Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.
The goal of this work is demonstrating, through the gradient observation of a of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of ( -system) was developed based on finite time ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypo
... Show MoreIn this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip ti
... Show MoreIn this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic
... Show MoreWestern Scholars have criticized al the material on the point of reliability . Some have taken the unduly Sceptical view that nothing is to be trusted except Quran . The present study is based on opposing view that at least the material in the early biographers is to be accepted as true , except where there are particular reasons for thinking that an anecdote has been distorted ( or invented ) through legal or political motives. It is also assumed that most of the background material culled from a large number of vaired works , is sound . This standpoint .I would claim , leads to a coherent view of Muhammad's life and achievement.
A Modified version of the Generlized standard addition method ( GSAM) was developed. This modified version was used for the quantitative determination of arginine (Arg) and glycine ( Gly) in arginine acetyl salicylate – glycine complex . According to this method two linear equations were solved to obtain the amounts of (Arg) and (Gly). The first equation was obtained by spectrophotometic measurement of the total absorbance of (Arg) and (Gly) colored complex with ninhydrin . The second equation was obtained by measuring the total acid consumed by total amino groups of (Arg) and ( Gly). The titration was carried out in non- aqueous media using perchloric acid in glacial acetic acid as a titrant. The developed metho
... Show MorePhysiological status and litter size can indeed have a significant impact on ewes' hematological parameters, which are essential indicators of their health. Therefore, this study examined the hematological profiles of ewes during pregnancy with single and twins in the Awassi ewes. The present study involved 232 ewes in good health and at sexual maturity. Among them, 123 ewes had single pregnancies, while 109 ewes had twin pregnancies. The age range of the ewes included in the study was between 3.5 and 4.5 years. Hematological tests were conducted on the sheep's blood samples promptly following collection. The findings demonstrated variations in hematological parameters among pregnant
... Show MoreData Driven Requirement Engineering (DDRE) represents a vision for a shift from the static traditional methods of doing requirements engineering to dynamic data-driven user-centered methods. Data available and the increasingly complex requirements of system software whose functions can adapt to changing needs to gain the trust of its users, an approach is needed in a continuous software engineering process. This need drives the emergence of new challenges in the discipline of requirements engineering to meet the required changes. The problem in this study was the method in data discrepancies which resulted in the needs elicitation process being hampered and in the end software development found discrepancies and could not meet the need
... Show MoreMercifulness is a trait of civilization, humanity, and a moral value in society, because it has an impact on social life and its role in spreading interdependence, joint liability, and solidarity among people. Mercifulness means spreading mercy, synergy, sympathy, and cooperation. Generally, a society that enjoys strong ties tends to have a kind of stability and development, as well as, is able to face the economic, political, and security crises. Conversely, a weak society leads to weak social cohesion and weak community infrastructure that is more vulnerable to social, economic, and political instability. Thus, this is the aim of the research that has used a social survey method applied to a sample of respondents who have reached (300)
... Show MoreHCl is separated from HCl –H2SO4 solution by membrane distillation process(MD). The flat –sheet membranes made from polyvinylidene fluoride (PVDF) and polypropylene (pp.). Plate and frame these types of membrane where used in the process. The feed is a mixture of HCl and H2SO4 acids compositions depended on metals treated object.HCl concentration increased in the permeate during the process but sulfuric acid increased gradually in the feed .During the concentration of solution acids concentrations in the feed at the beginning were 50 g/dm3 of sulfuric acid and 50 g/dm3 of hydrochloric acid at 333K feed temperature the permeate flux was 71 dm
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