The paper establishes explicit representations of the errors and residuals of approximate
solutions of triangular linear systems by Jordan elimination and of general linear algebraic
systems by Gauss-Jordan elimination as functions of the data perturbations and the rounding
errors in arithmetic floating-point operations. From these representations strict optimal
componentwise error and residual bounds are derived. Further, stability estimates for the
solutions are discussed. The error bounds for the solutions of triangular linear systems are
compared to the optimal error bounds for the solutions by back substitution and by Gaussian
elimination with back substitution, respectively. The results confirm in a very

Le professeur Taranne et La non-Communication

Language is the realistic and sensitive basis for any communication between two or more parties. It is an important workshop that prepares meanings and coding them according to a linguistic structure governed by agreed rules that speak to and coexist with everyone.

Whereas the forms of communication are: personal, mediator and mass, none of them can move away from language in their dealings and communication patterns. Since each has its own characteristics and skills, it must be launched in its fields through verbal and non-verbal symbols and wears the elements of influential language as intended.

It makes the recipient face two things: whether he fails to understand those symbols hence its purpose fail, or he meditates s

Modern digital technologies have affected the means of communication in terms of structure, function and methods of dealing with them, and the communication process has changed, becoming bilateral, reciprocal and interactive, after it was one-way and limited in circulation and the roles changed, so the receiver became the sender and reversed is correct, and the culture of the active user and the participant spread, and the communication process became continuous.
The international information network has provided new electronic channels in the media and communication that are not known and opened a new era for these means, which led to a trend towards digital media in an unprecedented way.
The new communication platforms are the re

The aim of our study is to solve a nonlinear epidemic model, which is the COVID-19 epidemic model in Iraq, through the application of initial value problems in the current study. The model has been presented as a system of ordinary differential equations that has parameters that change with time. Two numerical simulation methods are proposed to solve this model as suitable methods for solving systems whose coefficients change over time. These methods are the Mean Monte Carlo Runge-Kutta method (MMC_RK) and the Mean Latin Hypercube Runge-Kutta method (MLH_RK). The results of numerical simulation methods are compared with the results of the numerical Runge-Kutta 4th order method (RK4) from 2021 to 2025 using the absolute error, which prove

The novel groups of organic chromophores containing triphenylamine (TPA) (ATP-I to ATP-IV) have been constructed by structural modification of electron donors with substitution biphenyl and bipyridine rings inserting a π-linkage. Density functional theory (DFT) and time-dependent type of it (TD-DFT) have been operated to study results of donating ability of TPA and spacer on absorption, geometrical, photovoltaic, and energetic attributes of these sensitizers. Structural attributes have been revealed that incorporation of TPA, acceptor and π bridge include a perfect coplanar conformation in TPA-III. Based on frequency computations and ground-state optimization, bandgap (Eg) energy, ELUMO, EHOMO have been determined. For enlightening maximu

The security of message information has drawn more attention nowadays, so; cryptography has been used extensively. This research aims to generate secured cipher keys from retina information to increase the level of security. The proposed technique utilizes cryptography based on retina information. The main contribution is the original procedure used to generate three types of keys in one system from the retina vessel's end position and improve the technique of three systems, each with one key. The distances between the center of the diagonals of the retina image and the retina vessel's end (diagonal center-end (DCE)) represent the first key. The distances between the center of the radius of the retina and the retina vessel's end (ra

A robust video-bitrate adaptive scheme at client-aspect plays a significant role in keeping a good quality of video streaming technology experience. Video quality affects the amount of time the video has turned off playing due to the unfilled buffer state. Therefore to maintain a video streaming continuously with smooth bandwidth fluctuation, a video buffer structure based on adapting the video bitrate is considered in this work. Initially, the video buffer structure is formulated as an optimal control-theoretic problem that combines both video bitrate and video buffer feedback signals. While protecting the video buffer occupancy from exceeding the limited operating level can provide continuous video str

This paper presents a hybrid energy resources (HER) system consisting of solar PV, storage, and utility grid. It is a challenge in real time to extract maximum power point (MPP) from the PV solar under variations of the irradiance strength.  This work addresses challenges in identifying global MPP, dynamic algorithm behavior, tracking speed, adaptability to changing conditions, and accuracy. Shallow Neural Networks using the deep learning NARMA-L2 controller have been proposed. It is modeled to predict the reference voltage under different irradiance. The dynamic PV solar and nonlinearity have been trained to track the maximum power drawn from the PV solar systems in real time.

Moreover, the proposed controller i