This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

A novel fractal design scheme has been introduced in this paper to generate microstrip bandpass filter designs with miniaturized sizes for wireless applications. The presented fractal scheme is based on Minkowski-like prefractal geometry. The space-filling property and self-similarity of this fractal geometry has found to produce reduced size symmetrical structures corresponding to the successive iteration levels. The resulting filter designs are with sizes suitable for use in modern wireless communication systems. The performance of each of the generated bandpass filter structures up to the 2^nd iteration has been analyzed using a method of moments (MoM) based software IE3D, which is widely adopted in microwave research and in

The main goal of this paper is introducing and studying a new concept, which is named H-essential submodules, and we use it to construct another concept called Homessential modules. Several fundamental properties of these concepts are investigated, and other characterizations for each one of them is given. Moreover, many relationships of Homessential modules with other related concepts are studied such as Quasi-Dedekind, Uniform, Prime and Extending modules.

Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.

In this paper we introduce G-Rad-lifting module as aproper generalization of lifting module, some properties of this type of modules are investigated. We prove that if M is G-Rad- lifting and
, then
, and
are G-Rad- lifting, hence we Conclude the direct summand of G-Rad- lifting is also G-Rad- lifting. Also we prove that if M is a duo module with
and
are G- Rad- lifting then M is G-Rad- lifting.

Let R be an associative ring with identity, and let M be a unital left R-module, M is called totally generalized *cofinitely supplemented module for short ( T G*CS), if every submodule of M is a Generalized *cofinitely supplemented ( G*CS ). In this paper we prove among the results under certain condition the factor module of T G*CS is T G*CS and the finite sum of T G*CS is T G*CS.

Sub-threshold operation has received a lot of attention in limited performance applications.However, energy optimization of sub-threshold circuits should be performed with the concern of the performance limitation of such circuit. In this paper, a dual size design is proposed for energy minimization of sub-threshold CMOS circuits. The optimal downsizing factor is determined and assigned for some gates on the off-critical paths to minimize the energy at the maximum allowable performance. This assignment is performed using the proposed slack based genetic algorithm which is a heuristic-mixed evolutionary algorithm. Some gates are heuristically assigned to the original and the downsized design based on their slack time determined by static tim