Abstract:
In this paper we explore some categorical results of 2-crossed module of commutative algebras extending work of Porter in [18]. We also show that the forgetful functor from the category of 2-crossed modules to the category of k-algebras, taking {L, M, P, \partial_2, \partial_1} to the base algebra P, is fibred and cofibred considering the pullback (coinduced) and induced 2-crossed modules constructions, respectively. Also we consider free 2- crossed modules as an application of induced 2-crossed modules.

Abstract:
In this work, it is shown that the category XMod/P of crossed modules over fi?xed group P is an exact category and the complete proof of the embedding theorem of XMod/P into a set valued functor category is given.

Abstract:
In this paper we examine on a pair of adjoint functors $(\phi ^{\ast},\phi_{\ast})$ for a subcategory of the category of crossed modules over commutative algebras where $\phi ^{\ast}:\mathbf{XMod}$\textbf{/}$% Q\rightarrow $ $\mathbf{XMod/}P$, pullback, which enables us to move from crossed $Q$-modules to crossed $P$-modules by an algebra morphism $\phi :P\rightarrow Q$ and $\phi_{\ast}:\mathbf{XMod}$\textbf{/}$P\rightarrow $ $\mathbf{XMod/}Q$, induced. We note that this adjoint functor pair $(\phi ^{\ast},\phi_{\ast})$ makes $p:\mathbf{XMod}\rightarrow $ $k$\textbf{-Alg}into a bifibred category over $k$\textbf{-Alg}, the category of commutative algebras, where $p$ is given by $p(C,R,\partial)=R.$ Also, some examples and results on induced crossed modules are given.

Abstract:
Reported is an empirical study which shows that Post-Traumatic Embitterment Disorder (PTED) is the most appropriate psychological diagnosis for victims of workplace conflicts, particularly bullying. A group of 118 people all reporting conflict at work were evaluated with the LIPT questionnaire, the PTED self-rating scale and a guided psychological interview. 91.5% proved to be affected by a PTED, the slight majority males, aged between 31 and 40 years and subjected to bullying. The evidence suggests that some workplace conflict victims who are presently diagnosed and treated as depression or phobia can be in fact cases of PTED. The treatment may be adjusted and the PTED scale may be used as a screening in-strument similar to scales for anxiety and depressive disorders.

Abstract:
In this paper, principally supplemented modules are dened asgeneralizations of lifting, principally lifting and supplemented modules. Severalproperties of these modules are proved. New characterizations of principallysemiperfect rings are obtained using principally supplemented modules.

Multimedia content delivery to capable smart phones with
high-speed next-generation Internet connectivity is becoming commonplace.
However, the openness of delivery demands adaptive and robust management of
intellectual property rights. The purpose of this article is to describe a
framework to address the central issues in content delivery: a scalable
peer-to-peer-based content delivery model. Our method pairs the delivery with a
secure access control model that enables data providers to secure a return from
making their original content available. Our work resulted in a prototype
implementation written in Java that includes a client for the Android mobile
platform. Adding robust trust management to scalable peer-to-peer content
delivery is the major significance of our work.

Abstract:
The aim of this study is to combine four fundamental forces in a single equation. Dirac equation is written by putting the Yukawa potential as a representation of the strong and gravitational forces. The ordinary terms seen in the Dirac Equation are treated as the representations of the electromagnetic forces. The Lagrangian of the weak local interaction of the charged particles is converted to the energy representation according to the virial theorem and is put in the equation. Thus four fundamental forces are combined in a unique equation.

The virial theorem is written by using the canonical equations of motion in classical mechanics. A moving particle with an initial speed in an n-particle system is considered. The distance of the moving particle from the origin of the system to the final position is derived as a function of the kinetic energy of the particle. It is thought that the considered particle would not collide with other particles in the system. The relation between the final and initial distance of the particle from the origin of the system is given by a single equation.

The scattering of electron by a photon is a well-known reaction in physics. In this study, the change in the electron’s energy after the scattering is taken into account. The previous works are searched. In order to take into account this change in the electron’s energy in the equation of motion of the electron, the Dirac equation is used with the virial theorem. The scattered electron kinetic energy which is given to the electron by the loss in photon’s energy is related to the potential energy of the electron by the virial theorem which states that the potential energy is two times of the kinetic energy in minus sign. A first time application of the virial theorem on a scattered electron by a photon is included to the Dirac equation.