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.
A newly developed analytical method was conducted for the determination of Ketotifen fumarate (KTF) in pharmaceuticals drugs via quenching of continuous fluorescence of 9(10H)-Acridone (ACD). The method was applied using flow injection system of a new homemade ISNAG fluorimeter with fluorescence measurements at ± 90◦ via 2×4 solar cell. The calibration graph was linear in the range of 1-45 mmol/L, with correlation coefficient r = 0.9762 and the limit of detection 29.785 µg/sample from the stepwise dilution for the minimum concentration in the linear dynamic ranged of the calibration graph. The method was successfully applied to the determination of Ketotifen fumarate in two different pharma
... Show MoreThe study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy
... Show MoreThis paper is devoted to compare the performance of non-Bayesian estimators represented by the Maximum likelihood estimator of the scale parameter and reliability function of inverse Rayleigh distribution with Bayesian estimators obtained under two types of loss function specifically; the linear, exponential (LINEX) loss function and Entropy loss function, taking into consideration the informative and non-informative priors. The performance of such estimators assessed on the basis of mean square error (MSE) criterion. The Monte Carlo simulation experiments are conducted in order to obtain the required results.
In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov
... Show MoreThe purpose of this research is to design a list of the scientific and moral values that should be found in the content of the computer textbook for the second intermediate grade, as well as to analyze the content of the above- mentioned book by answering the following question:
What is the percentage of availability of scientific and moral values in the content of the computer textbook for Second Intermediate grade issued by the Iraqi Ministry of Education / the general directorate of the curriculum, for the academic year (2017-2018)?
In order to achieve the research objectives, the descriptive method (content analysis method) was adopted. The research community has been iden
... Show MoreThe external shocks are one of the phenomena that the Iraqi economy is exposed to over a period of time. It is referred to as changes and events that come from outside the economic system and extends to many economic variables. However, foreign direct investment may be severely affected due to the extreme sensitivity to changes and local and international developments. This type of trauma and its characteristics to help manage and cope with external shocks, and in order to avoid the standard problems experienced by some models of simple linear regression, multi-linear regression models were used with variables Scientific and other dummy variables .
The study foun
... Show MoreThe accountants are preparing the financial statements under the Monetary Unit Stability Assumption without taking into consideration the changement of prices for the monetary unit. The income statement accounts containing different items of expenses and revenues. These items are not paid or obtained at one date, because the value of monetary unit is changing from one date to another , also the financial position contains different items of current and fixed assets, also contains different items of long-term liabilities and ownership rights, the continuity of applying historical cost principle will make the financial statements misleading, The adoption of financial analyst of these statements will affects
... Show MoreThis study aims to the little impact of accounting financial performance (AFP) analysis on the money market in the Iraqi economy. Potentially limiting future market activity could be international risks and obstacles, which in turn could cause issues and crises (Shah & Jan, 2014; Bakhtiyarovich, 2020). The study concept was inspired by the recognition that there must be communication between the importance of the AFP analysis of the Iraqi securities market and the country’s financial and economic institutions. The sample of the study included ten Iraqi banks listed in the Iraq Stock Exchange (ISE) for the period 2010–2020. The three mathematical models included in the statistical analysis served as the basis for projectin
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