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.

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

The  first chapter

The importance of research and the need for him

We have recently increased prevalence of behavioral problems rate, especially among young people, and this has become clear to all. In the light of social changes, political and economic and security conditions and technological advances enormous, especially in the means of communication such as the Internet and satellite television and mobile phone, resulted in the entry of some habits and Western values on our society which led to a vibration private values with low economic situation and the increasing youth unemployment and the resulting frustrations led to a situation of social chaos that we see now in th

In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM), does not require to calculate Lagrange multiplier a

Because of the new political stage that Iraq is living in, which called on researchers to choose the subject of political marketing and increase its effectiveness through strategic intuition. The problem of research was reflected in the following question: How can strategic intuition be used to achieve efficiency in marketing marketing to achieve voter acceptance and achieve political success later on? ).

The research derives its importance from the fact that it is related to the developments in the concepts and areas of marketing in various fields, and it has a role in identifying the gain of new markets, where it is specialized to provide a political product and identify the mechanism of marketing the p

This work was conducted to study the treatment of industrial waste water, and more particularly those in the General Company of Electrical Industries.This waste water, has zinc ion with maximum concentration in solution of 90 ppm.
The reuse of such effluent can be made possible via appropriate treatments, such as chemical coagulation, Na2S is used as coagulant.
The parameters that influenced the waste water treatment are: temperature, pH, dose of coagulant and settling time.
It was found that the best condition for zinc removal, within the range of operation used ,were a temperature of 20C a pH value of 13 , a coagulant dose of 15 g Na2S /400ml solution and a settling time of 7 days. Under these conditions the zinc concentrat

            This study aims to identify how the Zakat Fund contributes to financing entrepreneurial projects; and the role that these projects play in achieving economic and social development, despite the importance that contracting projects have in most countries as the main engine of growth; however, they still face many challenges that In the forefront of which is the challenge of obtaining financing; in this regard, it is possible to resort to the use of Zakat funds in the Islamic economy as it is a funding source that is closely proportional to the characteristics and goals of entrepreneurial projects in achieving development;

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Researching performance audits according to the dimensions of financial sustainability in light of the scarcity of resources and economic and social transformations in the business environment is of utmost importance in the non-profit non-governmental organizations in achieving the goals and correct the path and address deviations, and help them in improving the outputs of processes and associated procedures and capacity The research was based on the hypothesis that the existence of a performance audit program in accordance with the dimensions of financial sustainability leads to the measurement of the commitment of the Olympic Committee. National Iraqi indicators of financial sustainability of the dimension of revenue in order to improv