The Semi-Group Property of Poisson Transformation and Snow's Inversion Formula

1963 ◽  
Vol 14 (2) ◽  
pp. 285 ◽  
Author(s):  
Harry Pollard
Keyword(s):  
Inversion Formula ◽  
Group Property ◽  
Semi Group ◽  
Poisson Transformation

PRESERVATION OF LOG-CONCAVITY AND LOG-CONVEXITY UNDER OPERATORS

2020 ◽  
pp. 1-14
Author(s):  
Wanwan Xia ◽  
Tiantian Mao ◽  
Taizhong Hu
Keyword(s):  
Distribution Function ◽  
Operations Research ◽  
Random Variable ◽  
Group Property ◽  
Semi Group ◽  
Real Numbers ◽  
Bernstein Type ◽  
Stochastic Comparisons ◽  
Weighted Distributions ◽  
The Family

Log-concavity [log-convexity] and their various properties play an increasingly important role in probability, statistics, operations research and other fields. In this paper, we first establish general preservation theorems of log-concavity and log-convexity under operator $\phi \longmapsto T(\phi , \theta )=\mathbb {E}[\phi (X_\theta )]$ , θ ∈ Θ, where Θ is an interval of real numbers or an interval of integers, and the random variable $X_\theta$ has a distribution function belonging to the family $\{F_\theta , \theta \in \Theta \}$ possessing the semi-group property. The proofs are based on the theory of stochastic comparisons and weighted distributions. The main results are applied to some special operators, for example, operators occurring in reliability, Bernstein-type operators and Beta-type operators. Several known results in the literature are recovered.

scholarly journals Duality and semi-group property for backward parabolic Itô equations

2010 ◽  
Vol 18 (1) ◽  
Author(s):  
Nikolai Dokuchaev
Keyword(s):  
Group Property ◽  
Semi Group

scholarly journals The Appell transform and the semigroup property for temperatures

1996 ◽  
Vol 60 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Elizabeth Kochneff ◽  
Yoram Sagher
Keyword(s):  
Heat Equation ◽  
Group Property ◽  
Semi Group ◽  
Semigroup Property ◽  
One Dimensional ◽  
The One

AbstractWe prove that if u(x, t) is a solution of the one dimensional heat equation and if A u(x, t) is its Appell transform, then u(x, t) has the semi-group (Huygens) property in a domain D if and only if A u(x, t) has the semi-group property in a dual region. We apply this result to simplify and extend some results of Rosenbloom and Widder.

scholarly journals A generalized sequential problem of Lane-Emden type via fractional calculus

2020 ◽  
Vol 6 (2) ◽  
pp. 168-183 ◽  
Author(s):  
Yazid Gouari ◽  
Zoubir Dahmani ◽  
Ameth Ndiaye
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Group Property ◽  
Semi Group ◽  
Singular Differential Equation ◽  
Banach Contraction ◽  
The Fixed Point Theorem

AbstractIn this paper, we combine the Riemann-Liouville integral operator and Caputo derivative to investigate a nonlinear time-singular differential equation of Lane Emden type. The considered problem involves n fractional Caputo derivatives under the conditions that neither commutativity nor semi group property is satisfied for these derivatives. We prove an existence and uniqueness analytic result by application of Banach contraction principle. Then, another result that deals with the existence of at least one solution is delivered and some sufficient conditions related to this result are established by means of the fixed point theorem of Schaefer. We end the paper by presenting to the reader some illustrative examples.

An inversion formula expressing the texture function in terms of angular distribution functions

1981 ◽  
Vol 42 (2) ◽  
pp. 161-165 ◽  
Author(s):  
J. Muller ◽  
C. Esling ◽  
H.J. Bunge
Keyword(s):  
Angular Distribution ◽  
Inversion Formula ◽  
Distribution Functions

Kelembagaan Masyarakat dan Struktur Agraria serta Keberlanjutan Sumberdaya Alam di Kawasan Capa

Agrotek ◽  
2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Mecky Sagrim
Keyword(s):  
Natural Resources ◽  
Local Community ◽  
Property Right ◽  
Local Institutions ◽  
Group Property ◽  
Young Shoot ◽  
Agrarian Structure

Aim of the research as follows: (1) inquisitive about variation of laws in regulating agrarian resources use, (2) function of traditional law in regulation at used of natural resources and related with existence on natural preservation-in formal law, and (3) inquiring influence outsider intervention to local institutions with the agrarian structure and relationship between expectation agrarian conflict. The unity of the study is Arfak community-as much as local community- was that administrative limited seatle in certain locations around natural preservation area of the Arfak Mountain. The trategy of the research is case study, while analysis of the data with qualitative manner. Result of the research is in the locations study beside property right of local community and movement of Arfak community from high land include at the resettlement programme. Not a problem related with economic subsistence with economic un-security because group property right community give free to the movement community for use to agriculture developing. For developing concept of forest sustainable as nit side to one side, income several NGO as well as role as institution relationship (young-shoot autonomy) for accommodation importance various party supra-village in relationship with existence natural preservation area of the Arfak Mountain and the party of local community in related of security in economic subsistence.

Sub-normed Z-linear Spaces on Commutative Semi-group

2012 ◽  
Vol 14 (2) ◽  
pp. 157
Author(s):  
Yanqiu WANG ◽  
Huaxin ZHAO
Keyword(s):  
Semi Group ◽  
Linear Spaces

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

scholarly journals Certain fundamental properties of generalized natural transform in generalized spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shrideh Khalaf Al-Omari ◽  
Serkan Araci
Keyword(s):  
Inversion Formula ◽  
Acta Math ◽  
Generalized Functions ◽  
General Nature ◽  
Qualitative Behavior ◽  
Fundamental Properties ◽  
Integrable Functions ◽  
Extended Operator ◽  
Definition Of ◽  
Space Of Integrable Functions

AbstractThis paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

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