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 detailed form
that the errors of the solutions by Jordan elimination and by Gauss-Jordan elimination cannot
be essentially greater than the possible maximal errors of the solutions by back substitution
and by Gaussian elimination, respectively. Finally, the theoretical results are illustrated by
two numerical examples.
Recently, complementary perfect corona domination in graphs was introduced. A dominating set S of a graph G is said to be a complementary perfect corona dominating set (CPCD – set) if each vertex in is either a pendent vertex or a support vertex and has a perfect matching. The minimum cardinality of a complementary perfect corona dominating set is called the complementary perfect corona domination number and is denoted by . In this paper, our parameter hasbeen discussed for power graphs of path and cycle.
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This research aims to know the intellectual picture the displaced people formed about aid organizations and determine whether they were positive or negative, the researchers used survey tool as standard to study the society represented by displaced people living in Baghdad camps from Shiites, Sunnis, Shabak, Turkmen, Christians, and Ezidis.
The researcher reached to important results and the most important thing he found is that displaced people living in camps included in this survey hold a positive opinion about organizations working to meet their demands but they complain about the shortfall in the health care side.
The research also found that displaced people from (Shabak, Turkmen, and Ezidi) minorities see that internati
To make iron oxide nanoparticles (IONPs), a simple chemical approach was used to combine iron chloride (FeCl2+FeCl3) salt with onion peel extract. According to the study, iron salts can be converted into IONPs by the biomolecules in onion peel extract. From FeCl2+FeCl3 to γ -Fe2O3, the approach changes iron oxide NPs' size, shape, purity and phases. In water treatment, γ -Fe2O3 NPs are critical for the removal of the color methylene blue (MB). X-ray diffraction (XRD), scanning electron microscopy (SEM), ultraviolet (UV-Vis) and photoluminescence (PL) spectroscopy were used to identify IONPs. Results from the XRD experiment showed crystals having a
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Tigris River water that comes from Turkey represents the main water resource of this river in Iraq. The expansion in water river implementations has formed a source of trouble for the workers in the water resources management field in Iraqi. Unfortunately, there is no agreement between Iraq and Turkey till now to share the water of this international river. Consequently, the optimal operation of water resources systems, particularly a multi-objective, multi-reservoir, is of the most necessity at the present time.
In this research two approaches, were used the dynamic programming (DP) approach and simulation model to find the optimal monthly operation of Ilisu Dam (from an Iraqi point of view) through a comp
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The purpose of this paper is to define fuzzy subspaces for fuzzy space of orderings and we prove some results about this definition in which it leads to a lot of new results on fuzzy space of orderings. Also we define the sum and product over such spaces such that: If f = < a1,…,an > and g = < b1,…bm>, their sum and product are f + g = < a1…,an, b1, …, bm> and f × g =