In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall

The increasing use of plastics in various aspects of modern life resulted in the availability of enormous amount of wastes, including a negative effect on the environment and humans. So it is necessary to find solutions to deal with these wastes and ensure to use them as solutions to use in concrete mix . In this research the production of concrete containing high and low density polyethylene has been used by (5, 10, 15)% as a replacement of part of the volume of sand, so as to obtain concrete good compressive strength as well as other benefits such as improved possibility of pumping concrete and reduce the loss of concrete for workability polymer is a material that is non-absorbable of water . It is also intended to dispose of these was

The numerical simulation for the low frequency waves in dusty plasma has been studied. The studying was done by taking two special cases depending on the direction of the propagation of the wave:First, when the propagation is parallel to the magnetic field K//B,this mode is called acoustic mode.Second,when K B this mode is called cyclotron mode.In addition, every one of the two modes divided into two modes depending on the range of the frequency.The Coulomb coupling parameter was studied, with temperature T,density of the dust particles Nd ,and the charge of the particle Qd.The low frequency electrostatic waves in dusty grains were studied. Also, the properties of ion-acoustic waves and ion-cyclotron waves are shown to modify even through

Receipt date:3/13/2021 accepted date:5/26/2021 Publication date:12/31/2021

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energy is one of the strategic resources within international politics, and this is through the existing competition between the international powers on it, and the global powers have begun to rely on interest in new areas, such as import, depending on new projects an

The issue of insurance against unlawful risks raises a jurisprudential and judicial debate between two opposing trends: the first considers coverage of these risks invalid due to their impact on public order or morals, while the second—which this research analyses—calls for the possibility of covering these risks in specific circumstances, based on contractual considerations in accordance with the principle that the contract is the law of the contracting parties, and based on the obligation to compensate the harmed third party—the victim—who has no connection to the unlawful act. In this context, our research highlights that contractual considerations can justify coverage of some unlawful risks, provided that the goal is to achieve

The holmium plasma induced by a 1064-nmQ-switched Nd:YAG laser in air was investigated. This work was done theoretically and experimentally.  Cowan code was used to get the emission spectra for different transition of the holmium target. In the experimental work, the evolution of the plasma was studied by acquiring spectral images at different laser pulse energies (600,650,700, 750, and 800 mJ). The repetition rates of (1Hz and 10Hz) in the UV region (200-400 nm). The results indicate that, the emission line intensities increase with increasing of the laser pulse energy and repetition rate. The strongest emission spectra appeared when the laser pulse energy is 800mJ and 10 Hz repetition rate at λ= 345.64nm, with the maximum intensi

Increased downscaling of CMOS circuits with respect to feature size and threshold voltage has a result of dramatically increasing in leakage current. So, leakage power reduction is an important design issue for active and standby modes as long as the technology scaling increased. In this paper, a simultaneous active and standby energy optimization methodology is proposed for 22 nm sub-threshold CMOS circuits. In the first phase, we investigate the dual threshold voltage design for active energy per cycle minimization. A slack based genetic algorithm is proposed to find the optimal reverse body bias assignment to set of noncritical paths gates to ensure low active energy per cycle with the maximum allowable frequency at the optimal supply vo