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.
Mass transfer was examined at a stationary rectangular copper electrode (cathode) by using the reduction of cupric ions as the electrochemical reaction. The influence of electrolyte temperature (25, 45, and 65 oC), and cupric ions concentration (4, 8, and 12 mM) on mass transfer coefficient were investigated by using limiting current technique. The mass transfer coefficient and hence the Sherwood number was correlated as Sh =
In this article it is proved experimentally that the photon is a particle that has mass and constant wavelength by explaining the effect of refractive index on the wavelength and the natural mass of photon. It is very difficult to measure the mass of photon, a simple and easy process was proposed in this paper to calculate the mass length of photon in vacuum (Y) and in medium (Y*), by measuring the length of laser beam in air (Lair) and in medium (Lmed). A new method was postulated to calculate refractive index by using these relations (n = Y*/Y), and (n = Lmed / Lair) which supposed a new theory of light.
The interaction of charged particles with the chemical elements involved in the synthesis of human tissues is one of the modern techniques in radiation therapy. One of these charged particles are alpha particles, where recent studies have confirmed their ability to generate radiation in a highly toxic localized manner because of its high ionization and short its range. In this work, We focused our study on the interaction of alpha particles with liquid water; since the water represents over 80% of the most-soft tissues, as well as, hydrogen, oxygen, and nitrogen ,because they are key chemical elements involved in the synthesis of most human tissues. The mass stopping powers of alpha particle with HଶO , COଶ, Oଶ, Hଶ and Nଶhave
... Show MoreIn this study the most stable isobar for some isobaric families (light and intermediate ) nuclei with mass number (A) equals to (15-30) & (101- 115) have been determined. This determination of stable nuclide can help to determine the suitable nuclide, which can be used in different fields.
Most stable isobar can be determined by two means. First: plot mass parabolas (plotting the binding energy (B.E) as a function of the atomic number (Z)) for these isobaric families, in this method most stable isobars represent the lowest point in mass parabola (the nuclide with the highest value of binding energy).
Second: calculated the atomic number for most stable isobar (ZA) value.
Our results show that
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The objective of this study was to develop neural network algorithm, (Multilayer Perceptron), based correlations for the prediction overall volumetric mass-transfer coefficient (kLa), in slurry bubble column for gas-liquid-solid systems. The Multilayer Perceptron is a novel technique based on the feature generation approach using back propagation neural network. Measurements of overall volumetric mass transfer coefficient were made with the air - Water, air - Glycerin and air - Alcohol systems as the liquid phase in bubble column of 0.15 m diameter. For operation with gas velocity in the range 0-20 cm/sec, the overall volumetric mass transfer coefficient was found to decrease w
... Show MoreThe study showed that all extracts (aqueous, ethanolic and acetonic) of the leaves of Eucalyptus and Myrtus plants had a inhibitory effect on the growth of all types of yeasts studied, acetone extract recorded the highest inhibition of yeastat 100ppm concentration,The inhibition was 35mm, 34mm, 24mm and 20mm for Candida parapsilosis, Candida glabrata, Candida tropicalis and Candida albicans respectively, The experiments above showed the least significant differences at 0.05 level.The results ofE. Cammldulensis ethanolic tincture analysis has shown the presence of 44 biologically active substances. The main Eucalyptus leaves component was: 2-Bicyclo (2-2.1) heptanol (12.37%), Ledol (8.23%),1,2,4- Benzenetriol (8.45%) and that contain spathul
... Show MoreThe plant Borago officinalis, which belongs to the Boraginaceae family and Celebrated as borage, is one of the useful medicinal plants cultivated in Iraq. It was used in olde medicine in Iraq, Irane, Syria and Europe for management of various diseases. It is commonly used as an atonic, tranquilliser, management of cough, sore throat, pneumonia, swelling, inflammatory diseases, antioxidant, and anticancer. This project provides the first comprehensive research done in Iraq to study the phytochemicals and the methods of extraction and isolation of active constituents from Borago officinalis cultivated in Iraq. The plant was harvested in spring from AL-Rifai, Nassiriyah city, IRAQ in February 2019.were w
... Show MoreThe elastic transverse electron scattering form factors have been studied for the 11Li nucleus using the Two- Frequency Shell Model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO) potential are used with two different oscillator parameters bcore and bhalo. According to this model, the core nucleons of 9Li nucleus are assumed to move in the model space of spsdpf. The outer halo (2-neutron) in 11Li is assumed to move in the pure 1p1/2, 1d5/2, 2s1/2 orbit. The shell model calculations are carried ou
... Show MoreGraph is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree are determined.
The moisture sorption isotherms of Mefenamic acid tablets were investigated by measuring the experimental equilibrium moisture content (EMC) using the static method of saturated salt solutions at three temperatures (25, 35, and 45°C) and water activity range from 0.056 to 0.8434. The results showed that EMC increased when relative humidity increased and the sorption capacity decreased, the tablets became less hygroscopic and more stable when the temperature increased at constant water activity. The sorption curves had a sigmoid shape, type II according to Brunauer’s classification. The hysteresis effect was significant along with the whole sorption process. The results were fitted to three models: Oswin, Smith, and Guggen
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