scholarly journals On Degrees of Modular Common Divisors and the Big PrimegcdAlgorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Vahagn Mikaelian
Keyword(s):  
Prime Divisors ◽  
Intermediate Expression Swell ◽  
Expression Swell ◽  
Intermediate Expression ◽  
Number Of Prime Divisors

We consider a few modifications of the Big prime modulargcdalgorithm for polynomials inZ[x]. Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors of a resultant, and on finding preliminary bounds on degrees of common divisors using auxiliary primes. These modifications are used to suggest improved algorithms forgcdcalculation and for coprime polynomials detection. To illustrate the ideas we apply the constructed algorithms on certain polynomials, in particular on polynomials from Knuth’s example of intermediate expression swell.

Hesitant fuzzy multi-attribute group decision making method based on weighted power operators in social network and their application

2021 ◽  
pp. 1-19
Author(s):  
Huiping Chen
Keyword(s):  
Decision Making ◽  
Social Network ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Point Of View ◽  
Pagerank Algorithm ◽  
Intermediate Expression Swell ◽  
Expression Swell ◽  
Intermediate Expression

 This paper aims to put forward a hesitant fuzzy multi-attribute group decision making (MAGDM) method based on the weighted power aggregation operators in social network. From the point of view of social network analysis, decision makers (DMs) are interconnected in the process of MAGDM. Furthermore, the dimension of the obtained hesitant fuzzy element (HFE) by original power operators will be greater with the increasing number of attributes and alternatives and DMs, which will lead to the problem of “intermediate expression swell". This paper combines the order operation laws with the power operators to redefine two novel hesitant fuzzy power aggregation operators to simplify the involved calculation and explore new operators’ properties. Meanwhile, when two given elements have different number of values, we use the strength of social ties and social influence to develop an algorithm for extending the HFEs objectively. On the other hand, the PageRank algorithm and the deviation method are used to determine DMs’ combined weights. The feasibility of the proposed hesitant fuzzy MAGDM method based on social network is illustrated by the application to the actual issue of decision making and the comparative analysis with the existing method.

scholarly journals On the number of prime divisors of the order of elliptic curves modulo p

2005 ◽  
Vol 117 (4) ◽  
pp. 341-352 ◽  
Author(s):  
Jörn Steuding ◽  
Annegret Weng
Keyword(s):  
Elliptic Curves ◽  
Prime Divisors ◽  
Modulo P ◽  
Number Of Prime Divisors

scholarly journals The distribution of the number of prime divisors of sums a + b

1988 ◽  
Vol 29 (1) ◽  
pp. 94-99 ◽  
Author(s):  
P.D.T.A Elliott ◽  
A Sárközy
Keyword(s):  
Prime Divisors ◽  
Number Of Prime Divisors

On the Normal Growth of Prime Factors of Integers

1992 ◽  
Vol 44 (6) ◽  
pp. 1121-1154 ◽  
Author(s):  
J. M. De Koninck ◽  
I. Kátai ◽  
A. Mercier
Keyword(s):  
Prime Factor ◽  
Continuous Distribution ◽  
Normal Growth ◽  
Distribution Functions ◽  
Prime Divisors ◽  
Simple Argument ◽  
Prime Factors ◽  
Almost All ◽  
Number Of Prime Divisors ◽  
Class Of Functions

AbstractLet h: [0,1] → R be such that and define .In 1966, Erdős [8] proved that holds for almost all n, which by using a simple argument implies that in the case h(u) = u, for almost all n, He further obtained that, for every z > 0 and almost all n, and that where ϕ, ψ, are continuous distribution functions. Several other results concerning the normal growth of prime factors of integers were obtained by Galambos [10], [11] and by De Koninck and Galambos [6].Let χ = ﹛xm : w ∈ N﹜ be a sequence of real numbers such that limm→∞ xm = +∞. For each x ∈ χ let be a set of primes p ≤x. Denote by p(n) the smallest prime factor of n. In this paper, we investigate the number of prime divisors p of n, belonging to for which Th(n,p) > z. Given Δ < 1, we study the behaviour of the function We also investigate the two functions , where, in each case, h belongs to a large class of functions.

scholarly journals On the residue class distribution of the number of prime divisors of an integer

2011 ◽  
Vol 202 ◽  
pp. 15-22 ◽  
Author(s):  
Michael Coons ◽  
Sander R. Dahmen
Keyword(s):  
Positive Integer ◽  
Error Term ◽  
Residue Class ◽  
Prime Divisors ◽  
Class Distribution ◽  
Multiplicity One ◽  
Counting Multiplicity ◽  
Number Of Prime Divisors

AbstractLet Ω(n) denote the number of prime divisors of n counting multiplicity. One can show that for any positive integer m and all j = 0,1,…,m – 1, we havewith α = 1. Building on work of Kubota and Yoshida, we show that for m > 2 and any j = 0,1,…,m – 1, the error term is not o(xα) for any α < 1.

Finite soluble groups admitting an automorphism of prime power order with few fixed points

1987 ◽  
Vol 102 (3) ◽  
pp. 431-441 ◽  
Author(s):  
Brian Hartley ◽  
Volker Turau
Keyword(s):  
Fixed Points ◽  
Soluble Group ◽  
Prime Power ◽  
Prime Power Order ◽  
Finite Soluble Group ◽  
Prime Divisors ◽  
Fitting Subgroup ◽  
Soluble Groups ◽  
Fitting Height ◽  
Number Of Prime Divisors

Let G be a finite soluble group with Fitting subgroup F(G). The Fitting series of G is defined, as usual, by F0(G) = 1 and Fi(G)/Fi−1(G) = F(G/Fi−1(G)) for i ≥ 1, and the Fitting height h = h(G) of G is the least integer such that Fn(G) = G. Suppose now that a finite soluble group A acts on G. Let k be the composition length of A, that is, the number of prime divisors (counting multiplicities) of |A|. There is a certain amount of evidence in favour of theCONJECTURE. |G:Fk(G)| is bounded by a number depending only on |A| and |CG(A)|.

Sign in / Sign up

Export Citation Format

Share Document