جستجوی مقالات مرتبط با کلیدواژه "continued fractions" در نشریات گروه "ریاضی"

EP numbers were introduced by Estrada and Pogliani in 2008. These are positive integers $E(n)$ defined as the product of $n$ and the sum of the digits of $n$. Estrada and Pogliani suspected that there may be infinitely many twin EP numbers; i.e. those pairs in this sequence that differ by one. It is relatively easy to show that three consecutive EP numbers do not exist, and that no pair $E(n)$ and $E(m)$ can be twins for infinitely many bases $b$. The main contribution of our work is the result that indeed there are infinitely many twin EP numbers over any base. The proof is constructive and makes use of elementary properties of natural numbers. The forms of the twin EP numbers presented are derived from continued fractions. The behavior of the series of the reciprocals of twin EP numbers is also considered.

In this paper we find all solutions of four kinds of the Diophantine equations x 2 ± Vtxy − y 2 ± x = 0 and x 2 ± Vtxy − y 2 ± y = 0, for an odd number t, and, x 2 ± Vtxy + y 2 − x = 0 and x 2 ± Vtxy + y 2 − y = 0, for an even number t, where Vn is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed to be exponentially distributed and are mutually independent. We have obtained the transient-state probabilities in terms of modified Bessel function of the first kind by employing probability generating function, continued fractions and Laplace transform. In addition, we have also obtained some other performance measures.

We investigate the long-term behavior of solutions of the di erence equation x_n+1 = x_nx_n-3 - 1; n = 0; 1; :: :; where the initial conditions x-3; x-2; x-1; x0 are real numbers. In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.