Recurrent aphthous stomatitis (RAS) is a prevalent and complicated disorder and its management is directed toward treatment of symptoms. The purpose of this study was to compare the efficacy of three herbal preparations in the management of RAS. One hundred and one out of 115 patients with minor aphthae were selected and randomly divided into four groups. Groups A, B and C received topical prep...

Introduction 2 1. The Group Law on Pell Conics and Elliptic Curves 2 1.1. Group Law on Conics 2 1.2. Group Law on Elliptic curves 3 2. The Group Structure 3 2.1. Finite Fields 3 2.2. p-adic Numbers 3 2.3. Integral and Rational Points 4 3. Applications 4 3.1. Primality Tests 4 3.2. Factorization Methods 5 4. 2-Descent 5 4.1. Selmer and Tate-Shafarevich Group 5 4.2. Heights 6 5. Analytic Methods ...

The well-known Birch and Swinnerton-Dyer conjecture gives a deep connection between the leading coefficient of the L-series and the arithmetic properties of an abelian variety. Both are very important and subtle. This paper is part of an effort to compute the analytic side explicitly in a special case. Indeed, we are interested in the central derivative of certain algebraic Hecke L-series, rela...