In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

The feature extraction step plays major role for proper object classification and recognition, this step depends mainly on correct object detection in the given scene, the object detection algorithms may result with some noises that affect the final object shape, a novel approach is introduced in this paper for filling the holes in that object for better object detection and for correct feature extraction, this method is based on the hole definition which is the black pixel surrounded by a connected boundary region, and hence trying to find a connected contour region that surrounds the background pixel using roadmap racing algorithm, the method shows a good results in 2D space objects.
Keywords: object filling, object detection, objec

The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.

We have studied some types of ideals in a KU-semigroup by using the concept of a bipolar fuzzy set. Bipolar fuzzy S-ideals and bipolar fuzzy k-ideals are introduced, and some properties are investigated. Also, some relations between a bipolar fuzzy k-ideal and k-ideal are discussed. Moreover, a bipolar fuzzy k-ideal under homomorphism and the product of two bipolar fuzzy k-ideals are studied.

The concept of forming the living space in the American strategic thought has an
important position it is regarded as an strategic movement that it supports the American
United States with the huge capabilities in its own concern that enables it to approach of
American administration , we find that of different historical periods it works to establish that
the geopolitical dimension which is accompanied with the ability of American response for
the evens that in its own turn enables the American united states to seize the growing chances
in the global strategic environment This study includes five chapters :
- Chapter one: The idea of living space.
- Chapter two: Geopolitical dimension of living space theory.
-

В статье рассматривается вопрос об использовании мультимедийных средств для оптимизации процесса формирования коммуникативной компетенции  в иракской аудитории с привлечением компьютерных технологий. Статья посвящена  использованию мультимедийных технологий  и  различных  приемов формирования интереса к русскому языку. Включение в процесс обучения коммуникативно-значимого, аутентичн

In this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

In this paper, a modified derivation has been introduced to analyze the construction of C-space. The profit from using C-space is to make the process of path planning more safety and easer. After getting the C-space construction and map for two-link planar robot arm, which include all the possible situations of collision between robot parts and obstacle(s), the A* algorithm, which is usually used to find a heuristic path on Cartesian W-space, has been used to find a heuristic path on C-space map. Several modifications are needed to apply the methodology for a manipulator with degrees of freedom more than two. The results of C-space map, which are derived by the modified analysis, prove the accuracy of the overall C-space mapping and cons

Na⁺/K⁺-ATPase is a prevalent enzyme that maintains the Na⁺ and K⁺ gradients across the cell membrane by transporting three Na⁺ out and two K⁺ into the cell, the aim of this study  is to provide detailed mechanistic insights, potentially with important effects on physiological regulation of active Na and K transport in tissues of Aerobic Thyroid Patient. Thyroid tissues were obtained from a 35 year old patients, the operation was carried out at the Al-Hadi Specialist Hospital in Samarra city, the sample was stored at -20^ºC until used. The purification protocol included Salt Precipitation, Ion Exchange Chromatography, Gel Filtration and E