In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

The purpose of this paper is to define fuzzy subspaces for fuzzy space of orderings and we prove some results about this definition in which it leads to a lot of new results on fuzzy space of orderings. Also we define the sum and product over such spaces such that: If f = < a1,…,an > and g = < b1,…bm>, their sum and product are f + g = < a1…,an, b1, …, bm> and f × g =. for all a1,…,an,b1,…,bm ? G

Family social institution mission in the community, if and repaired Magistrate society and often lead that institution a positive role in the socialization, but a variety of factors ailing infect system family Vtfkdh role effective and influential in society and stands at the forefront of those factors disintegration family, whether caused by the death of one or both parents, divorce or separation, or whether the result of domestic weakness and poor family behavioral practices. And gaining the study of great importance and that the scarcity of studies that address the problem of delinquency female, is no secret that stand on the fact the role of disintegration family in the events of that problem will help and a large degree in the devel

Tigris River water that comes from Turkey represents the main water resource of this river in Iraq. The expansion in water river implementations has formed a source of trouble for the workers in the water resources management field in Iraqi. Unfortunately, there is no agreement between Iraq and Turkey till now to share the water of this international river. Consequently, the optimal operation of water resources systems, particularly a multi-objective, multi-reservoir, is of the most necessity at the present time.

 In this research two approaches, were used the dynamic programming (DP) approach and simulation model to find the optimal monthly operation of Ilisu Dam (from an Iraqi point of view) through a comp

Many critics suggest that Beckett’s early plays are comic because they focus their analyses on the use comic elements. Waiting for Godot is one of Beckett’s early plays, and it has been heavily analyzed and read as a comic text partly because its subtitle is “a tragicomedy in two acts” and also because of the comic techniques used in the play. The present paper, however, attempts to read the play as a piece in which comedy fails to produce any effects on the characters who remain apparently very desperate and frustrated throughout the play. The characters perform different comic acts, but they do not really feel amused or entertained. The paper suggests that the acts these characters put on stage are only means to pass t

numerical study is applied to the mercury-argon mixture by solving the boltzman transport equation for different mixture percentage.

Recently, complementary perfect corona domination in graphs was introduced. A dominating set S of a graph G is said to be a complementary perfect corona dominating set (CPCD – set) if each vertex in  is either a pendent vertex or a support vertex and  has a perfect matching. The minimum cardinality of a complementary perfect corona dominating set is called the complementary perfect corona domination number and is denoted by . In this paper, our parameter hasbeen discussed for power graphs of path and cycle.