In this article, first a density by the name ”The bimodal standard normal density” is introduced and denoted by bφ(z). Then, a definition for the kurtosis of bimodal densities relative to bφ(z) is presented. Finally, to illustrate the introduced kurtosis, a few examples are provided and a real data set is studied, too.

The fire phenomenon can cause the loss of structural materials resistance which may end to damage or even structural total collapse. Physical and chemical changes in concrete due to firing also make serious structural defects in concrete structures. Therefore, prevention of reduction of concrete resistance is attended in this research. The primary idea is based on decreasing concrete thermal conductivity to increase chemical and physical resistance. Because of low density and porosity light weight aggregate concrete has low thermal conductivity which can postpone the resistant loss due to high temperature. A set of tests performed to achieve an optimum light weight aggregate concrete mix design in room normal temperature by changing the amount of sensitive mix components and controlling compressive strength and density. In next step some effective additives were implemented to make the optimum mix design against high temperature. For this purpose, 9 different mix designs obtained from the Taguchi method were prepared. For each mix design, 9 test specimens were made. At each, ambient temperature, 400 ͦC and 800 ͦC, three samples of each design are tested. The experiments conducted in this research include testing of compressive strength, ultrasonic pulse, and weight loss and heat effect on the appearance of lightweight concrete. It was seen that the effect of temperature above 400 ͦC is more significant on concrete compressive strength and in temperatures below 400 ͦC density loss is more considerable. The results of tests indicate that reducing the water to cement ratio and using super plasticizer has a desirable effect on the physical and mechanical properties of lightweight concrete at higher temperatures. However, test results showed that the presence of silica fume up to 15 percent of weight of cement can’t improve the strength of lightweight concrete neither in ambient nor in elevated temperature. Optimum mix design lost about 49 percent of compressive strength in 800 ͦC. Also it was observed that loss of density and compressive strength due to elevated temperature are in direct relation.

The procedures for measuring, mixing, transporting, and placing heavyweight concrete are similar to those used in conventional concrete construction; however, special expertise and thorough planning are necessary for the successful completion of this type of concrete .The use of heavyweight concrete in construction is a specialized field, Heavyweight concrete is used in counterweights of bascule and lift bridges, but it is generally used in radiation shielding structures to absorb gamma rays and differs from normal weight concrete by having a higher density and special compositions to improve its attenuation properties. When heavyweight shielding concrete is used to attenuate neutrons, sufficient material of light atomic weight, which produces hydrogen, should be included in the concrete mixture. Some aggregates are used because of their ability to retain water of crystallization at elevated temperatures, which ensures a source of hydrogen not necessarily available in heavyweight aggregate Cements would be suitable for conventional concrete and produce the required physical properties, are suitable for use in heavyweight concrete. Low-alkali cement should be used when alkali-reactive constituents are present in the aggregates and a moderate or low-heat cement should be used for massive members, To avoid high and rapid heat of hydration and resultant cracking, it is advisable not to use Type III cement or accelerators unless the concrete temperature is controlled by specially designed refrigeration systems. Thorough examination and evaluation of heavyweight aggregate sources are necessary to obtain material suitable for the type of shielding required. These sources are limited, and a material survey should be conducted to determine availability, chemical and physical qualities. The supplier’s sources should be inspected to evaluate rock composition, abrasion resistance, and density since these properties may vary from one location to another within a deposit. The purchaser must realize that mineral ores are not as uniform as normal weight concrete aggregates and make appropriate allowances Limited resources and increasing use of concrete, particularly in the industrial production cause that the heavyconcrete be useful. In order to optimize production of heavyconcrete, the most basic parameters that must be changed is the mix design. Optimization of the concrete mixture design is a process of search for a mixture for which the sum of the costs of the ingredients is lowest, yet satisfying the required performance of concrete, such as workability strength and durability. For this purpose, heavy concrete mix design optimization model is firstly defined and then optimal mix design will be achieved, by using an optimization algorithm. The experimental data were utilized to carry out analysis of variance. To develop a polynomial regression model for compressive strength in terms of the five design factors ( cement, coarse aggregate, fine aggregate, water and density ) considered in this study The numerical results shows that the amounts of coarse aggregate and cement are simultaneously reduced and amount of the fine aggregate is increased in the optimum mix design. Considering mass production concrete in nuclear power plants, this optimal mix design methods and reduce the cost of concrete can greatly reduce the cost of construction

A mixture distribution is compound of two or more statistical distributions.We find a mixture distributions when the sampling is from a non-homogeneouspopulation. For example, the mixed failure time distribution of healthy and faultycomponents, weight distribution of animals with different ages or durations of cardiacpatients after surgery in different age groups will live. In this cases the curveof density function of intimacy can be multimodal in the population. Also in manycases encountered with characteristics that can set their values belong to real numbersand in fact because these characteristics usually emerge are naturally so itseems that the normal distribution is appropriate to describe them. But more studycharacteristics, we find the situation for the study population was not completelysymmetrical, and to the right or left have skewness. Thus, the variable with valuesin real numbers would be desired asymmetry. This can lead to defining the distributionof skewed-normal. Thus, at first we examine the mixture distributions and thenthe skewed-normal distribution and at the end by defining the mixture distributionwith skewed-normal components, we will find the estimations of the parameters inthis model using EM- algorithm.

The normal distribution plays an important role in statistical analysis. However, a researcher may also wish to construct another symmetric distributions which fit the data better than the normal distribution. For this purpose, more flexible distributions have been introduced. In this thesis, we introduce some of such distributions. We first introduce the slash distribution as a family of mixed-normal scale distributions. The slash distribution can be used instead of normal distribution, in many situations. We also introduce Skew-slash. Then, a new modified-slash distribution is discussed. We also study a modified Skew-slash distribution. Some properties of the distributions discussed in this thesis are given. In particular, we present the stochastic representations, density functions and moments of the distributions.

Covering problem tries to locate the least number of facilities and each demand has at least one facility located within a specific distance.This paper considers a cross entropy algorithm for solving the mixed integer nonlinear programming (MINLP) for covering location model.The model is solved to determine the best covering value.Also, this paper proposes aCross Entropy (CE) algorithm considering multivariate normal density function for solving large scale problems.For showing capabilities of the proposed algorithm, it is compared with GAMS.Finally, a numerical exampleand a case study are expressed to illustrate the proposed model. For case study, Tehran's special drugstores consider and determine how to locate 7 more drugstores to cover all 22 districts in Tehran.

The globally increasing epidemic of diabetes will lead to serious problems including diabetic nephropathy and kidney diseases in near future. The first clinical diagnosable stage in a diabetic kidney disease is microalbuminuria (urinary albumin excretion of 30 - 300 g/24 hours).. This prospective cohort study investigated the risk factors of microalbuminuria in patients with type 2 diabetes who had been registered in endocrine and metabolism research center in Isfahan city, Iran..Patients and This prospective cohort study was performed on 90 diabetic type 2 patients with microalbuminuria, who were selected according to the consecutive sample selection method during 6 years. Data were collected through regular and systematic measurements of serum albumin as the response variable and body mass index, systolic and diastolic blood pressure, the duration of diabetes, glycosylated hemoglobin (HbA1c), total cholesterol, triglyceride (TG), fasting blood sugar (FBS), low-density lipoprotein (LDL), and high-density lipoprotein (HDL) as the related factors. Non-normal mixed models were used to investigate the impact of effective factors on the amount of excreted serum albumin.. According to the deviance information criterion (DIC = 56.2), the non-normal mixed effects model with the skewed t distribution had a best fit and indicated that HbA1c, HDL and total cholesterol had a significant effect on the amount of albumin in urine (P < 0.05).. Using nonnormal mixed models may lead to the best results as compared to common normality assumption..

In previous studies, the normal mixture, as well as the Markov process, were used to model the financial return, separately. In this study, the normal mixture model is extended to the Markov mixture of normals. The mixture weights in every state are considered time-varying and as a function of past observations, so the limit of constant weight assumption is removed. The proposed model is estimated using Bayesian inference and a Gibbs sampling algorithm has been created to compute posterior density. The performance of algorithm is tested with simulation, then a two-state Markov time-varying Mixed Normal-GARCH model (MMN) with one and two components in every state, as well as limited cases (mean zero), were compared by comparison of their likelihood function. Finally, the model is applied to S&P500 and TEPIX daily return and results show that MMN models with two components provide better results than MMN model with one component which is so-called Markov switching GARCH model.

Lexical richness in written language production has been examined in different contexts and in relation to different genres but research into the effects of within-genre topics on lexical richness is still limited and takes little account of learners’ perspectives. The present study therefore sought to understand the effects of topics on lexical richness (lexical density, lexical diversity and lexical sophistication) in written essays by Vietnamese EFL learners. Data were collected from sixty-four English-major university students who each wrote four essays on four different topics across two genres (persuasive and descriptive) in their normal classes as progress tests. Ten students were also interviewed after they had completed all the essays to understand their perceptions of the writing topics. Lextutor’s VocabProfile was used to obtain measures of lexical density, lexical diversity and lexical sophistication. The results showed mixed effects of writing topics on these three lexical measures. Learner perspectives provided insights into how cognitive and affective individual factors contributed to the complexity of topic influence. Pedagogical implications are discussed in regard to how to enhance productive lexical use in writing through task selection and instructional planning.

In order to investigate the effect of organic zinc (Zn) supplement in broiler chicken nutrition that reared at high stock density, this experiment was done by using 2 levels of density (10 and 16 birds/m2) and 4 levels of Zn (40, 80, 120 and 160 ppm) in a completely randomized design with 4×2 factorial arrangement. The results showed that birds with higher stocking density had lower feed intake (FI) and feed conversion ratio (FCR) compared to those in normal density from d 1-21 and birds with normal stocking density had lowest FI and FCR from d 22-42 (P<0.05). Cecal population of Coliform decreased in normal and high stock density by increasing Zn level in the diet (P<0.05). Apparent ileal digestibility of crude protein significantly increased by increasing the levels of Zn in the diet in normal and high stock density (P<0.05). These data suggest that dietary supplementation of Zn significantly increased ileal digestibility of crude protein and organic matter and also, decreased cecal population of Coliform and E. coli in high and normal stocking density without affecting the performance of broilers.