\(\mathcal{I}\)-convergence and \(\tau^{*}\)-closedness of \(\mathcal{I}\)-compact sets

2017 ◽  
Vol 8 (1) ◽  
pp. 78
Author(s):  
Navpreet Singh Noorie ◽  
Nitakshi Goyal
Keyword(s):  
Compact Set ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Sets ◽  
Accumulation Points ◽  
Necessary And Sufficient ◽  
The Relationship

We introduce the convergence and accumulation points of a filter with respect to an ideal and also give the relationship between them and with the usual convergence and accumulation points of a filter. We use these results to obtain necessary and sufficient condition for an \(\mathcal{I}\)-compact set to be \(\tau^{*}\)-closed in \(S_2\) and normal spaces. Finally the sufficient condition for an \(\mathcal{I}\)-compact set to be \(\tau^{*}\)-closed in \(S_2\) mod $\mathcal{I}$ spaces are obtained.

scholarly journals Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Roberto C. Raimondo
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Boundary Behavior ◽  
Berezin Transform ◽  
Planar Domain ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Planar Domains ◽  
Necessary And Sufficient ◽  
The Relationship

We study the problem of the boundedness and compactness of when and is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of

scholarly journals On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

scholarly journals Some remarks on the spaceR2(E)

1983 ◽  
Vol 6 (3) ◽  
pp. 459-466
Author(s):  
Claes Fernström
Keyword(s):  
Compact Subset ◽  
Complex Plane ◽  
Rational Functions ◽  
Compact Set ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Point Evaluation ◽  
Bounded Point Evaluation ◽  
Point Evaluations ◽  
Necessary And Sufficient

LetEbe a compact subset of the complex plane. We denote byR(E)the algebra consisting of the rational functions with poles offE. The closure ofR(E)inLp(E),1≤p<∞, is denoted byRp(E). In this paper we consider the casep=2. In section 2 we introduce the notion of weak bounded point evaluation of orderβand identify the existence of a weak bounded point evaluation of orderβ,β>1, as a necessary and sufficient condition forR2(E)≠L2(E). We also construct a compact setEsuch thatR2(E)has an isolated bounded point evaluation. In section 3 we examine the smoothness properties of functions inR2(E)at those points which admit bounded point evaluations.

scholarly journals Generalized Bertrand Curves in Minkowski 3-Space

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2199
Author(s):  
Chunxiao Zhang ◽  
Donghe Pei
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bertrand Curve ◽  
Necessary And Sufficient ◽  
The Relationship

We define a generalized lightlike Bertrand curve pair and a generalized non-lightlike Bertrand curve pair, discuss their properties and prove the necessary and sufficient condition of a curve which is a generalized lightlike or a generalized non-lightlike Bertrand curve. Moreover, we study the relationship between slant helices and generalized Bertrand curves.

On subprojectivity domains of g-semiartinian modules

2020 ◽  
pp. 2150119
Author(s):  
Yılmaz Durğun ◽  
Ayşe Çobankaya
Keyword(s):  
Homomorphic Image ◽  
Proper Class ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
The Relationship

The aim of this paper is to reveal the relationship between the proper class generated projectively by g-semiartinian modules and the subprojectivity domains of g-semiartinian modules. A module [Formula: see text] is called g-semiartinian if every nonzero homomorphic image of [Formula: see text] has a singular simple submodule. It is proven that every g-semiartinian right [Formula: see text]-module has an epic projective envelope if and only if [Formula: see text] is a right PS ring if and only if every subprojectivity domain of any g-semiartinian right [Formula: see text]-module is closed under submodules. A g-semiartinian module whose domain of subprojectivity as small as possible is called gsap-indigent. We investigated the structure of rings whose (simple, coatomic) g-semiartinian right modules are gsap-indigent or projective. Furthermore, over right PS rings, necessary and sufficient condition to be gsap-indigent module was determined.

scholarly journals ŁOJASIEWICZ-TYPE INEQUALITIES AND GLOBAL ERROR BOUNDS FOR NONSMOOTH DEFINABLE FUNCTIONS IN O-MINIMAL STRUCTURES

2015 ◽  
Vol 93 (1) ◽  
pp. 99-112
Author(s):  
DŨNG PHI HOÀNG
Keyword(s):  
Error Bound ◽  
Global Error ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Global Error Bound ◽  
Minimal Structure ◽  
Palais Smale Condition ◽  
Necessary And Sufficient ◽  
Definable Functions ◽  
The Relationship

In this paper, we give some Łojasiewicz-type inequalities for continuous definable functions in an o-minimal structure. We also give a necessary and sufficient condition for the existence of a global error bound and the relationship between the Palais–Smale condition and this global error bound. Moreover, we give a Łojasiewicz nonsmooth gradient inequality at infinity near the fibre for continuous definable functions in an o-minimal structure.

20.—Deficiency Indices of Polynomials in Symmetric Differential Expressions, II

1975 ◽  
Vol 73 ◽  
pp. 301-306 ◽  
Author(s):  
Anton Zettl
Keyword(s):  
Hilbert Space ◽  
Differential Expression ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Real Polynomial ◽  
Deficiency Indices ◽  
Linear Differential ◽  
Image Position ◽  
Necessary And Sufficient ◽  
The Relationship

SynopsisGiven a symmetric (formally self-adjoint) ordinary linear differential expression L which is regular on the interval [0, ∞) and has C∞ coefficients, we investigate the relationship between the deficiency indices of L and those of p(L), where p(x) is any real polynomial of degree k > 1. Previously we established the following inequalities: (a) For k even, say k = 2r, N+(p(L)), N−(p(L)) ≧ r[N+(L)+N−(L)] and (b) for k odd, say k = 2r+1where N+(M), N−(M) denote the deficiency indices of the symmetric expression M (or of the minimal operator associated with M in the Hilbert space L2(0, ∞)) corresponding to the upper and lower half-planes, respectively. Here we give a necessary and sufficient condition for equality to hold in the above inequalities.

On the Relationship between the Supply-Driven and the Demand-Driven Input — Output Model

1989 ◽  
Vol 21 (11) ◽  
pp. 1533-1539 ◽  
Author(s):  
E Dietzenbacher
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Input Output ◽  
Demand Pull ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Fixed Input ◽  
The Relationship

In this paper, the relationship between the assumptions in the supply-driven and the demand-driven input-output model is discussed. A necessary and sufficient condition is given for the stability of the input coefficients, the output coefficients, and both coefficients. For both models, the effects of a demand pull on the total outputs and on the primary inputs are analytically expressed. Also, the effects of a supply push on the total outputs and on the final outputs are expressed, again for both models. In general, the assumption of fixed input coefficients in the demand-driven model does not hold, but computations are still based on it. A necessary and sufficient condition is given for the correctness of the computed total outputs, both for a demand pull and a supply push. Similar results are obtained for the supply-driven input — output model.

Ideal convergence of nets of functions with values in uniform spaces

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6281-6292
Author(s):  
Athanasios Megaritis
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Uniform Space ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Sets ◽  
Uniform Spaces ◽  
Ideal Convergence ◽  
Necessary And Sufficient

We consider the pointwise, uniform, quasi-uniform, and the almost uniform I-convergence for a net (fd)d?D of functions from a topological space X into a uniform space (Y,U), where I is an ideal on D. The purpose of the present paper is to provide ideal versions of some classical results and to extend these to nets of functions with values in uniform spaces. In particular, we define the notion of I-equicontinuous family of functions on which pointwise and uniform I-convergence coincide on compact sets. Generalizing the theorem of Arzel?, we give a necessary and sufficient condition for a net of continuous functions from a compact space into a uniform space to I-converge pointwise to a continuous function.

scholarly journals CONDITION OF FINITENESS OF COLENGTH OF VARIETY OF LEIBNITZ ALGEBRAS

2017 ◽  
Vol 20 (10) ◽  
pp. 84-90
Author(s):  
A.V. Polovinkina ◽  
T.V. Skoraya
Keyword(s):  
Symmetric Group ◽  
Free Algebra ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Base Field ◽  
Direct Sum ◽  
Zero Characteristic ◽  
Necessary And Sufficient ◽  
Relationship Of ◽  
The Relationship

This paper is devoted to the varieties of Leibnitz algebras over a field of zero characteristic. All information about the variety in case of zero characteristic of the base field is contained in the space of multilinear elements of its relatively free algebra. Multilinear component of variety is considered as a module of symmetric group and splits into a direct sum of irreducible submodules, the sum of multiplicities of which is called colength of variety. This paper investigates the identities that are performed in varieties with finite colength and also the relationship of this varieties with known varieties of Lie and Leibnitz algebras with this property. We prove necessary and sufficient condition for a finiteness of colength of variety of Leibnitz algebras.

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