This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of ri

Throughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings

The Arab literature in Andalusia was distinguished by its special nature, in addition to the distinction of its influencing rhythm in our souls, it represents the natural extension of the Arab-Islamic civilization in Morocco, that civilization that collapsed with insecurity and stability and the exit of Muslim Arabs from those countries and the defeat of Muslims, their civilization has ceased, and only remains of them witnessing For its leaders in a safe and stable life, but literature in Andalusia underwent many experiences that express the lives of Arab Muslims there, especially what distinguished the Andalusian Muslims from their many battles and conquests, but they did not suffer as their support during the fall of Andalusia and the

The purposes of study are to measure the perceived competence and the locus of control among sixth-grade students, to identify the statistical differences between the perceived competence and the locus of control among sixth-grade students regarding the variable of gender, achievement, and economical status, and lastly, explore the correlation relationship between perceived competence and locus of control among sixth-grade students, To do this, the researchers have constructed two scales: one to measure the perceived competence based on bandura's theory (social-cognitive theory) which consisted of (26) items and the other to measure the locus of control based on Rotter's theory (social-learning theory) which included (25) items. The samp

The quality of Global Navigation Satellite Systems (GNSS) networks are considerably influenced by the configuration of the observed baselines. Where, this study aims to find an optimal configuration for GNSS baselines in terms of the number and distribution  of baselines to improve the quality criteria of the GNSS networks. First order design problem (FOD) was applied in this research to optimize GNSS network baselines configuration, and based on sequential adjustment method to solve its objective functions.

FOD for optimum precision (FOD-p) was the proposed model which based on the design criteria of A-optimality and E-optimality. These design criteria were selected as objective functions of precision, whic

The paper deals with the traveling wave cylindrical heating systems. The analysis presented is analytical and a multi-layer model using cylindrical geometry is used to obtain the theoretical results. To validate the theoretical results, a practical model is constructed, tested and the results are compared with the theoretical ones. Comparison showed that the adopted analytical method is efficient in describing the performance of such induction heating systems.

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