The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

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.

The objective of this research paper is two-fold. The first is a precise reading of the theoretical underpinnings of each of the strategic approaches: "Market approach" for (M. Porter), and the alternative resource-based approach (R B V), advocates for the idea that the two approaches are complementary. Secondly, we will discuss the possibility of combining the two competitive strategies: cost leadership and differentiation. Finally, we propose a consensual approach that we call "dual domination". 

Water quality sensors have recently received a lot of attention due to their impact on human health. Due to their distinct features, environmental sensors are based on carbon quantum dots (CQDs). In this study, CQDs were prepared using the electro-chemical method, where the structural and optical properties were studied. These quantum dots were used in the environmental sensor application after mixing them with three different materials: CQDs, Alq3 polymer and CQDs and Alq3 solutions using two different methods: drop casting and spin coating, and depositing them on silicon. The sensitivity of the water pollutants was studied for each case of the prepared samples after measuring the change in resistance of the samples at a temperature of

There is an evidence that channel estimation in communication systems plays a crucial issue in recovering the transmitted data. In recent years, there has been an increasing interest to solve problems due to channel estimation and equalization especially when the channel impulse response is fast time varying Rician fading distribution that means channel impulse response change rapidly. Therefore, there must be an optimal channel estimation and equalization to recover transmitted data. However. this paper attempt to compare epsilon normalized least mean square (ε-NLMS) and recursive least squares (RLS) algorithms by computing their performance ability to track multiple fast time varying Rician fading channel with different values of Doppler