Generalized Reverse Derivations on Semiprime Rings

In this paper we extend our ideas from reverse derivation towards the Generalized reverse derivations on semiprime rings. In this Paper, we prove that if d is a non-zero reverse derivation of a semi prime ring R and f is a generalized reverse derivation, thenis a strong commutativity preserving. Using this, we prove that R is commutative.

Jordan u-Generalized Reverse Derivations on Semiprime Rings

In this paper, we prove that if G is a Jordan u-generalized reverse derivation of a semi prime ring R of char.≠2, then G is a u-generalized reverse derivation. Similarly, we show that if G is a Jordan u-* generalized reverse derivation of a semi prime ring R of char.≠2, then G is a u-*generalized reverse derivation. We also prove that the commutativity of R if G([x,y]) =0.

Slant and Hemislant Submanifolds of a 3-Dimensional Indefinite Trans-Sasakian Manifold

In this paper we would like to establish some of the properties of slant and hemislant submanifoldsof an indefinite trans-Sasakian manifold. We have four sections in this paper. Section (1) isintroductory. In Section (2) we recall some necessary details of an indefinite trans-Sasakian manifold.In Section (3) we have obtained some interesting properties on a totally umbilical slant submanifoldsof an indefinite trans-Sasakian manifold. Finally, in Section (4), some results on integrability conditionsof the distributions of hemislant submanifolds of an indefinite trans-Sasakian manifold havebeen obtained.

Beal Conjecture

Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the field of number theory.

The Simplest Meijer's G-Function G0,11,0 as the Radial Functions of the Hydrogen Atom

The purpose of this paper is to show that how the sub-family of Meijer's G-functions, G0,11,0, deduces all the radial states of the Hydrogen atom. By introducing two postulates and using operator method similar with the method used for the simple harmonic oscillator we obtain all the excited radial states of the Hydrogen atom from the ground state. It is just needed to use two properties of Meijer's G-functions.

The Meijer's G-Functions: Convenient for Describing β Decay in Unstable Nuclei

The purpose of this paper is to show that the Meijer's G-functions which include all elementary and most of the special functions can describe some phenomena in nuclear physics. In fact, some interesting properties of Meijer's G-functions triggered us to apply these functions in the process β decay. These functions act as "wave functions" for parent and daughter nuclei.

A Note on Multiplicative Triple Fibonacci Sequences

In this paper, multiplicative triple Fibonacci sequences have been discussed. Here the results obtained by Singh et.al [3] have been extended. Some new theorems have been established.

Blow-Up Phenomena and Global Existence to a Weakly Dissipative Shallow Water Equation

We first establish the local well-posedness for a weakly dissipative shallow water equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. Then two blow-up results are derived for certain initial profiles. Finally, We study the long time behavior of the solutions.

The Proof of the Beal’s Conjecture

The truly marvellous proof of The Fermat's Last Theorem (FLT). Two false proofs of FLT for n = 4. The incomplete proof of FLT for odd prime numbers n ∈ Ρ. The proof of The Beal's Conjecture. The Beal's Theorem.