This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

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In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

Three-dimensional (3D) reconstruction from images is a most beneficial method of object regeneration by using a photo-realistic way that can be used in many fields. For industrial fields, it can be used to visualize the cracks within alloys or walls. In medical fields, it has been used as 3D scanner to reconstruct some human organs such as internal nose for plastic surgery or to reconstruct ear canal for fabricating a hearing aid device, and others. These applications need high accuracy details and measurement that represent the main issue which should be taken in consideration, also the other issues are cost, movability, and ease of use which should be taken into consideration. This work has presented an approach for design and construc

The aim of this paper is to construct cyclic subgroups of the projective general linear group over  from the companion matrix, and then form caps of various degrees in . Geometric properties of these caps as secant distributions and index distributions are given and determined if they are complete. Also, partitioned of  into disjoint lines is discussed.

Computer vision seeks to mimic the human visual system and plays an essential role in artificial intelligence. It is based on different signal reprocessing techniques; therefore, developing efficient techniques becomes essential to achieving fast and reliable processing. Various signal preprocessing operations have been used for computer vision, including smoothing techniques, signal analyzing, resizing, sharpening, and enhancement, to reduce reluctant falsifications, segmentation, and image feature improvement. For example, to reduce the noise in a disturbed signal, smoothing kernels can be effectively used. This is achievedby convolving the distributed signal with smoothing kernels. In addition, orthogonal moments (OMs) are a cruc

In this paper a prey - predator model with harvesting on predator species with infectious disease in prey population only has been proposed and analyzed. Further, in this model, Holling type-IV functional response for the predation of susceptible prey and Lotka-Volterra functional response for the predation of infected prey as well as linear incidence rate for describing the transition of disease are used. Our aim is to study the effect of harvesting and disease on the dynamics of this model.

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.