A $p+1$ method of factoring

Turning Euler's Factoring Method into a Factoring Algorithm

An algorithm is presented which, given a positive integer n, will either factor n or prove it to be prime. The algorithm takes O(«) steps.

Speeding Fermat's factoring method

A factoring method is presented which, heuristically, splits composite n in O(n1/4+ ) steps. There are two ideas: an integer approximation to √ (q/p) provides an O(n1/2+ ) algorithm in which n is represented as the difference of two rational squares; observing that if a prime m divides a square, then m2 divides that square, a heuristic speed-up to O(n1/4+ ) steps is achieved. The method is well...

Factoring Networks by a Statistical Method

We show that it is possible to factor a multi-layered classiication network with a large output layer into a number of smaller networks, where the product of the sizes of the output layers equals the size of the original output layer. No assumptions of statistical independence are required.

A Sieve Method for Factoring Numbers

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...