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 specific cases of time-dependent diffusion equations. Moreover, the maximum absolute error () is determined to demonstrate the accuracy of the proposed techniques.
In this paper, we study the growth of solutions of the second order linear complex differential equations insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .
Mosquitoes like Culex quinquefasciatus are the primary vector that transmits many causes of diseases such as filariasis, Japanese encephalitis, and West Nile virus, in many countries around the world. The development in the scientific fields, such as nanotechnology, leads to use this technique in control programs of insects including mosquitoes through the use of green synthesis of nanoemulsions based on plant products such as castor oil. Castor oil nanoemulsion was formulated in various ratios comprising of castor oil, ethanol, tween 80, and deionized water by ultrasonication. Thermodynamic assay improved that the formula of (10 ml) of castor oil, ethanol (5ml), tween 80 (14 ml) and deionized water (71ml) was mor
... Show MoreThe article presents the results of studies of the species composition of phytopathogens of winter soft wheat grain affected by ear fusarium. For the first time, studies were conducted using a complex of electron microscopic, molecular genetics, and mycological methods. The species F. graminearum dominated in all samples (frequency of occurrence 42.8%). The species F. avenaceum (23.3%), F. sporotrichioides and F. equiseti (8.8% each) were noted with high frequency. Next in descending order of frequency of occurrence: F. oxysporum, F. boothii, F. poae, F. proliferatum, F. accumatum, F. incarnatum, F. vorosii, F. tricinctum, F. cerealis, F. sambuticum. For the first time, 7 species were found for the plain zone of the Pre-Caucasus: F.
... Show MoreThe recent development in statistics has made statistical distributions the focus of researchers in the process of compensating for some distribution parameters with fixed values and obtaining a new distribution, in this study, the distribution of Kumaraswamy was studied from the constant distributions of the two parameters. The characteristics of the distribution were discussed through the presentation of the probability density function (p.d.f), the cumulative distribution function (c.d.f.), the ratio of r, the reliability function and the hazard function. The parameters of the Kumaraswamy distribution were estimated using MLE, ME, LSEE by using the simulation method for different sampling sizes and using preli
... Show MoreIn the present work usedNd:YAG laser systems of different output characteristic were employed to study the drilling process of material used in scientific and industrial fields. This material include Manganese hard steel. Our study went into the affecting parameters in drilling of Manganese hard steel by laser. Drilling process is achieved through material absorption of part of the incident laser beam. It is the resultant of interfering both, laser beam and material properties and the focusing conditions of the beam. The results as shown that the increase in the laser pulse energy over the used level has raised the hole diameter, depth and increased the hole taper. In addition to that a hole taper was affected by the laser energy, the fo
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The methods of the Principal Components and Partial Least Squares can be regard very important methods in the regression analysis, whe
... Show MoreThe power generation of solar photovoltaic (PV) technology is being implemented in every nation worldwide due to its environmentally clean characteristics. Therefore, PV technology is significantly growing in the present applications and usage of PV power systems. Despite the strength of the PV arrays in power systems, the arrays remain susceptible to certain faults. An effective supply requires economic returns, the security of the equipment and humans, precise fault identification, diagnosis, and interruption tools. Meanwhile, the faults in unidentified arc lead to serious fire hazards to commercial, residential, and utility-scale PV systems. To ensure secure and dependable distribution of electricity, the detection of such ha
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