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.
The research aims to achieve proof of convergence between optimal costs and standard costs in calculating costs for the economic unit, support efforts aimed at adopting optimal costs in cost accounts and accounting thought in general, and achieve benefit from the theory of convergence between optimal costs and standard costs in the field of achieving actual costs in The economic unit in order to reduce and converge, and this came to address the possibility of adopting the concept of optimal costs in the production costs calculations for the purposes of rationalizing administrative decisions, and rationalizing the preparation of financial statements within management accounting.
The research concluded that
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This research is an attempt to explain the Qur’anic verses of the vision in the practical divine vision on the Day of Resurrection, and the legal texts narrated from the Companions regarding the vision of the Prophet, may God’s prayers and peace be upon him, regarding the vision of the Prophet, may God bless him and grant him peace, regarding the vision of the Prophet, may God’s prayers and peace be upon him, regarding the vision of the Prophet, may God bless him and grant him peace He was greeted with regard to vision, and he explained the two sayings of Ibn Abbas and Aisha on the same subject, including an area of conflict between them.
This research of the thesis includes the preparation and identification of two new tetra dentate Schiff's base ligand . (H4L1 ) and then binuclear complexes with a group of transition metal ions in addition to cadmium with the general formula. [M2(L1)Cl2(H2O)2] M+2=[Mn,Co,Ni,Cu and Cd] The prepared complexes and ligands were identified by in pared(FT-IR) spectroscopy ,Ultra violet-visible(UV-visible) spectroscopy and H-NMR spectroscopy of the prepared ligand, also microanalysis (C.H.N) of some of the prepared compounds has been carried out and the melting points, the molar conductivity and magnetic susceptibility
. New Schiff base ligand 2-((4-amino-5-(3, 4, 5-trimethoxybenzyl) pyrimidin2-ylimino) (phenyl)methyl)benzoic acid] = [HL] was synthesized using microwave irradiation trimethoprim and 2-benzoyl benzoic acid. Mixed ligand complexes of Mn((ІІ), Co(ІІ), Ni(ІІ), Cu(ІІ), Zn(ІІ) and Cd(ІІ) are reacted in ethanol with Schiff base ligand [HL] and 8-hydroxyquinoline [HQ] then reacted with metal salts in ethanol as a solvent in (1:1:1) ratio. The ligand [HL] is characterized by FTIR, UV-Vis, melting point, elemental microanalysis (C.H.N), 1H-NMR, 13C-NMR, and mass spectra. The mixed ligand complexes are characterized by infrared spectra, electronic spectra, (C.H.N), melting point, atomic absorption, molar conductance and magnetic m
... Show MoreBackground: In young adults, multiple sclerosis is a prevalent chronic inflammatory demyelinating condition. It is characterized by white matter affection, but many individuals also have significant gray matter involvement. A double-inversion recovery pulse (DIR) pattern was recently proposed to improve the visibility of multiple sclerosis lesions. Objective: To find out how well a DIR sequence, FLAIR, and T2-weighted pulse sequences can find MS lesions in the supratentorial and infratentorial regions. Methods: A total of 37 patients with established diagnoses of multiple sclerosis were included in this cross-sectional study. Brain MRI was done using double inversion recovery, T2, and FLAIR sequences. The number of lesions was count
... Show MoreThe Co (II), Ni (II) ,Cu(II), Zn(II) ,Cd(II) and Hg(II) complexes of mixed of amino acid (L-Alanine ) and Trimethoprim antibiotic were synthesized. The complexes were characterized using melting point, conductivity measurement and determination the percentage of the metal in the complexes by flame (AAS). Magnetic susceptibility, Spectroscopic Method [FTIR and UV-Vis]. The general formula have been given for the prepared mixed ligand complexes [M(Ala)2(TMP)(H2O)] where L- alanine (abbreviated as (Ala ) = (C5H9NO2) deprotonated primary ligand, L- Alanine ion .= (C5H8NO2 -) Trimethoprim (abbreviated as (TMP ) = C10H11N3O3S M(II) = Co (II),Ni(II) ,Cu(II), Zn(II) ,Cd(II) and Hg(II). The results showed that the deprotonated L- Alanine by KOH (Ala
... Show MoreBackground: Tumor necrosis factor-alpha (TNF-α) and interleukins play important roles in the pathogenesis of rheumatoid arthritis (RA). Genetic research has been employed to find many of the missing connections between genetic risk variations and causal genetic components. Objective: The goal of this study is to look at the genetic variations of TNF-α and interleukins in Iraqi RA patients and see how they relate to disease severity or response to biological therapy. Method: Using specific keywords, the authors conducted a systematic and comprehensive search to identify relevant Iraqi studies examining the genetic variations of TNF-α and interleukins in Iraqi RA patients and how they relate to disease severity or response to biolo
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