The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica^®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4^th order Runge-Kutta meth

          Graphite Coated Electrodes (GCE) based on molecularly imprinted polymers were fabricated for the selective potentiometric determination of Risperidone (Ris). The molecularly imprinted (MIP) and nonimprinted (NIP) polymers were synthesized by bulk polymerization using (Ris.) as a template, acrylic acid (AA) and acrylamide (AAm) as monomers, ethylene glycol dimethacrylate (EGDMA) as a cross-linker and benzoyl peroxide (BPO) as an initiator. The imprinted membranes and the non-imprinted membranes were prepared using dioctyl phthalate (DOP) and Dibutylphthalate (DBP) as plasticizers in PVC matrix. The membranes were coated on graphite electrodes. The MIP electrodes using

Gumbel distribution was dealt with great care by researchers and statisticians. There are traditional methods to estimate two parameters of Gumbel distribution known as Maximum Likelihood, the Method of Moments and recently the method of re-sampling called (Jackknife). However, these methods suffer from some mathematical difficulties in solving them analytically. Accordingly, there are other non-traditional methods, like the principle of the nearest neighbors, used in computer science especially, artificial intelligence algorithms, including the genetic algorithm, the artificial neural network algorithm, and others that may to be classified as meta-heuristic methods. Moreover, this principle of nearest neighbors has useful statistical featu

Audio security is an important aspect in various areas of communication. This paper deals with audio encryption as many of the data communication depends on audio data.  In this paper, a new proposal of audio encryption system has been introduced. The system can be divided into two phases, the first phase focuses on generating a high-quality Pseudo Random Number generator (PRNGs) using elementary, periodic and hybrid rules of cellular automata (CA). The system suggests a new combination of CA rules in an endeavor to provide high randomness and to improve the strength of the proposed cryptosystem. Whereas the second phase produces the Enhanced Rivest Cipher 5 (ERC5) algorithm which employs the generated Random Number Sequence (RNS) i

Objective: to evaluate the results of (Modification of Russe method) in treatment of nonunion fracture scaphoid bone by bone graft with external splintage (plaster of paris cast (pop ). Methods:Prospective study done on 26 patients (24 male, 2 female), age range between 25-42 years (mean age 34 years), fracture site at middle 1/3 with minimal displacements with no carpal bone or radial bone injury, technique of Matte- Russe method (explore the bone through volar approach using bone graft from iliac crest (cortico-cancellous peg plus cancellus bone) with thumb spica for 90 days with period of follow up 12-18 months. Results: out of 26 patients treated by this method , 23 patients (88.5%) union was achieved radiologically by the end of 3rd mo

Objective: to evaluate the results of (Modification of Russe method) in treatment of nonunion fracture scaphoid bone by bone graft with external splintage (plaster of paris cast (pop ).
Methods:Prospective study done on 26 patients (24 male, 2 female), age range between 25-42 years (mean age 34 years), fracture site at middle 1/3 with minimal displacements with no carpal bone or radial bone injury, technique of Matte- Russe method (explore the bone through volar approach using bone graft from iliac crest (cortico-cancellous peg plus cancellus bone) with thumb spica for 90 days with period of follow up 12-18 months.
Results: out of 26 patients treated by this method , 23 patients (88.5%) union was achieved radiologically by the end

  In this paper, we introduce a new class of sets, namely , s*g--open sets and we show that the family of all s*g--open subsets of a topological space ) ,X(  from a topology on X which is finer than  . Also , we study the characterizations and basic properties of s*g-open sets and s*g--closed sets . Moreover, we use these sets to define and study a new class of functions, namely , s*g-  -continuous functions and s*g-  -irresolute functions in topological spaces . Some properties of these functions have been studied .

In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials