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 medical practice, nonsteroidal anti-inflammatory drugs (NSAIDs) are often used to treat osteoarthritis and rheumatoid arthritis. Ibuprofen is a well-known NSAID, analgesic, and antipyretic medication. This chemical is an active ingredient of several oral medications that are offered in tablet, gel pellet, and syrup forms and has higher efficacy, tolerance, and side effect rates than other compounds, including pyrazolone derivatives. We present a unique plasma-assisted desorption/ionization mass spectrometry (PADI-MS) approach for improving pharmaceutically important solids using an ibuprofen tablet as a model solid sample. The goal of the study is to create an innovative mass spectrometric method that could be used for quick and accur

The aim: to evaluate combined microscopy techniques for determining the morphological and optical properties of methadone hydrochloride (MDN) crystals. Materials and methods: MDN crystal formation was optimized using a closed container method and crystals were characterized using polarized light microscope (PLM), scanning electron microscopy (SEM) and confocal microscopy (CM). SEM and CM were used to determine MDN crystal thickness and study its relationship with crystal retardation colours using the Michel-Levy Birefringence approach. Results: Dimensions (mean±SD) of diamond shaped MDN crystals were confirmed using SEM and CM. Crystals were 46.4±15.2 Vs 32.0±8.3 µm long, 28.03±8.2 Vs 20.85±5.5 µm wide, and 6.62±

Motives: Baghdad is the capital city and an important political, administrative, social, cultural and economic centre of Iraq. Baghdad’s growth and development has been significantly influenced by efforts to accommodate various needs of its steadily growing population. Uncontrolled population and urban growth have exerted negative effects in numerous dimensions, including environmental sustainability because urban expansion occurred in green spaces within the city and the surrounding areas.Aim: The aim of this study was to examine the planning solutions in Baghdad’s green areas in the past and at present, and to identify the key changes in the city’s green areas, including changes in the ratio of green urban spaces to the tota

In order to understand the effect of (length of pile / diameter of pile) ratio on the load carrying capacity and settlement reduction behavior of piled raft resting on loose sand, laboratory model tests were conducted on small-scale models. The parameters studied were the effect of pile length and the number of piles. The load settlement behavior obtained from the tests has been validated by using 3-D finite element in ABAQUS program, was adopted to understand the load carrying response of piled raft and settlement reduction. The results of experimental work show that the increase in (Lp/dp) ratio led to increase in load carrying capacity by piled raft from (19.75 to 29.35%), (14.18 to 28.87%) and (0 to 16.49%) , the maximum load carried

The amount of protein in the serum depends on the balance between the rate of its synthesis, and that of its catabolism or loss. Abnormal metabolism may result from nutritional deficiency, enzyme deficiency, abnormal secretion of hormones, or the actions of drugs and toxins. Renal cancer is the third most common malignancy of the genitourinary system, and accounts for 3% of adult malignancies globally. Total serum proteins were measured in malignant kidney tumor, benign kidney tumors, and non tumoral kidney diseases patient groups, as well as in healthy individuals. A significant decrease (p< 0.001) of total serum protein levels in patients with malignant kidney tumors when compared with those of benign tumors, non tumoral diseases, and hea

Improving in assembling technology has provided machines of higher evaluation with better resistances and managed behavior. This machinery led to remarkably higher dynamic forces and therefore higher stresses. In this paper, a dynamic investigation of rectangular machine diesel and gas engines foundation at the top surface of one-layer dry sand with various states (i.e., loose, medium and dense) was carried out. The dynamic investigation is performed numerically by utilizing limited component programming, PLAXIS 3D. The soil is accepted as flexible totally plastic material submits to Mohr-Coulomb yield basis. A harmonic load is applied at the foundation with amplitude of 10 kPa at a frequency of (10, 15 and 20) HZ and se

In order to understand the effect of (length of pile / diameter of pile) ratio on the load carrying capacity and settlement reduction behavior of piled raft resting on loose sand, laboratory model tests were conducted on small-scale models. The parameters studied were the effect of pile length and the number of piles. The load settlement behavior obtained from the tests has been validated by using 3-D finite element in ABAQUS program, was adopted to understand the load carrying response of piled raft and settlement reduction. The results of experimental work show that the increase in (Lp/dp) ratio led to increase in load carrying capacity by piled raft from (19.75 to 29.35%), (14.18 to 28.87%) and (0 to 16.49%) , the maximum load carr

The research aims to measure the sustainability of the Iraqi economy for the period 1990-2018 as well as to show the impact of fluctuations in the level of GDP on financial sustainability, where financial sustainability is the necessary and sufficient condition for achieving economic and financial balance in the country, as financial sustainability reflects the movement of the state budget and its relationship to GDP through the indicators of deficit, fiscal surplus and public debt internal and external, as well as reflecting the art of managing public debt, and the more managed public debt is achieved, the more the management of public debt is achieved financial sustainability. for the state in the sense that there is a reciprocal