Results 51 to 59 of about 654 (59)

Mild hydrolysis of chemically stable valerolactams by a biocatalytic ATP-dependent system fueled by metaphosphate.

Green Chem
Roth S, Gandomkar S, Rossi F, Hall M.
europepmc   +1 more source

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A probabilistic solution for the Syracuse conjecture

, 2021
We prove the veracity of the Syracuse conjecture by establishing that starting from an arbitrary positive integer, the Syracuse process will never reach any integer reached before and then we conclude by using a probabilistic (a random walk) approach ...
El ghazi Imad
semanticscholar   +1 more source

A STUDY OF COFFICIENTS DERIVED FROM ETA FUNCTIONS

, 2021
The main purpose and motivation of this work is to investigate and provide some new results for coefficients derived from eta quotients related to 3. The result of this paper involve some restricted divisor numbers and their convolution sums.
J. So, Jihyun Hwang, Daeyeoul Kim
semanticscholar   +1 more source

On Fermat power GCD matrices defined on special sets of positive integers

Applied Mathematical Sciences, 2019
In this article, we define the n×n Fermat Power GCD matrices defined on non factor-closed and non gcd-closed sets. A complete characterization of their factorizations, determinants, reciprocals, and inverses are given. Mathematics Subject Classification:
Y. Awad, Ragheb Mghames, H. Chehade, W. Zeid   +3 more
semanticscholar   +1 more source

Euler's φ-function over the domain of Gaussian integers

Applied Mathematical Sciences, 2019
If n = d1d2...dk is a product of positive integer, then the φ-function is defined as φ(n) = (d1 − 1)(d2 − 1)...(dk − 1), which is considered as a generalization for Euler’s function whenever n is a product of distinct primes. In this paper, we extend the
Y. Awad, W. Zeid, H. Chehade
semanticscholar   +1 more source

The range of the sum-of-proper-divisors function

, 2015
Answering a question of Erdős, we show that a positive proportion of even numbers are in the form s(n), where s(n) = σ(n)− n, the sum of proper divisors of n.
F. Luca, C. Pomerance
semanticscholar   +1 more source

Computational considerations on the representation of number-theoretic functions by arithmetic terms

Journal of Logic and Computation
We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the $ p $-adic valuation, the number-of-divisors function, the sum-of-divisors function,
Mihai Prunescu, Lorenzo Sauras Altuzarra
semanticscholar   +1 more source

A proof of a conjecture on monotonic behavior of the largest eigenvalue of a number-theoretic matrix

, 2015
In this study we investigate the monotonic behavior of the largest eigenvalue of the n×n matrix EnTEn, where the i j− entry of En is 1 if j|i and 0 otherwise and hence we present a proof of a part of the Mattila-Haukkanen conjecture [16]. MSC2010. 15A18,
E. Altınışık, Ş. Büyükköse
semanticscholar   +1 more source

Amicable Numbers and Groups II

, 2014
In this paper, we introduce the special amicable numbers. Afterward we extended the notion of special amicable numbers to finite groups. Also, we will compare amicable numbers (groups) and special amicable numbers (groups).
H. Khosravi, E. Faryad
semanticscholar   +1 more source