On a new Class of Tempered Stable Distributions: Moments and Regular Variation

We extend the class of tempered stable distributions, which were first introduced in Rosiński (2007). Our new class allows for more structure and more variety of the tail behaviors. We discuss various subclasses and the relations between them. To characterize the possible tails, we give detailed results about finiteness of various moments. We also give necessary and sufficient conditions for the tails to be regularly varying. This last part allows us to characterize the domain of attraction to which a particular tempered stable distribution belongs.

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On a topology between Tα and Tγα

Filomat ◽

10.2298/fil1910209a ◽

2019 ◽

Vol 33 (10) ◽

pp. 3209-3221

Author(s):

Dimitrije Andrijevic

Keyword(s):

Topological Space ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Closure Operators ◽

New Class ◽

Necessary And Sufficient

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

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Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems

Mathematics ◽

10.3390/math8050749 ◽

2020 ◽

Vol 8 (5) ◽

pp. 749 ◽

Cited By ~ 1

Author(s):

Yury Khokhlov ◽

Victor Korolev ◽

Alexander Zeifman

Keyword(s):

Limit Theorems ◽

Probability Distributions ◽

Sufficient Conditions ◽

Stable Distributions ◽

Necessary And Sufficient Conditions ◽

Independent Random Variables ◽

Random Vectors ◽

Scale Mixtures ◽

Elliptically Contoured ◽

Necessary And Sufficient

In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution are introduced. Some properties of these distributions are discussed. The main focus is on the representations of the corresponding random vectors as products of independent random variables and vectors. In these products, relations are traced of the distributions of the involved terms with popular probability distributions. As examples of distributions of the class of scale mixtures of multivariate stable distributions, multivariate generalized Linnik distributions and multivariate generalized Mittag–Leffler distributions are considered in detail. Their relations with multivariate ‘ordinary’ Linnik distributions, multivariate normal, stable and Laplace laws as well as with univariate Mittag–Leffler and generalized Mittag–Leffler distributions are discussed. Limit theorems are proved presenting necessary and sufficient conditions for the convergence of the distributions of random sequences with independent random indices (including sums of a random number of random vectors and multivariate statistics constructed from samples with random sizes) to scale mixtures of multivariate elliptically contoured stable distributions. The property of scale-mixed multivariate elliptically contoured stable distributions to be both scale mixtures of a non-trivial multivariate stable distribution and a normal scale mixture is used to obtain necessary and sufficient conditions for the convergence of the distributions of random sums of random vectors with covariance matrices to the multivariate generalized Linnik distribution.

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A unifying approach for some nonexpansiveness conditions on modular vector spaces

Nonlinear Analysis Modelling and Control ◽

10.15388/namc.2020.25.18044 ◽

2020 ◽

Vol 25 (5) ◽

Cited By ~ 1

Author(s):

Andrea Bejenaru ◽

Mihai Postolache

Keyword(s):

Fixed Points ◽

Banach Spaces ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Vector Spaces ◽

Minimizing Sequences ◽

Ishikawa Iteration ◽

New Class ◽

Condition C ◽

Necessary And Sufficient

This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

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Positive fractional 2D continuous-discrete linear systems

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.2478/v10175-011-0071-5 ◽

2011 ◽

Vol 59 (4) ◽

pp. 575-579 ◽

Cited By ~ 3

Author(s):

T. Kaczorek

Keyword(s):

Linear Systems ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

New Class ◽

Discrete Linear Systems ◽

Necessary And Sufficient

Positive fractional 2D continuous-discrete linear systemsA new class of positive fractional 2D continuous-discrete linear systems is introduced. The solution to the equations describing by the new class of systems is derived. Necessary and sufficient conditions for the positivity of the fractional 2D continuous-discrete linear systems are established.

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ON A NEW CLASS OF IMPLICATIONS: (g,min)-IMPLICATIONS AND SEVERAL CLASSICAL TAUTOLOGIES

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512500018 ◽

2012 ◽

Vol 20 (01) ◽

pp. 1-20 ◽

Cited By ~ 14

Author(s):

HUA-WEN LIU

Keyword(s):

Classical Logic ◽

Functional Equations ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Triangular Norms ◽

Basic Properties ◽

New Class ◽

Fuzzy Implications ◽

Necessary And Sufficient

A new class of fuzzy implications, called (g, min )-implications, is introduced by means of the additive generators of continuous Archimedean t-conorms, called g-generators. Basic properties of these implications are discussed. It is shown that the (g, min )-implications are really a new class different from the known ( S , N )-, R -, QL - and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz. law of importation, contraction law and distributivity over triangular norms ( t -norms) and triangular conorms ( t -conorms) are investigated. A series of necessary and sufficient conditions are proposed, under which the corresponding functional equations are satisfied.

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On branchwise implicative BCI-algebras

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171202004970 ◽

2002 ◽

Vol 29 (7) ◽

pp. 417-425 ◽

Cited By ~ 2

Author(s):

Muhammad Anwar Chaudhry

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

New Class ◽

Necessary And Sufficient

We introduce a new class of BCI-algebras, namely the class of branchwise implicative BCI-algebras. This class contains the class of implicative BCK-algebras, the class of weakly implicative BCI-algebras (Chaudhry, 1990), and the class of medial BCI-algebras. We investigate necessary and sufficient conditions for two types of BCI-algebras to be branchwise implicative BCI-algebras.

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Boolean Zero Square (BZS) Semigroups

Sultan Qaboos University Journal for Science [SQUJS] ◽

10.53539/squjs.vol26iss1pp31-39 ◽

2021 ◽

Vol 26 (1) ◽

pp. 31-39

Author(s):

Pinto G.A.

Keyword(s):

Inverse Semigroup ◽

Simple Semigroup ◽

Sufficient Conditions ◽

Zero Element ◽

Necessary And Sufficient Conditions ◽

Equivalence Relations ◽

New Class ◽

Necessary And Sufficient

We introduce a new class of semigroups, that we call BZS - Boolean Zero Square-semigroups. A semigroup S with a zero element, 0, is said to be a BZS semigroup if, for every , we have or . We obtain some properties that describe the behaviour of the Green’s equivalence relations , , and . Necessary and sufficient conditions for a BZS semigroup to be a band and an inverse semigroup are obtained. A characterisation of a special type of BZS completely 0-simple semigroup is presented.

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Exchange Ideals with All Idempotents Central

Algebra Colloquium ◽

10.1142/s1005386713000618 ◽

2013 ◽

Vol 20 (04) ◽

pp. 643-652

Author(s):

Huanyin Chen

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

New Class ◽

Necessary And Sufficient

In this paper we investigate necessary and sufficient conditions on an ideal under which it is an exchange ideal with all idempotents central. Related examples are constructed by means of ideal-extensions. A kind of uniqueness in such ideals is also studied. These provide a new class of such ideals.

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Reachability of Cone Fractional Continuous-Time Linear Systems

International Journal of Applied Mathematics and Computer Science ◽

10.2478/v10006-009-0008-4 ◽

2009 ◽

Vol 19 (1) ◽

pp. 89-94 ◽

Cited By ~ 12

Author(s):

Tadeusz Kaczorek

Keyword(s):

Linear System ◽

Linear Systems ◽

Continuous Time ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Fractional Systems ◽

New Class ◽

Necessary And Sufficient ◽

Time Linear

Reachability of Cone Fractional Continuous-Time Linear SystemsA new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.

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