Estimation of the Greatest Common Divisor of many polynomials using hybrid computations performed by the ERES method

2005 ◽  
Vol 2 (3) ◽  
pp. 293-305 ◽  
Author(s):  
Dimitrios Christou ◽  
Marilena Mitrouli
Keyword(s):  
Greatest Common Divisor

Greatest common divisor of matrices one of which is a disappear matrix

2014 ◽  
Vol 66 (3) ◽  
pp. 479-485 ◽  
Author(s):  
A. M. Romaniv ◽  
V. P. Shchedryk
Keyword(s):  
Greatest Common Divisor

scholarly journals Co-prime Probability for Nonabelian Metabelian Groups of Order Less than 24 and Their Related Graphs

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nurfarah Zulkifli ◽  
Nor Muhainiah Mohd Ali
Keyword(s):  
Finite Group ◽  
Prime Graph ◽  
Greatest Common Divisor ◽  
Metabelian Groups ◽  
A Finite Group ◽  
Random Pair

Let G be a finite group. The probability of a random pair of elements in G are said to be co-prime when the greatest common divisor of order x and y, where x and y in G, is equal to one. Meanwhile the co-prime graph of a group is defined as a graph whose vertices are elements of G and two distinct vertices are adjacent if and only if the greatest common divisor of order x and y is equal to one. In this paper, the co-prime probability and its graph such as the type and the properties of the graph are determined.

scholarly journals Universal Evolutionary Model for Periodical Species

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Eric Goles ◽  
Ivan Slapničar ◽  
Marco A. Lardies
Keyword(s):  
Fitness Function ◽  
Evolutionary Model ◽  
Prime Numbers ◽  
Life Cycles ◽  
The Other ◽  
Exclusion Principle ◽  
Greatest Common Divisor ◽  
Predator Prey ◽  
Integer Multiple ◽  
New Period

Real-world examples of periodical species range from cicadas, whose life cycles are large prime numbers, like 13 or 17, to bamboos, whose periods are large multiples of small primes, like 40 or even 120. The periodicity is caused by interaction of species, be it a predator-prey relationship, symbiosis, commensalism, or competition exclusion principle. We propose a simple mathematical model, which explains and models all those principles, including listed extremal cases. This rather universal, qualitative model is based on the concept of a local fitness function, where a randomly chosen new period is selected if the value of the global fitness function of the species increases. Arithmetically speaking, the different interactions are related to only four principles: given a couple of integer periods either (1) their greatest common divisor is one, (2) one of the periods is prime, (3) both periods are equal, or (4) one period is an integer multiple of the other.

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