On Prime number varieties and their applications
EASL-Vol. 3 (2020), Issue 3, pp. 30 – 36 Open Access Full-Text PDF
Y. Gayathri Narayana, V. Yegnanarayanan
Abstract: Prime numbers and their variations are extremely useful in applied research areas such as cryptography, feedback and control in engineering. In this paper we discuss about prime numbers, perfect numbers, even perfect and odd perfect numbers, amicable numbers, semiprimes, mersenne prime numbers, triangular numbers, distribution of primes, relation between \(\pi\) and prime numbers. In the process we also obtain interesting properties of some of them and raise a set of open problems for further exploration.
Block procedure for solving stiff initial value problems using probabilists Hermite polynomials
EASL-Vol. 3 (2020), Issue 3, pp. 20 – 29 Open Access Full-Text PDF
Lelise Mulatu, Alemayehu Shiferaw, Solomon Gebregiorgis
Abstract: In this paper, a block linear multistep method (LMM) with step number 4 \((k = 4)\) through collocation and interpolation techniques using probabilists Hermite polynomial as basis function which produces a family of block scheme with maximum order five has been proposed for the numerical solution of stiff problems in ODEs. The method is found to be consistent, convergent, and zero stable.The accuracy of the method is tested with two stiff first order initial value problems. The results are compared with fourth order Runge Kutta (RK4) method and a block LMM developed by Berhan et al. [1]. All numerical examples are solved with the aid of MATLAB software after the schemes are developed using MAPLE software.
On some properties of generalized Fibonacci polynomials
ODAM-Vol. 3 (2020), Issue 3, pp. 4 – 13 Open Access Full-Text PDF
Fidel Oduol
Abstract: Fibonacci polynomials have been generalized mainly by two ways: by maintaining the recurrence relation and varying the initial conditions and by varying the recurrence relation and maintaining the initial conditions. In this paper, both the recurrence relation and initial conditions of generalized Fibonacci polynomials are varied and defined by recurrence relation as \(R_n(x)=axR_{n-1}(x)+bR_{n-2}(x)\) for all \(n\geq2,\) with initial conditions \(R_0(x)=2p\) and \(R_1(x)=px+q\) where \(a\) and \(b\) are positive integers and \(p\) and \(q\) are non-negative integers. Further some fundamental properties of these generalized polynomials such as explicit sum formula, sum of first \(n\) terms, sum of first \(n\) terms with (odd or even) indices and generalized identity are derived by Binet’s formula and generating function only.
Degree tolerant number of power graph: finite Albenian group
ODAM-Vol. 3 (2020), Issue 3, pp. 1 – 3 Open Access Full-Text PDF
Johan Kok
Abstract: The degree tolerant number of the power graph of the finite Albenian group, \(\mathbb{Z}_n\) under addition modulo \(n\), \(n\in \mathbb{N}\) is investigated. A surprising simple result, \(\chi_{dt}(\mathcal{P}((\mathbb{Z}_{n},+_{n}))) = k\) for the product of primes, \(n=p_1p_2p_3\cdots p_k\) is presented.
Boundedness of Calderón-Zygmund operators and their commutator on Morrey-Herz Spaces with variable exponents
OMS-Vol. 4 (2020), Issue 1, pp. 323 – 336 Open Access Full-Text PDF
Omer Abdalrhman, Afif Abdalmonem, Shuangping Tao
Abstract: In this paper, the boundedness of Calderón-Zygmund operators is obtained on Morrey-Herz spaces with variable exponents \(MK_{q(\cdot),p(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n})\) and several norm inequalities for the commutator generated by Calderón-Zygmund operators, BMO function and Lipschitz function are given.
COVID-19, a brief overview of virus reproductive emergent behavior
EASL-Vol. 3 (2020), Issue 3, pp. 15 – 19 Open Access Full-Text PDF
Charles Roberto Telles
Abstract: Researches were investigated from January to March, \(2020\), searching for empirical evidences and theoretical approaches at that time to determine a mathematical modeling for COVID-\(19\) transmission for individual/community infection. It was found that despite traditional forms of transmission of the virus SARS-COV-\(2\) through SIR model equations early detected on \(2020\), empirical evidences suggested the use of more dynamic mathematical modeling aspects for this equation in order to estimate the disease spreading patterns. The SIR equation modeling limitations were found as far as common epidemic preventive methods did not explain effectively the spreading patterns of disease transmission due to the virus association with the human emergent behavior in a complex network model.
