A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ₀ erfc (x+y)/√8ct and θ( t,x,y,z) =θ₀ erfc (x+y+z/√12ct)

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

This paper proposed a new  method to study functional non-parametric regression data analysis with conditional expectation in the case that the covariates  are functional and the Principal Component Analysis was utilized to de-correlate the multivariate response variables. It  utilized the formula of the Nadaraya Watson estimator (K-Nearest Neighbour (KNN)) for prediction with different types of the semi-metrics, (which are based on Second Derivative and Functional Principal Component Analysis (FPCA))  for measureing the closeness between curves.  Root Mean Square Errors is used for the  implementation of this model which is then compared to the independent response method. R program is used for analysing data. Then, when  the cov

In this study, mean free path and positron elastic-inelastic scattering are modeled for the elements hydrogen (H), carbon (C), nitrogen (N), oxygen (O), phosphorus (P), sulfur (S), chlorine (Cl), potassium (K) and iodine (I). Despite the enormous amounts of data required, the Monte Carlo (MC) method was applied, allowing for a very accurate simulation of positron interaction collisions in live cells. Here, the MC simulation of the interaction of positrons was reported with breast, liver, and thyroid at normal incidence angles, with energies ranging from 45 eV to 0.2 MeV. The model provides a straightforward analytic formula for the random sampling of positron scattering. ICRU44 was used to compile the elemental composition data. In this

Signal denoising is directly related to sample estimation of received signals, either by estimating the equation parameters for the target reflections or the surrounding noise and clutter accompanying the data of interest. Radar signals recorded using analogue or digital devices are not immune to noise. Random or white noise with no coherency is mainly produced in the form of random electrons, and caused by heat, environment, and stray circuitry loses. These factors influence the output signal voltage, thus creating detectable noise. Differential Evolution (DE) is an effectual, competent, and robust optimisation method used to solve different problems in the engineering and scientific domains, such as in signal processing. This paper looks

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.

       Finally, all algori

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

In today's digital era, the importance of securing information has reached critical levels. Steganography is one of the methods used for this purpose by hiding sensitive data within other files. This study introduces an approach utilizing a chaotic dynamic system as a random key generator, governing both the selection of hiding locations within an image and the amount of data concealed in each location. The security of the steganography approach is considerably improved by using this random procedure. A 3D dynamic system with nine parameters influencing its behavior was carefully chosen. For each parameter, suitable interval values were determined to guarantee the system's chaotic behavior. Analysis of chaotic performance is given using the

  Many production companies suffers from big losses because of  high production cost and low profits for several reasons, including raw materials high prices and no taxes impose on imported goods also consumer protection law deactivation and national product and customs law, so most of consumers buy imported goods because it is characterized by modern specifications and low prices.

  The production company also suffers from uncertainty in the cost, volume of production, sales, and availability of raw materials and workers number because they vary according to the seasons of the year.

  I had adopted in this research fuzzy linear program model with fuzzy figures