This paper dealing with Colombeau extension of the Einstein field equations using apparatus of the Colombeau generalized function [1]-[2] and contemporary generalization of the classical Lorentzian geometry named in literature Colombeau distributional geometry, see for example [5]-[30] and [15][31]. The regularizations of singularities present in some Colombeau solutions of the Einstein equations is an important […]

Aims: A shape optimization technique is developed, using the boundary element method, for two-dimensional anisotropic structures to study the effects of anisotropy on the displacements and stresses, then minimize weight while satisfying certain constraints upon stresses and geometry. Study Design:  Original Research Paper. Place and Duration of Study: Jamoum University College, Mathematics Department, between June […]

Limit is a basic concept of calculus. However, according to the updated definition, the limit of periodic function at infinity is not in existence. This conclusion of description does not suit with the periodic phenomenon. For example, the temperature on earth is changed periodically every year since the birth of the earth (viewed as t=0). […]

This chapter studies a prominent class of recursively-defined combinatorial functions, namely, the binomial and multinomial coefficients and probabilities. The chapter reviews the basic notions and mathematical definitions of these four functions. Subsequently, it characterizes each of these functions via a recursive relation that is valid over a certain two-dimensional or multi-dimensional region and is supplemented […]

The strong equality of classical tautologies and their proof complexities comparative analysis in certain proof systems were given by first author in previous studies. Here we introduce the analogous notions of strong equality for non-classical (intuitionistic and minimal) tautologies and investigate the relations between the proof complexity measures of strongly equal non-classical tautologies in some […]

Aims: A practicalshape optimization technique is developed, using the dual reciprocity boundary element method (DRBEM) with the golden-section search algorithm based on uniform bicubic B-splines, for rotating magneto-thermo-viscoelastic functionally graded anisotropic (FGA) structures subjected to a moving heat source in the context of the Green and Naghdi theory of type III. Study Design: Original Research […]

Aims: We give some families of functions which are meromorphic outside a compact countable set B of essential singularities. Our aim is to give some examples of the stable set (called the Fatou set) and the unstable set (called the Julia set) since there are not many examples of parametric family of this class of […]

In this Chapter we obtain a contradictions in formal set theories under assumption that these theories have omega-models or nonstandard model with standard part. An possible generalization of Lob’s theorem is considered. Main results are: (i) ¬Con(ZF C+∃MZFCst), (ii) ¬Con(N F+∃MNFst), (iii) ¬Con(ZF C2), (iv) let k be an inaccessible cardinal then ¬Con(ZF C+∃κ), (v) […]

The  main  thrust of the  paper  is to provide  an interesting and  useful for students example  of using bitwise  operations in  programming languages C  ++ and  Java. As an example, we describe an algorithm for receiving a Latin square of arbitrary order.   So we will outline some techniques for the use of bitwise operations. The  […]

Aims: Classic Petri nets also known as place transition nets provide many interesting and useful features for system modeling. They are however limited by the place types that are used. A novel approach is presented in this work. A matrix vector transition net model is created and is used to model complex system behavior. This […]