scholarly journals Fixed Points of the Dickson Polynomials of the Second Kind

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Adama Diene ◽  
Mohamed A. Salim
Keyword(s):  
Fixed Points ◽  
Finite Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dickson Polynomials ◽  
Necessary And Sufficient

The permutation behavior of Dickson polynomials of the first kind has been extensively studied, while such behavior for Dickson polynomials of the second kind is less known. Necessary and sufficient conditions for a polynomial of the second kind to be a permutation over some finite fields have been established by Cohen, Matthew, and Henderson. We introduce a new way to define these polynomials and determine the number of their fixed points.

scholarly journals A unifying approach for some nonexpansiveness conditions on modular vector spaces

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Andrea Bejenaru ◽  
Mihai Postolache
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Vector Spaces ◽  
Minimizing Sequences ◽  
Ishikawa Iteration ◽  
New Class ◽  
Condition C ◽  
Necessary And Sufficient

This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

scholarly journals SOME FAMILIES OF PERMUTATION POLYNOMIALS OVER FINITE FIELDS

2008 ◽  
Vol 04 (05) ◽  
pp. 851-857 ◽  
Author(s):  
MICHAEL E. ZIEVE
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Permutation Polynomials ◽  
Polynomials Over Finite Fields ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for a polynomial of the form xr(1 + xv + x2v + ⋯ + xkv)t to permute the elements of the finite field 𝔽q. Our results yield especially simple criteria in case (q - 1)/ gcd (q - 1, v) is a small prime.

Additivity of the Pn-Integral (2)

1982 ◽  
Vol 34 (2) ◽  
pp. 506-512
Author(s):  
G. E. Cross
Keyword(s):  
Fixed Points ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Definition Of ◽  
Necessary And Sufficient

The problem of additivity of the Pn-integral on abutting intervals was considered in [2] and in [5]. It was noted in [2] that the necessary and sufficient conditions for additivity for the P2-integral obtained by Skvorcov in [5] could be completely generalized to the Pn-integral, n > 2, if a key lemma (corresponding to Skvorcov's Lemma 3 [6]) could be proved. We provide a proof of that lemma in this paper and hence obtain the general additivity result.The definitions and notation of [2] are used in the following, except that we shall take the following as the definition of Pn-major and minor functions:Definition 1.1. Let f(x) be a function defined in [a, b] and let a1, i = 1, 2, …, n, be fixed points such that a = a1 < a2 < … < an = b.

scholarly journals Hermitian Self-Orthogonal Constacyclic Codes over Finite Fields

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Amita Sahni ◽  
Poonam Trama Sehgal
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Mds Codes ◽  
Constacyclic Codes ◽  
Necessary And Sufficient ◽  
Defining Sets

Necessary and sufficient conditions for the existence of Hermitian self-orthogonal constacyclic codes of length n over a finite field Fq2, n coprime to q, are found. The defining sets and corresponding generator polynomials of these codes are also characterised. A formula for the number of Hermitian self-orthogonal constacyclic codes of length n over a finite field Fq2 is obtained. Conditions for the existence of numerous MDS Hermitian self-orthogonal constacyclic codes are obtained. The defining set and the number of such MDS codes are also found.

scholarly journals On characterizations of fixed points

2001 ◽  
Vol 27 (7) ◽  
pp. 391-397 ◽  
Author(s):  
Zeqing Liu ◽  
Lili Zhang ◽  
Shin Min Kang
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Equivalent Condition ◽  
Compact Mapping ◽  
Necessary And Sufficient

We give some necessary and sufficient conditions for the existence of fixed points of a family of self mappings of a metric space and we establish an equivalent condition for the existence of fixed points of a continuous compact mapping of a metric space.

scholarly journals Analytic functions over valued fields

1990 ◽  
Vol 13 (2) ◽  
pp. 247-252
Author(s):  
R. Bhaskaran ◽  
V. Karunakaran
Keyword(s):  
Unit Ball ◽  
Fixed Points ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Ball ◽  
Valued Fields ◽  
Complete Field ◽  
Necessary And Sufficient

LetKbe a non-archimedean, non-trivially (rank 1) valued complete field.B,B0denote the closed and open unit ball ofKrespectively. Necessary and sufficient conditions for analytic functions defined onB,B0with values inKto be injective, necessary and sufficient conditions for fixed points, the problem of subordination are studied in this paper.

scholarly journals RECONSTRUCTING MULTISETS OVER COMMUTATIVE GROUPOIDS AND AFFINE FUNCTIONS OVER NONASSOCIATIVE SEMIRINGS

2014 ◽  
Vol 24 (01) ◽  
pp. 11-31 ◽  
Author(s):  
ERKKO LEHTONEN
Keyword(s):  
Finite Fields ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Reconstruction Problem ◽  
Affine Functions ◽  
Necessary And Sufficient

A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of multisets are determined. These results find an application in a different kind of reconstruction problem for functions of several arguments and identification minors: classes of linear or affine functions over nonassociative semirings are shown to be weakly reconstructible. Moreover, affine functions of sufficiently large arity over finite fields are reconstructible.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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