This Book is the second edition that intended to be textbook studied for undergraduate/ postgraduate course in mathematical statistics. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces events and probability review. Chapter Two devotes to random variables in their two types: discrete and continuous with definitions of probability mass function, probability density function and cumulative distribution function as well. Chapter Three discusses mathematical expectation with its special types such as: moments, moment generating function and other related topics. Chapter Four deals with some special discrete distributions: (Discrete Uniform, Bernoulli, Binomial, Poisson, Geometric, Negative Binomial and Hypergeometric) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Chapter Five deals with some special continuous distributions: (Uniform, Normal, Exponential, Gamma and Beta) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Many solved examples are intended in this book (obtaining mean and variance of distributions by m.g.f.). Chapter Six introduces univariate discrete and continuous transformations, i.e., one dimensional variables and their yielding probability distributions. Chapter Seven devotes to truncation of distributions from left, right or both sides, beside the probability distribution of order statistics. Chapter Eight discusses mathematical features of joint, marginal and conditional distributions, as well as independency via covariance and correlation of bivariate distributions. Chapter Nine deals with some special topics such as getting distribution for some transformation from multidimensional random variables by using moment generating function (m.g.f.) and cumulative distribution function (C.D.F.) Many solved examples (about 100) are intended in this book, in addition to a variety of unsolved relied problems (about 150) at the end of each chapter to enrich the statistical knowledge of our readers.
In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.
The aim of the current study is the investigation of tensile behavior of the semi - crystalline polymers : polypropylene (PP ) , high density polyethylene(HDPE) and low density polyethylene (LDPE) . The energy to break or deformation was determined as a function of extension rates , ( PP) was break at extension rate (5) mm/min but (HDPE) break at higher extension rates (25) mm/min while( LDPE) not break even at very high extension rates but it is deformation or failure .
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
... Show MoreObjective: The aim of this work was to detect terpenes other than boswellic acid derivatives in olibanum of Boswellia Serrata found in Iraq. Methods: The olibanum of Boswellia Serrata was macerated in methanol for one day, then filtration. Filter at was concentrated till reddish brown syrupy residue was gained, (3%) potassium hydroxide was added till basification. This basic solution was stirred continuously until a uniform emulsion was formed, then extracted with chloroform in a separatory funnel; the chloroform fraction was analyzed by GC /MS spectrometry. Results: GC /MS analysis reveal the presence of terpenes and non-terpenes constituents. Conclusion: Most of the detected terpenes were sesquiterpenes and the least one was di-terpenes.
The groundwater recharge from rainfall for the main shallow aquifer in the northeastern Missan governorate south of Iraq is investigated via classical and refined chloride mass balance techniques. Application of both techniques reveals that the mean annual groundwater recharge is 0.82 mm/y. The annual recharge received by the aquifer approximately reaches to three million cubic meters after multiply this figure by the area of the study area (about 1856 km2). This figure represents a renewable storage from which a sustainable management of the groundwater reserve could be implemented. The techniques applied are robust, costly-effective, and could be used with other methods such as groundwater table fluctuation method to give a more realis
... Show MoreObjective: The study aim is to identify factors that may contribute to children’s weight status variations. Methodology: A descriptive cross sectional study is carried out has been conducted at the AL- Samawah city in Primary Health Care Centers for the purpose of the screening children’s weight status of Age One to five Years Old. This study is started from December 16th 2018 to February 14th 2019. A(non propriety) purposive sample comprised of (20) primary health centers (10 main and 10 sub) are selected of 500 children who visit the primary health care center during the period for the purpose of the study; Data was collected through using a questionnaire designed and developed for the purpose of the study . It consists of two main
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Diazotization reaction between quinolin-2-ol and (2-chloro-1-(4-(N-(5-methylisoxazol-3-yl)sulfamoyl)phenyl)-2l4-diazyn-1-ium was carried out resulting in ligand-HL, this in turn reacted with the next metal ions (Ni2+, Pt4+, Pd2+, and Mn2+) forming stable complexes with unique geometries such as (tetrahedral for both Ni2+ and Mn2+, octahedral for Pt4+ and square planer for Pd2+ ). The creation of such complexes was detected by employing spectroscopic means involving ultraviolet-visible which proved the obtained geometries, fourier transfer proved the formation of azo group and the coordination with metal ion through it. Pyrolysis (TGA &
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In order to make an improvement associated with rotating biological contactor (RBC), a new design of biofilm reactor called as Rotating perforated disc biological contactor (RPBC) was developed in which the rotating discs are perforated. The transfer of oxygen from air to wastewater was investigated. Mass-transfer coefficient (KLa) in the liquid phase was determined by measuring the rate transfer of oxygen. A laboratory scale of (RPBC) consisted of a semicircular trough was used with a working capacity of 40 liters capacity of liquid. Synthetic wastewater was used as a liquid phase, while air was used as a gas phase.
The effects of m
... Show MoreCupressus sempervirens L., Cupressaceae, that is known as evergreen cypress, Mediterranean cypress and in Arabic called “al -Sarw. It is an evergreen, medium sized, longevity, and wide distributed over all the world. The plant represents an important member of conifer plants which characterized with aromatic leaves and cones. Cupressus sempervirens have been ethnobotanical uses as an antiseptic, relief of cough, astringent, antispasmodic, wound healing and anti-inflammatory. Aims of this work are phytochemical analysis, isolation and structural identification of Quercitroside (quercitrin) and essential oil in Iraqi C. sempervirens. Isolation of quercitrin was
... Show MoreIn this study, a new Azo ligand 5-((2-(1H-indol-2-yl)ethyl)diazinyl)-2-aminophenol is synthesized from a reaction of Tryptamine with 2-aminophenol. The ligand and their metal ion complexes Ni(II), Pd(II) , Pt(IV) and Au(III) have been synthesized and characterized by various analytical techniques, including elemental microanalysis, metal content, chloride-containing, measurement of electrical conductivity, magnetic susceptibility, 1H and 13C-NMR, FT-IR, UV-Vis, mass spectra (MS), and thermal analysis (TGA and DSC) curves. The DCS curve was used to calculate the thermodynamic parameters ΔH, ΔS, and ΔG. The characterization results promote the metal complexes of azo ligand structures. The results indicate that the
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