A simple new solution of the Diophantine equation $A^3+B^3+C^3=D^3$

Practical Solution of the Diophantine Equation

Let p be an odd prime and a, b positive integers. In this note we prove that the problem of the determination of the integer solutions to the equation y2 = x(x + 2apb)(x − 2apb) can be easily reduced to the resolution of the unit equation u+ √ 2v = 1 over Q( √ 2, √ p). The solutions of the latter equation are given by Wildanger’s algorithm.

A SIMPLE SOLUTION OF THE DIOPHANTINE EQUATION x+y = z+t

solution of security constrained unit commitment problem by a new multi-objective optimization method

چکیده-پخش بار بهینه به عنوان یکی از ابزار زیر بنایی برای تحلیل سیستم های قدرت پیچیده ،برای مدت طولانی مورد بررسی قرار گرفته است.پخش بار بهینه توابع هدف یک سیستم قدرت از جمله تابع هزینه سوخت ،آلودگی ،تلفات را بهینه می کند،و هم زمان قیود سیستم قدرت را نیز برآورده می کند.در کلی ترین حالتopf یک مساله بهینه سازی غیر خطی ،غیر محدب،مقیاس بزرگ،و ایستا می باشد که می تواند شامل متغیرهای کنترلی پیوسته و گ...

Hardware Solution of a First-Order Diophantine Equation

In this paper we present the theoretical framework for enumerating the solutions of the Diophantine equation (1) that helps us define the sets of points, of a nested loop, that can be executed in parallel. The analytical expression for finding those points is given below: + + + = 1 2 ... n i i i c (1) where i1, i2,..., in, ≤ ≤ ∀ = 0 , 1 ... p p i L p n are the loop indices, Lp is the loop bound...

A new Approximation to the solution of the linear matrix equation AXB = C

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....