scholarly journals Equivalent Characterization on Besov Space

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Cong He ◽  
Jingchun Chen
Keyword(s):  
Besov Space ◽  
Fourier Multiplier ◽  
Mixed Derivative ◽  
Real Interpolation ◽  
Single Variable ◽  
Equivalent Relation ◽  
Equivalent Characterization

In this paper, we give an equivalent characterization of the Besov space. This reveals the equivalent relation between the mixed derivative norm and single-variable norm. Fourier multiplier, real interpolation, and Littlewood-Paley decomposition are applied.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

Induced L-bornological vector spaces and L-Mackey convergence1

2021 ◽  
Vol 40 (1) ◽  
pp. 1277-1285
Author(s):  
Zhen-yu Jin ◽  
Cong-hua Yan
Keyword(s):  
Complete Lattice ◽  
Vector Spaces ◽  
Specific Description ◽  
Equivalent Characterization ◽  
Fuzzy Setting

Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.

Representations and cohomologies of regular Hom-pre-Lie algebras

2019 ◽  
Vol 19 (08) ◽  
pp. 2050149
Author(s):  
Shanshan Liu ◽  
Lina Song ◽  
Rong Tang
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Cohomology Theory ◽  
Trivial Representation ◽  
Linear Deformation ◽  
Dual Representations ◽  
Regular Representations ◽  
Equivalent Characterization ◽  
Tensor Representations

In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of regular Hom-pre-Lie algebras in terms of the cohomology theory of regular Hom-Lie algebras. As applications, we study linear deformations of regular Hom-pre-Lie algebras, which are characterized by the second cohomology groups of regular Hom-pre-Lie algebras with the coefficients in the regular representations. The notion of a Nijenhuis operator on a regular Hom-pre-Lie algebra is introduced which can generate a trivial linear deformation of a regular Hom-pre-Lie algebra. Finally, we introduce the notion of a Hessian structure on a regular Hom-pre-Lie algebra, which is a symmetric nondegenerate 2-cocycle with the coefficient in the trivial representation. We also introduce the notion of an [Formula: see text]-operator on a regular Hom-pre-Lie algebra, by which we give an equivalent characterization of a Hessian structure.

scholarly journals ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhi-Ang Zhou
Keyword(s):  
Saddle Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Saddle Points ◽  
Linear Spaces ◽  
Equivalent Characterization ◽  
Generalized Cone Subconvexlikeness ◽  
Real Linear ◽  
The Relationship

We studyϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization ofϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between theϵ-Henig saddle point of the Lagrangian set-valued map and theϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.

Exceptional algebraic properties of the three quadratic irrationalities observed in quasicrystals

2001 ◽  
Vol 79 (2-3) ◽  
pp. 687-696 ◽  
Author(s):  
Z Masáková ◽  
J Patera ◽  
E Pelantová
Keyword(s):  
Binary Operation ◽  
Rational Numbers ◽  
Point Sets ◽  
Irrational Numbers ◽  
Algebraic Properties ◽  
Equivalent Characterization

There are only three irrationalities directly related to experimentally observed quasicrystals, namely, those which appear in extensions of rational numbers by Ö5, Ö2, Ö3. In this article, we demonstrate that the algebraically defined aperiodic point sets with precisely these three irrational numbers play an exceptional role. The exceptional role stems from the possibility of equivalent characterization of these point sets using one binary operation. PACS Nos.: 61.90+d, 61.50-f

scholarly journals On a conjecture of Seneta on regular variation of truncated moments

2021 ◽  
Vol 109 (123) ◽  
pp. 77-82
Author(s):  
Péter Kevei
Keyword(s):  
Distribution Function ◽  
Relative Stability ◽  
Regular Variation ◽  
Domain Of Attraction ◽  
Random Variable ◽  
Nonnegative Random Variable ◽  
Equivalent Characterization ◽  
Regularly Varying ◽  
Normal Law

We prove that h?(x) = ??x0 y??1F?(y)dy is regularly varying with index ? [0, ?) if and only if V?(x) = ?[0,x] y?dF(y) is regularly varying with the same index, where ? > 0, F(x) is a distribution function of a nonnegative random variable, and F?(x) = 1?F(x). This contains at ? = 0, ?= 1 a result of Rogozin [8] on relative stability, and at ? = 0, ? = 2 a new, equivalent characterization of the domain of attraction of the normal law. For ? = 0 and ? > 0 our result implies a recent conjecture by Seneta [9].

scholarly journals On Well-Founded and Recursive Coalgebras

2020 ◽  
pp. 17-36
Author(s):  
Jiří Adámek ◽  
Stefan Milius ◽  
Lawrence S. Moss
Keyword(s):  
General Proof ◽  
Initial Algebra ◽  
Equivalent Characterization ◽  
Algebra Morphism ◽  
Recursion Theorem ◽  
The Relationship ◽  
Well Foundedness

AbstractThis paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a new, shorter proof that this is the coreflection in the category of all well-founded coalgebras. We present a new more general proof of Taylor’s General Recursion Theorem that every well-founded coalgebra is recursive, and we study conditions which imply the converse. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-to-algebra morphism to the initial algebra.

Sign in / Sign up

Export Citation Format

Share Document