Let p denote a prime. In this article we provide the first published lower bounds for the greatest prime factor of p−1 exceeding (p−1) 1 2 in which the constants are effectively computable. As a result we prove that it is possible to calculate a value x0 such that for every x > x0 there is a p < x with the greatest prime factor of p − 1 exceeding x 3 5 . The novelty of our approach is the avoid...

In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

This paper attempts to predict heavy metals (Pb, Zn and Cu) in the groundwater from Arak city, using support vector regression model(SVR) by taking major elements (HCO3, SO4) in the groundwater from Arak city. 150 data samples and several models were trained and tested using collected data to determine the optimum model in which each model involved two inputs and three outputs. This SVR model f...

One of the most important and widely-studied questions in computational number theory is how to efficiently compute the prime factorizations of large integers. Among other applications, fast prime-factorization algorithms would break the widely-used RSA cryptosystem, and be of great interest in complexity theory. In particular, there is no algorithm which can factor an integer n in polynomial t...

In this note, we establish a mass formula for self-orthogonal codes over Zp2, where p is a prime. As a consequence, an alternative proof of the known mass formulas for self-dual codes over Zp2 is obtained. We also establish a mass formula for even quaternary codes, which includes a mass formula for Type II quaternary codes as a special case. On study leave from the Institute of Mathematics, Uni...

Long binary sequences related to cyclic difference sets are investigated. Among all known constructions of cyclic difference sets we show that only sequences constructed from Hadamard difference sets can have an asymptotic nonzero merit factor. Maximal length shift register sequences, Legendre, and twin-prime sequences are all constructed from Hadamard difference sets. We prove that the asympto...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.