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

  In this paper we introduce a new class of degree of best algebraic approximation polynomial Α,, for unbounded functions in weighted space Lp,α(X), 1 ∞ .We shall prove direct and converse theorems for best algebraic approximation in terms modulus of smoothness in weighted space

This paper is concerned with introducing and studying the first new approximation operators using mixed degree system and second new approximation operators using mixed degree system which are the core concept in this paper. In addition, the approximations of graphs using the operators first lower and first upper are accurate then the approximations obtained by using the operators second lower and second upper sincefirst accuracy less then second accuracy. For this reason, we study in detail the properties of second lower and second upper in this paper. Furthermore, we summarize the results for the properties of approximation operators second lower and second upper when the graph G is arbitrary, serial 1, serial 2, reflexive, symmetric, tra

There are many studies dealt with handoff management in mobile communication systems and some of these studies presented handoff schemes to manage this important process in cellular network. All previous schemes used relative signal strength (RSS) measurements. In this work, a new proposed handoff scheme had been presented depending not only on the RSS measurements but also used the threshold distance and neighboring BSS power margins in order to improve the handoff management process. We submitted here a threshold RSS as a condition to make a handoff when a mobile station moves from one cell to another this at first, then we submitted also a specified margin between the current received signal and the ongoing BS's received signal must be s

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

This paper proposes a new structure of the hybrid neural controller based on the identification model for nonlinear systems. The goal of this work is to employ the structure of the Modified Elman Neural Network (MENN) model into the NARMA-L2 structure instead of Multi-Layer Perceptron (MLP) model in order to construct a new hybrid neural structure that can be used as an identifier model and a nonlinear controller for the SISO linear or nonlinear systems. Weight parameters of the hybrid neural structure with its serial-parallel configuration are adapted by using the Back propagation learning algorithm. The ability of the proposed hybrid neural structure for nonlinear system has achieved a fast learning with minimum number

The aim of the current research is to find out the extent to which algebraic thinking skills are included in the mathematics textbook for the third intermediate grade for the academic year (2020-2021) by answering the main research question:What algebraic thinking skills are included in the mathematics textbook for middle third grade?The descriptive and analytical approach was used, and to achieve the goal of the research, a list of the main algebraic thinking skills and the sub-skills were prepared, and after analyzing the content of the mathematics textbook, the stability of the analysis was verified through the analysis over time and across individuals using the Holsti equation, and

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .