scholarly journals Mannheim Curves in Nonflat 3-Dimensional Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wenjing Zhao ◽  
Donghe Pei ◽  
Xinyu Cao
Keyword(s):  
Linear Relationship ◽  
Dimensional Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
De Sitter ◽  
Space Forms ◽  
3 Dimensional ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
The Given

We consider the Mannheim curves in nonflat 3-dimensional space forms (Riemannian or Lorentzian) and we give the concept of Mannheim curves. In addition, we investigate the properties of nonnull Mannheim curves and their partner curves. We come to the conclusion that a necessary and sufficient condition is that a linear relationship with constant coefficients will exist between the curvature and the torsion of the given original curves. In the case of null curve, we reveal that there are no null Mannheim curves in the 3-dimensional de Sitter space.

scholarly journals On 3-Dimensional Contact Metric Generalized(k,μ)-Space Forms

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
D. G. Prakasha ◽  
Shyamal Kumar Hui ◽  
Kakasab Mirji
Keyword(s):  
Constant Curvature ◽  
Space Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Forms ◽  
3 Dimensional ◽  
Projectively Flat ◽  
Necessary And Sufficient

The present paper deals with a study of 3-dimensional contact metric generalized(k,μ)-space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized(k,μ)-space form withQϕ=ϕQto be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric andξ-projectively flat, respectively.

scholarly journals Bipartite graphs with close domination and k-domination numbers

2020 ◽  
Vol 18 (1) ◽  
pp. 873-885
Author(s):  
Gülnaz Boruzanlı Ekinci ◽  
Csilla Bujtás
Keyword(s):  
Positive Integer ◽  
Dominating Set ◽  
Domination Number ◽  
Bipartite Graphs ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Minimum Cardinality ◽  
Vertex Set ◽  
Necessary And Sufficient ◽  
The Given

Abstract Let k be a positive integer and let G be a graph with vertex set V(G) . A subset D\subseteq V(G) is a k -dominating set if every vertex outside D is adjacent to at least k vertices in D . The k -domination number {\gamma }_{k}(G) is the minimum cardinality of a k -dominating set in G . For any graph G , we know that {\gamma }_{k}(G)\ge \gamma (G)+k-2 where \text{Δ}(G)\ge k\ge 2 and this bound is sharp for every k\ge 2 . In this paper, we characterize bipartite graphs satisfying the equality for k\ge 3 and present a necessary and sufficient condition for a bipartite graph to satisfy the equality hereditarily when k=3 . We also prove that the problem of deciding whether a graph satisfies the given equality is NP-hard in general.

scholarly journals Characterizations of majorization on summable sequences

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2193-2202
Author(s):  
Kosuru Raju ◽  
Subhajit Saha
Keyword(s):  
Sequence Space ◽  
Dimensional Space ◽  
Sufficient Condition ◽  
Infinite Dimensional Space ◽  
Necessary And Sufficient Condition ◽  
Infinite Dimensional ◽  
Summable Sequence ◽  
Necessary And Sufficient

In this paper, we prove a necessary and sufficient condition for majorization on the summable sequence space. For this we redefine the notion of majorization on an infinite dimensional space and therein investigate properties of the majorization. We also prove the infinite dimensional Schur-Horn type and Hardy-Littlewood-P?lya type theorems.

scholarly journals An application of bivariate polynomial factorization on decoding of Reed-Solomon based codes

2018 ◽  
Vol 12 (1) ◽  
pp. 166-177
Author(s):  
Ivan Pavkov ◽  
Nebojsa Ralevic ◽  
Ljubo Nedovic
Keyword(s):  
Efficient Algorithm ◽  
Sufficient Condition ◽  
Polynomial Factorization ◽  
Necessary And Sufficient Condition ◽  
Bivariate Polynomials ◽  
Bivariate Polynomial ◽  
Integer Coefficients ◽  
Necessary And Sufficient ◽  
The Given

A necessary and sufficient condition for the existence of a non-trivial factorization of an arbitrary bivariate polynomial with integer coefficients was presented in [2]. In this paper we develop an efficient algorithm for factoring bivariate polynomials with integer coefficients. Also, we shall give a proof of the optimality of the algorithm. For a given codeword, formed by mixing up two codewords, the algorithm recovers those codewords directly by factoring corresponding bivariate polynomial. Our algorithm determines uniquely the given polynomials which are used in forming the mixture of two codewords.

scholarly journals How Does Misperception Affect Zero-Determinant Strategies In Iterated Prisoner’s Dilemma?

2021 ◽  
Author(s):  
Zhaoyang Cheng ◽  
Guanpu Chen ◽  
Yiguang Hong
Keyword(s):  
Linear Relationship ◽  
Expected Utility ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
The Other ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Iterated Prisoner's Dilemma ◽  
Necessary And Sufficient ◽  
Iterated Prisoner’S Dilemma

Abstract Zero-determinant (ZD) strategies have attracted wide attention in Iterated Prisoner’s Dilemma (IPD) games, since the player equipped with ZD strategies can unilaterally enforce the two players’ expected utilities subjected to a linear relation. On the other hand, uncertainties, which may be caused by misperception, occur in IPD inevitably in practical circumstances. To better understand the situation, we consider the influence of misperception on ZD strategies in IPD, where the two players, player X and player Y , have different cognitions, but player X detects the misperception and it is believed to make ZD strategies by player Y. We provide a necessary and sufficient condition for the ZD strategies in IPD with misperception, where there is also a linear relationship between players’ utilities in player X’s cognition. Then we explore bounds of players’ expected utility deviation from a linear relationship in player X’s cognition with also improving its own utility.

scholarly journals On the notion ofL 1-completeness of a stochastic flow on a manifold

2002 ◽  
Vol 7 (12) ◽  
pp. 627-635 ◽  
Author(s):  
Yu. E. Gliklikh ◽  
L. A. Morozova
Keyword(s):  
Functional Space ◽  
Riemannian Metric ◽  
Stochastic Flow ◽  
Time Interval ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
The Given

We introduce the notion ofL 1-completeness for a stochastic flow on manifold and prove a necessary and sufficient condition for a flow to beL 1-complete.L 1-completeness means that the flow is complete (i.e., exists on the given time interval) and that it belongs to some sort ofL 1-functional space, natural for manifolds where no Riemannian metric is specified.

scholarly journals On locally conformal Kähler space forms

1985 ◽  
Vol 8 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Koji Matsumoto
Keyword(s):  
Space Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Covariant Differentiation ◽  
Space Forms ◽  
Riemannian Curvature Tensor ◽  
Locally Conformal Kähler ◽  
Necessary And Sufficient ◽  
Locally Conformal ◽  
Lee Form

Anm-dimensional locally conformal Kähler manifold (l.c.K-manifold) is characterized as a Hermitian manifold admitting a global closedl-formαλ(called the Lee form) whose structure(Fμλ,gμλ)satisfies∇νFμλ=−βμgνλ+βλgνμ−αμFνλ+αλFνμ, where∇λdenotes the covariant differentiation with respect to the Hermitian metricgμλ,βλ=−Fλϵαϵ,Fμλ=Fμϵgϵλand the indicesν,μ,…,λrun over the range1,2,…,m.For l. c. K-manifolds, I. Vaisman [4] gave a typical example and T. Kashiwada ([1], [2],[3]) gave a lot of interesting properties about such manifolds.In this paper, we shall study certain properties of l. c. K-space forms. In§2, we shall mainly get the necessary and sufficient condition that an l. c. K-space form is an Einstein one and the Riemannian curvature tensor with respect togμλwill be expressed without the tensor fieldPμλ. In§3, we shall get the necessary and sufficient condition that the length of the Lee form is constant and the sufficient condition that a compact l. c. K-space form becomes a complex space form. In the last§4, we shall prove that there does not exist a non-trivial recurrent l. c. K-space form.

scholarly journals Properly embedded and immersed minimal surfaces in the Heisenberg group

2004 ◽  
Vol 70 (3) ◽  
pp. 507-520 ◽  
Author(s):  
Jih-Hsin Cheng ◽  
Jenn-Fang Hwang
Keyword(s):  
Heisenberg Group ◽  
Minimal Surface ◽  
Explicit Expression ◽  
Minimal Surfaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Minimal Graphs ◽  
3 Dimensional ◽  
Necessary And Sufficient ◽  
Band Type

We study properly embedded and immersed p(pseudohermitian)-minimal surfaces in the 3-dimensional Heisenberg group. From the recent work of Cheng, Hwang, Malchiodi, and Yang, we learn that such surfaces must be ruled surfaces. There are two types of such surfaces: band type and annulus type according to their topology. We givn an explicit expression for these surfaces. Among band types there is a class of properly embedded p-minimal surfaces of so called helicoid type. We classify all the helicoid type p-minimal surfaces. This class of p-minimal surfaces includes all the entire p-minimal graphs (except contact planes) over any plane. Moreover, we give a necessary and sufficient condition for such a p-minimal surface to have no singular points. For general complete immersed p-minimal surfaces, we prove a half space theorem and give a criterion for the properness.

scholarly journals f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms

2019 ◽  
Vol 27 (3) ◽  
pp. 97-112
Author(s):  
Shyamal Kumar Hui ◽  
Daniel Breaz ◽  
Pradip Mandal
Keyword(s):  
Space Form ◽  
Ambient Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Forms ◽  
Necessary And Sufficient

AbstractHere we have studied f-biharmonic and bi-f-harmonic submanifolds of generalized (k, µ)-space-forms and obtained a necessary and sufficient condition on a submanifold of generalized (k, µ)-space-form to be f-biharmonic and bi-f-harmonic submanifold. We have also studied f-biharmonic hypersurfaces of said ambient space forms.

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