In this work, the differential evolution algorithm behavior under a fixed point arithmetic is analyzed also using half-precision floating (FP) numbers of 16 bits, and these last are known as FP16. paper, it considered that important to analyze (DE) in circumstances with goal reducing its consumption power, storage size variables, improve speed behavior. All aspects become if one needs design de...

This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under triangular intuitionistic fuzzy sets by using its correlation coefficient. In situations where the information or the data is of the form of triangular intuitionistic fuzzy numbers (TIFNs), some arithmetic aggregation operators h...

We study arithmetic properties of a new treebased number representation, Recursively run-length compressed natural numbers, defined by applying recursively a run-length encoding of their binary digits. Our representation supports novel algorithms that, in the best case, collapse the complexity of various computations by superexponential factors and in the worse case are within a constant factor...

hold. The above defined q-zeta values (1) present several new interesting problems in the theory of diophantine approximations and transcendental numbers; these problems are extensions of the corresponding problems for ordinary zeta values and we state some of them in Section 3 of this note. Our nearest aim is to demonstrate how some recent contributions to the arithmetic study of the numbers ζ...

An injective map from the vertex set of a graph G—its order may not be finite—to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is c...

It is known that the numbers which occur in Apéry’s proof of the irrationality of ζ(2) have many interesting congruences properties while the associated generating function satisfies a second order differential equation. We prove congruences for numbers which arise in Beukers’ and Zagier’s study of integral solutions of Apéry-like differential equations.

Assuming a weak version of a conjecture of Heath-Brown on the least prime in a residue class, we show that for any coprime integers a and m > 1, there are infinitely many Carmichael numbers in the arithmetic progression a mod m.

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. The p-adic norm is normalized so that |p|p 1/p. Let N be the set of natural numbers and Z N ∪ {0}. Let UD Zp be the space of uniformly differentiable functions on Zp. For f ∈ ...

In this paper, we study the sums of k-Fibonacci numbers with indexes in an arithmetic sequence, say anþ r for fixed integers a and r. This enables us to give in a straightforward way several formulas for the sums of such numbers. 2008 Elsevier Inc. All rights reserved.