The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

The mediation system is based on settling the dispute amicably through the intervention of a third party by bringing views closer away from the judiciary, which is an amicable way to settle disputes, which disputants resort to voluntarily, but some Western legislation has begun to impose resorting to mediation to settle disputes compulsorily, to take advantage of its advantages, get rid of the disadvantages of resorting to the judiciary in some disputes, and relieve pressure on the courts.

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

A simple setup of random number generator is proposed. The random number generation is based on the shot-noise fluctuations in a p-i-n photodiode. These fluctuations that are defined as shot noise are based on a stationary random process whose statistical properties reflect Poisson statistics associated with photon streams. It has its origin in the quantum nature of light and it is related to vacuum fluctuations. Two photodiodes were used and their shot noise fluctuations were subtracted. The difference was applied to a comparator to obtain the random sequence.

Polarization manipulation elements operating at visible wavelengths represent a critical component of quantum communication sub-systems, equivalent to their telecom wavelength counterparts. The method proposed involves rotating the optic axis of the polarized input light by an angle of 45 degree, thereby converting the fundamental transverse electric (TE0) mode to the fundamental transverse magnetic (TM0) mode. This paper outlines an integrated gallium phosphide-waveguide polarization rotator, which relies on the rotation of a horizontal slot by 45 degree at a wavelength of 700 nm. This will ultimately lead to the conception of a mode hybridization phenomenon in the waveguide. The simulation results demonstrate a polarization co

Stereolithography (SLA) has become an essential photocuring 3D printing process for producing parts of complex shapes from photosensitive resin exposed to UV light. The selection of the best printing parameters for good accuracy and surface quality can be further complicated by the geometric complexity of the models. This work introduces multiobjective optimization of SLA printing of 3D dental bridges based on simple CAD objects. The effect of the best combination of a low-cost resin 3D printer’s machine parameter settings, namely normal exposure time, bottom exposure time and bottom layers for less dimensional deviation and surface roughness, was studied. A multiobjective optimization method was utilized, combining the Taguchi me

The futuristic age requires progress in handwork or even sub-machine dependency and Brain-Computer Interface (BCI) provides the necessary BCI procession. As the article suggests, it is a pathway between the signals created by a human brain thinking and the computer, which can translate the signal transmitted into action. BCI-processed brain activity is typically measured using EEG. Throughout this article, further intend to provide an available and up-to-date review of EEG-based BCI, concentrating on its technical aspects. In specific, we present several essential neuroscience backgrounds that describe well how to build an EEG-based BCI, including evaluating which signal processing, software, and hardware techniques to use. Individu