Showing papers by "Iran University of Science and Technology published in 1986"
TL;DR: In this paper, it was shown that T4 is irrational, which implies that X and 'T2 are also irrational, and that 'T4 = 4r/s.
Abstract: It is well known that the number v is transcendental; the proof is complicated. However, there are several elementary proofs that X and v 2 are irrational; see for example [1]. Using a simple trick, we will easily show that T4 is irrational, which of course implies that X and 'T2 are also irrational. THEOREM. 'T4 is irrational. Proof. Suppose v 4 is rational. Then there are positive integers r and s such that 'i4 = 4r/s. Let a = v (1 + i)/2, let p denote an integer of the form 1 + 4jrs(j = 1, 2,. .. ), and let 1p3 f (x4 -1P (1) IP = a4p-3sPj ( _ 1)! (ea(x-1) e-a(x-l) + ieia(x-l) ie-ia(x-l)) dx.
28 citations
TL;DR: An algorithm is developed for generating suboptimal cycle bases corresponding to localized statical bases, leading to highly sparse flexibility matrices.
20 citations
TL;DR: In this article, a method useful for estimation of the probabilities of future large earthquakes is described and illustrated numerically, which overcomes some of the limitations of other statistical methods often used for the prediction of large earthquakes.
19 citations
TL;DR: Some methods for solving the differential equation of the nonlinear anharmonic motion of an oscillator are considered in this paper, where the different given solutions are compared and compared in terms of their performance.
11 citations
2 citations
TL;DR: In this paper, the authors considered the nature of stationary axisymmetric convection in a rotating layer of fluid heated from below and derived the nonlinear amplitude equation for the case of rigid boundaries.
1 citations