On subprojectivity domains of g-semiartinian modules

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.

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

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2011/164843 ◽

2011 ◽

Vol 2011 ◽

pp. 1-26 ◽

Cited By ~ 1

Author(s):

Roberto C. Raimondo

Keyword(s):

Bergman Space ◽

Toeplitz Operators ◽

Boundary Behavior ◽

Berezin Transform ◽

Planar Domain ◽

Sufficient Condition ◽

Planar Domains ◽

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

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

Journal of Mathematical Analysis and Modeling ◽

10.48185/jmam.v2i2.276 ◽

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 ◽

First Order ◽

Recurrence Property ◽

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-$BC-RF_{n}$.

Complete Cohomology for Extriangulated Categories

Algebra Colloquium ◽

10.1142/s1005386721000547 ◽

2021 ◽

Vol 28 (04) ◽

pp. 701-720

Author(s):

Jiangsheng Hu ◽

Dongdong Zhang ◽

Tiwei Zhao ◽

Panyue Zhou

Keyword(s):

Projective Dimension ◽

Proper Class ◽

Sufficient Condition ◽

Injective Dimension ◽

General Technique ◽

Gorenstein Algebra ◽

Projective Resolutions ◽

Necessary And Sufficient

Let [Formula: see text] be an extriangulated category with a proper class [Formula: see text] of [Formula: see text]-triangles. We study complete cohomology of objects in [Formula: see text] by applying [Formula: see text]-projective resolutions and [Formula: see text]-injective coresolutions constructed in [Formula: see text]. Vanishing of complete cohomology detects objects with finite [Formula: see text]-projective dimension and finite [Formula: see text]-injective dimension. As a consequence, we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein. Moreover, we give a general technique for computing complete cohomology of objects with finite [Formula: see text]-[Formula: see text]projective dimension. As an application, the relations between [Formula: see text]-projective dimension and [Formula: see text]-[Formula: see text]projective dimension for objects in [Formula: see text] are given.

Generalized Bertrand Curves in Minkowski 3-Space

Mathematics ◽

10.3390/math8122199 ◽

2020 ◽

Vol 8 (12) ◽

pp. 2199

Author(s):

Chunxiao Zhang ◽

Donghe Pei

Keyword(s):

Sufficient Condition ◽

Bertrand Curve ◽

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.

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

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972715000726 ◽

2015 ◽

Vol 93 (1) ◽

pp. 99-112

Author(s):

DŨNG PHI HOÀNG

Keyword(s):

Error Bound ◽

Global Error ◽

Sufficient Condition ◽

Global Error Bound ◽

Minimal Structure ◽

Palais Smale Condition ◽

Definable Functions ◽

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

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500016450 ◽

1975 ◽

Vol 73 ◽

pp. 301-306 ◽

Cited By ~ 6

Author(s):

Anton Zettl

Keyword(s):

Hilbert Space ◽

Differential Expression ◽

Sufficient Condition ◽

Real Polynomial ◽

Deficiency Indices ◽

Linear Differential ◽

Image Position ◽

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

Environment and Planning A Economy and Space ◽

10.1068/a211533 ◽

1989 ◽

Vol 21 (11) ◽

pp. 1533-1539 ◽

Cited By ~ 16

Author(s):

E Dietzenbacher

Keyword(s):

Sufficient Condition ◽

Input Output ◽

Demand Pull ◽

The Stability ◽

Fixed Input ◽

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.

CONDITION OF FINITENESS OF COLENGTH OF VARIETY OF LEIBNITZ ALGEBRAS

Vestnik of Samara University Natural Science Series ◽

10.18287/2541-7525-2014-20-10-84-90 ◽

2017 ◽

Vol 20 (10) ◽

pp. 84-90

Author(s):

A.V. Polovinkina ◽

T.V. Skoraya

Keyword(s):

Symmetric Group ◽

Free Algebra ◽

Sufficient Condition ◽

Base Field ◽

Direct Sum ◽

Zero Characteristic ◽

Relationship Of ◽

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.

Idyllic Chronotope in Taras Prohasko’s Novel “The UnSimple”

Path of Science ◽

10.22178/pos.70-8 ◽

2021 ◽

Vol 7 (5) ◽

pp. 3001-3005

Author(s):

Svitlana Ryabykh ◽

Keyword(s):

Human Life ◽

Sufficient Condition ◽

The Novel ◽

Important Place ◽

The World ◽

Man And Nature ◽

The Individual ◽

The article focuses on the standard features of different idyllic chronotope associated with the unity of the folklore period. Emphasis is placed on the inseparability of human life from a particular place where ancestors lived and where descendants will live. In Taras Prohasko’s novel “The UnSimple”, great importance is attached to family traditions, according to which children at the age of fifteen were shown places related to family history. M. Bakhtin calls this feature the unity of place. This feature unites generations, blurs the time boundaries between the individual life of each person and different periods of the same life. The rhythmic cycle of time is demonstrated in the novel “The UnSimple” on the example of Sebastian and his Anna, who was the only possible woman in his life. In Taras Prokhasko’s novel, the opinion is affirmed that the home for most people is an idyllic place, the basis of biography and the result of existence. It is a place where a person feels protected and confident. The relationship between man and nature in work is shown idealized. Through an exaggerated image of floriculture, the author offers an alternative world in which a responsible, caring, careful attitude to the world around us prevails. It is proved that in Taras Prohasko’s novel “The UnSimple”, the landscape is both a necessary and sufficient condition for a complete human life. It was found that the most important place in T. Prokhasko’s prose is given to the epic of family places, which are the basis of the idyllic chronotope.

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

Journal of Advanced Studies in Topology ◽

10.20454/jast.2017.1289 ◽

2017 ◽

Vol 8 (1) ◽

pp. 78

Author(s):

Navpreet Singh Noorie ◽

Nitakshi Goyal

Keyword(s):

Compact Set ◽

Sufficient Condition ◽

Compact Sets ◽

Accumulation Points ◽

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.