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.
Background: Hyperthyroidism occurs due to over production of thyroid hormones, one types of hyperthyroidism was Graves, disease. Hyperthyroidism is characterized by high level of serum thyroxin, triiodothyronine and low level of thyroid stimulated hormones. Material and Methods: fifty two hyperthyroid patients, thirty patients under treatment with carbimazole and other twenty two patients under treatment with radioactive iodine, and sixty healthy control group. The average salivary flow rate was calculated as ml/5mint.The concentration of calcium, potassium, and total protein were determined in the salivary supernatant sample. This is done through different biochemical tests. Determination of salivary IgA is done by ELIZA. Results: The most
... Show MoreBackground: The study of human leukocytes (HLA) alleles, and haplotype frequencies within populations provide an important source of information for anthropological investigation, organ and hematopoietic stem cell transplantation as well as disease association, certain diseases showed association with specific alleles specially those of known or suspected hereditary origin or immunological basis, whether simple renal cyst is congenital or acquired is still unclear and need to be investigated.Objectives: To study the genetic aspect of simple renal cysts by detecting the gene frequency and the haplotype of HLA class I of patients with simple renal cysts, and to find the presence of these cysts in other family members.Method: Thirty patient
... Show MoreJoints are among the most widespread geologic structures as they are found in most each exposure of rock. They differ greatly in appearance, dimensions, and arrangement, besides they occur in quite different tectonic environments. This study is important because joints provide evidence on what kind of stress produced them (history of deformation) and also because they change the characteristics of the rocks in which they occur. The Measured data of joints from the studied area which are located in the high folded zone – Northeast of Iraq, were classified according to their relationship with the tectonic axes by projecting them stereographically using Schmidt net in GEOrient ver.9.5.0 software. The joint systems revealed the orientation of
... Show MoreThe genetic diversity was studied in sixteen barley Hordeum vulgar L. species cultivated in Iraq , which are differ in their ability to drought stress tolerance by using random amplified polymorphic DNA polymerase chain reaction (RAPD - PCR ) .Barley species was evaluated to drought stress after treatment the plant seedling at germination stages to different concentration of polyethylene glycol (PEDG6000) . The results showed that the Broaq and Arefat species have the highest tolerance to drought stress in contrast the rest of Barly species like Alkhair, Alwarkaa, Ebaa99, Shoaa, Alrafidain,Sameer Rehana 3 , forat9 , jazeral ,and ebaa7 revealed sensitivity to drought stress . The primes which used RAPD technique
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This paper deals with two preys and stage-structured predator model with anti-predator behavior. Sufficient conditions that ensure the appearance of local and Hopf bifurcation of the system have been achieved, and it’s observed that near the free predator, the free second prey and the free first prey equilibrium points there are transcritical or pitchfork and no saddle node. While near the coexistence equilibrium point there is transcritical, pitchfork and saddle node bifurcation. For the Hopf bifurcation near the coexistence equilibrium point have been studied. Further, numerical analysis has been used to validate the main results.
In solar-thermal adsorption/desorption processes, it is not always possible to preserve equal operating times for the adsorption/desorption modes due to the fluctuating supply nature of the source which largely affects the system’s operating conditions. This paper seeks to examine the impact of adopting unequal adsorption/desorption times on the entire cooling performance of solar adsorption systems. A cooling system with silica gel–water as adsorbent-adsorbate pair has been built and tested under the climatic condition of Iraq. A mathematical model has been established to predict the system performance, and the results are successfully validated via the experimental findings. The results show that, the system can be operational
... Show MoreABSTRACT Background: According to Branemark’s protocol, the waiting period between tooth extraction and implant placement is 6–8 months; this is the late placement technique. Achieving and maintaining implant stability are prerequisites for a dental implant to be successful. Resonance Frequency Analysis (RFA) is a noninvasive diagnostic method that measures implant stability. The aim of this study was to investigate the influence of treatment protocol and implant dimensions on primary implant stability utilizing RFA. Materials and methods: This study included 63 Iraqi patients (37 male, 26 female; ranging 22-66 years). According to treatment protocol, the sample was divided into 2 groups; A (delayed) & B (immediate). Dental im
... Show MoreCocoon of larva
This paper presents the non-linear finite element method to study the behavior of four reinforced rectangular concrete MD beams with web circular openings tested under two-point load. The numerical finite elements methods have been used in a much more practical way to achieve approximate solutions for more complex problems. The ABAQUS /CAE is chosen to explore the behavior of MD beams. This paper also studies, the effect of both size and shape of the circular apertures of MD beams. The strengthening technique that used in this paper is externally strengthening using CFRP around the opening in the MD beams. The numerical results were compared to the experimental results in terms of ultimate load failure and displace
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