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 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 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 the extension of orders in ordered modules

1970 ◽  
Vol 2 (1) ◽  
pp. 81-88 ◽  
Author(s):  
P. Ribenboim
Keyword(s):  
Abelian Groups ◽  
Independent Set ◽  
Total Order ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Ordered Ring ◽  
The Given

We introduce the notion of a positively independent set of elements in an ordered module. With this concept we determine a necessary and sufficient condition which insures that on a strictly ordered module over a strictly ordered ring there exists a strict total order refining the given order. This generalizes a previous result of Fuchs, concerning the case of ordered abelian groups.As an application, let R be a strictly ordered totally ordered ring and let M be the R-module of all mappings from a set I into R, with pointwise order; then this order on M may be refined to a strict total order.

scholarly journals On smallest radical and semi-simple classes

1971 ◽  
Vol 12 (2) ◽  
pp. 98-104 ◽  
Author(s):  
W. G. Leavitt ◽  
J. F. Watters
Keyword(s):  
Admissible Function ◽  
Radical Class ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Universal Class ◽  
Necessary And Sufficient ◽  
The Given

In a recent paper [5] one of us has given a sufficient condition to be satisfied by a given property of radical classes within a universal class w in order that, for any subclass ℳ of w, there should be a smallest radical class having the given property and containing ℳ. The sufficient condition is that the classof all radical classes with the given property can be characterised as the class of all radical classes fixed by an admissible function F (see Section 1 below). In this paper a necessary and sufficient condition is derived and the corresponding result for semi-simpleclasses is also presented. These results are given in Section 2.

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.

Gregarious star factorization of the tensor product of graphs

2018 ◽  
Vol 10 (04) ◽  
pp. 1850055
Author(s):  
P. Hemalatha
Keyword(s):  
Tensor Product ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
The Given ◽  
Product Of Graphs

In this paper, it is shown that the necessary and sufficient condition for the existence of an [Formula: see text]-factorization of [Formula: see text] is [Formula: see text] for some integer [Formula: see text] for the given integers [Formula: see text] and [Formula: see text]

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

Sign in / Sign up

Export Citation Format

Share Document