On some P-Q modular equations of degree 45

Solving Simultaneous Modular Equations of Low Degree

We consider the problem of solving systems of equations Pi(x) 0 (mod ni) i = 1 : : : k where Pi are polynomials of degree d and the ni are distinct relatively prime numbers and x < min(ni). We prove that if k > d(d+1) 2 we can recover x in polynomial time provided min(ni) > 2 d . As a consequence the RSA cryptosystem used with a small exponent is not a good choice to use as a public key cryptos...

45 - On some equations over finite fields par IOULIA BAOULINA

Explicit Equations of Some Elliptic Modular Surfaces

We present explicit equations of semi-stable elliptic surfaces (i.e., having only type In singular fibers) which are associated to the torsion-free genus zero congruence subgroups of the modular group as classified by A. Sebbar.

On the degree of regularity of some equations

n In this paper we investigate the behaviour of the solutions of equations ~i=t aix, = b, where ~--~=~ ai = 0 and b # 0, with respect to colorings of the set N of positive integers. It tunas out that for any b # 0 there exists an 8-coloring of N, admitting no monochromatic solution of x3 -x2 = x2 x l + b. For this equation, for b odd and 2-colorings, only an odd-even coloring prevents a monochr...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...