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 4th order Runge-Kutta method (RK4), which gives very good agreement. In addition, the convergence of the proposed approximate methods is given based on one of the Banach fixed point theorem results.
Three N-(hydroxylphenyl) dimethylmaleimides were directly prepared in good yields (81-86)% from the reaction of dimethylmaleic anhydride with amino phenols. The prepared imides were esterified to the corresponding benzoates, methacrylates and cinnamates via their reaction with different acid chlorides in the presence of triethylamine. The prepared esters were tested as plasticizers for PVC via preparing of thirty six samples of PVC with the prepared esters in certain weight ratio followed by recording their softening points. Comparison the results with the universal plasticizers for PVC (DOP) and (DBP) indicated that the prepared esters in general have high plasticizing efficiency.
This study used deep eutectic solvent (DES) as the liquid membrane in a bulk liquid membrane system (BLM) to remove glycerol from waste cooking oil‐based biodiesel. The DES was prepared from choline chloride and tetraethylene glycol at a molar ratio of 1:5. Diethyl ether was employed as a novel strip phase for the glycerol in BLM. The effects of the DES: biodiesel ratio, stirring speed, and extraction time on the extraction and stripping efficiencies were investigated. The results showed that BLM could give better glycerol removal from biodiesel than mechanical shaking. Increasing the DES: biodiesel ratio, stirring speed, and extraction time can enhance glycerol removal from the feed phase, achievi
In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modifications are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.
Various methods are utilized providing complexity for cryptosystem with the aim to increase the security and avoiding hacker attack. Hybrid cryptosystem is one of these cryptosystems which is used two types of cryptosystems and has many applications in data transmitted. This research, proposed a novel method that used power exponent instead of using the prime number directly and also providing complexity of asymmetric cryptosystems. This method has been applied theoretically in two public systems RSA and EL-Gamal. Power RSA and Power EL-Gamal are modified asymmetric cryptosystems, in which the power number is kept by the sender and the receiver. Moreover, we use group theory to prove that these cryptosystems work properly. Our exten
... Show MoreA new human-based heuristic optimization method, named the Snooker-Based Optimization Algorithm (SBOA), is introduced in this study. The inspiration for this method is drawn from the traits of sales elites—those qualities every salesperson aspires to possess. Typically, salespersons strive to enhance their skills through autonomous learning or by seeking guidance from others. Furthermore, they engage in regular communication with customers to gain approval for their products or services. Building upon this concept, SBOA aims to find the optimal solution within a given search space, traversing all positions to obtain all possible values. To assesses the feasibility and effectiveness of SBOA in comparison to other algorithms, we conducte
... Show MoreModern French novel has gained a distinctive status in the history of French literature during the first half of the twentieth century. This is due to many factors including the new literary descriptive objective style adopted by novelists like Alain Robbe – Grillet that has long been regarded as the outstanding writer of the nouveau roman, as well as its major spokesman, a representative writer and a leading theoretician of the new novel that has broken the classical rules of the one hero and evolved, through questioning the relationship of man and the world and reevaluating the limits of contemporary fiction , into creating a new form of narrative.
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... Show MoreAll-optical canonical logic units at 40 Gb/s using bidirectional four-wave mixing (FWM) in highly nonlinear fiber are proposed and experimentally demonstrated. Clear temporal waveforms and correct pattern streams are successfully observed in the experiment. This scheme can reduce the amount of nonlinear devices and enlarge the computing capacity compared with general ones. The numerical simulations are made to analyze the relationship between the FWM efficiency and the position of two interactional signals. © 2015 Chinese Laser Press