the setting ofpartial metric spaces. An example is given to illustrate our result. 

Deciphering Biotic Interactions and Their Role in Soil Microbial Community Assembly and Functions

2022

Microbial communities play a key role in ecosystem functioning as well as in plant, animal, and human welfare. Their assembly relies on different processes commonly referred to as abiotic and biotic filters. Despite the widespread emphasis on abiotic filters in terrestrial ecosystems, a growing body of evidence suggests that interactions between microorganisms play a critical role in community assembly. However, the contribution of these interactions to microbial community assembly and the factors influencing them have not been clearly established. In most cases, biotic interactions between microorganisms have been investigated based on cocultures of a handful of strains, completely overloo…