This paper delves into some significant performance measures (PMs) of a bulk arrival queueing system with constant batch size b, according to arrival rates and service rates being fuzzy parameters. The bulk arrival queuing system deals with observation arrival into the queuing system as a constant group size before allowing individual customers entering to the service. This leads to obtaining a new tool with the aid of generating function methods. The corresponding traditional bulk queueing system model is more convenient under an uncertain environment. The α-cut approach is applied with the conventional Zadeh's extension principle (ZEP) to transform the triangular membership functions (Mem. Fs) fuzzy queues into a family of conventional b

The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

The research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used

In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period  The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and  the hazard function are found. The behaviour of probability density function for MWPDTI distrib

The theoretical analysis depends on the Classical Laminated Plate Theory (CLPT) that is based on the Von-K ráman Theory and Kirchhov Hypothesis in the deflection analysis during elastic limit as well as the Hooke's laws of calculation the stresses. New function for boundary condition is used to solve the forth degree of differential equations which depends on variety sources of advanced engineering mathematics. The behavior of composite laminated plates, symmetric and anti-symmetric of cross-ply angle, under out-of-plane loads (uniform distributed loads) with two different boundary conditions are investigated to obtain the central deflection for mid-plane by using the Ritz method. The computer programs is built using Ma

The research deals with the principle of the prohibition of international waterway diversion in the law of international watercourses. The research reviews individual and collective doctrinal efforts that have touched upon the principle as an internationally wrongful act because of its serious damage and consequences for downstream States. The research addresses the nature of the principle of the prohibition of diversion of international watercourses; its various effects; principles of international law establishing the principle of prohibition of diversion; and its application in State practice and international justice. This principle has been enshrined in most international treaties and judicial decisions. The principle of prohibition

The study aims to build a water quality index that fits the Iraqi aquatic systems and reflects the environmental reality of Iraqi water. The developed Iraqi Water Quality Index (IQWQI) includes physical and chemical components. To build the IQWQI, Delphi method was used to communicate with local and global experts in water quality indices for their opinion regarding the best and most important parameter we can use in building the index and the established weight of each parameter. From the data obtained in this study, 70% were used for building the model and 30% for evaluating the model. Multiple scenarios were applied to the model inputs to study the effects of increasing parameters. The model was built 4 by 4 until it reached 17 parame

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov