Integral Representations Of Sl_2(z/nz)

The aim of this work is to determine for which commutative rings integral representations of SL_2(Z/nZ) exist and to explicitly compute them. We start with R = Z/pZ and then consider Z=p^\lambda Z. A new approach will be used to do this based on the Weil representation. We then consider general finite rings Z/nZ by extending methods described in [26]. We make extensive use of group theory, linear representations of finite groups, ring theory, algebraic geometry, and number theory. From number theory we will employ results regarding modular forms, Legendre symbols, Hilbert symbols, and quadratic forms. We consider the works of Andre Weil[38], Alexandre Nobs[23][24] and Udo Riese[26]. We explicitly compute the irreducible representations for several odd primes using Nobs and Wolfart\u27s methods. Then we will explore Riese\u27s[26] construction of the integral representations of SL2(A_\lambda) and explicitly compute them as the paper only proves the existence. We will use integrality results of the Weil representations by Luca Candelori, Shaul Zemel, and Yilong Wang (to appear). Then we will extend Reise\u27s results to construct integral representations for rings that are not of the form A_\lambda

Simulation of Mathematical Models in Genetic Analysis

In recent years a new field of statistics has become of importance in many branches of experimental science. This is the Monte Carlo Method, so called because it is based on simulation of stochastic processes. By stochastic process, it is meant some possible physical process in the real world that has some random or stochastic element in its structure. This is the subject which may appropriately be called the dynamic part of statistics or the statistics of change, in contrast with the static statistical problems which have so far been the more systematically studied. Many obvious examples of such processes are to be found in various branches of science and technology, for example, the phenomenon of Brownian Motion, the growth of a bacterial colony, the fluctuating numbers of electrons and protons in a cosmic ray shower or the random segregation and assortment of genes (chemical entities responsible for governing physical traits for the plant and animal systems) under linkage condition. Their occurrences are predominant in the fields of medicine, genetics, physics, oceanography, economics, engineering and industry, to name only a few scientific disciplines. The scientists making measurements in his laboratory, the meteriologist attempting to forecast weather, the control systems engineer designing a servomechanism (such as an aircraft or a thermostatic control), the electrical engineer designing a communication system (such as the radio link between entertainer and audience or the apparatus and cables that transmit messages from one point to another), economist studying price fluctuations in business cycles and the neurosurgion studying brain wave records, all are encountering problems to which the theory of stochastic processes may be relevant. Let us consider a few of these processes in a little more detail. In statistical physics many parts of the theory of stochastic processes were developed in correlation with the study of fluctuations and noise in physical systems (Einstein, 1905; Smoluchowski, 1906; and Schottky, 1918). Consequently, the theory of stochastic processes can be regarded as the mathematical foundation of statistical physics. The stochastic models for population growth consider the size and composition of a population which is constantly fluctuating. These are mostly considered by Bailey (1957), Bartlett (1960), and Bharucha-Reid (1960). In communication theory a wide variety of problems involving communication and/or control such as the problem of automatic tracking of moving objects, the reception of radio signals in the presence of natural and artificial disturbances, the reproduction of sound and images, the design of guidance systems, the design of control systems for industrial processes may be regarded as special cases of the following general problem; that is, let T denote a set of points in a time axis such that at each point t in T an observation has been made of a random variable X(t). Given the observations [x(t), t ϵT] and a quantity Z related to the observation, one desires to from in an optimum manner, estimates of, and tests of hypothesis about Z and various functions h(Z)

Interpreting iron studies

No abstract available

Determination of bioanalytical parameters for the standardization of Abroma augusta

AbstractObjectiveTo set the analytical parameters for simultaneous determination of different phytochemicals present in the Abroma augusta (A. augusta).MethodsDifferent phytochemical test including total phenol and total flavonoid content were carried out in the present investigation. Further, a rapid and simple high-performance thin-layer chromatographic (HPTLC) method was developed for the qualitative and quantitative analysis. Moreover antimicrobial study was also performed in the present investigation to know the presence of biological contamination.ResultsPreliminary phytochemical analysis revealed the presence of glycoside, alkaloid, carbohydrate and steroid in the A. augusta. Total phenol and total flavonoid content were found to be 0.29% and 0.50% w/w respectively. All tested microorganism in the A. augusta extract were found to be under the limit. Chloroform: methanol: acetic acid: H2O (170:25:25:4) was used as a solvent system for the qualitative and quantitative analysis through HPTLC Method. HPTLC analysis revealed 1.87 % w/w of linoleic acid in the A. augusta extract.ConclusionsResults showed that the selected parameters in the present investigation would set the new standards for the qualitative and quantitative analysis of A. augusta

Study of salivary α-amylase immunoglobulin, a and flow rate in diabetic subjects: a cross sectional study

Background: Diabetes is possibly the mainly common metabolic syndrome with salivary inference. However, lack of literature on the possible relationship between diabetes and salivary α-amylase, Immunoglobulin-A (IgA) and flow rate. Therefore, present study aims to estimate of salivary α-amylase, immunoglobulin-A and flow rate in diabetic subjects of Indian population.Methods: The present cross sectional study was done on 60 subjects of diabetes mellitus (T2DM) and 60 subjects’ non-diabetic healthy controls at Banas medical college and our hospital. The subject’s demographic and anthropometric parameters were recorded; detailed history and clinical examination were performed in the entire cases. The un-stimulated saliva was collected in the fasting state. Salivary flow rate, biochemical variables and IgA were analyzed. Data which was collected was statistically analyzed.Results: The results showed that salivary glucose (p0.05) between diabetic and non-diabetic subjects.Conclusions: In our study, we conclude that significant differences were reported in salivary flow rate, α-amylase and IgA between diabetics and non diabetics. Therefore, we suggested that estimation of salivary parameters might be a cost effective and a non invasive choice for screening, diagnosis and monitoring of diabetes instead of blood

Study of salivary electrolyte in type 2 diabetes mellitus patients of North Gujarat region of India

Background: A lack of literature on the probable relationship between diabetes and salivary electrolyte. Therefore, present study aims to study of salivary electrolyte in type 2 diabetes mellitus patients of North Gujarat region of India.Methods: The present cross sectional study was done on 60 subjects of diabetes mellitus (T2DM) and 60 subjects’ non-diabetic healthy controls at Banas medical college and our hospital. The subject’s demographic and anthropometric parameters were recorded; detailed history and clinical examination were performed in the entire cases. The saliva was collected in the fasting state during resting state. Salivary pH, flow rate, biochemical variables and electrolytes were analyzed. Data which was collected was statistically analyzed.Results: Predominance of the T2DM subjects was in the age group of 41-45 years. Mean value for age (p<0.05), body mass index (p<0.01), waist- hip ratio (p<0.05), salivary Potassium (p<0.001), glucose (p<0.001), Chloride (p<0.01), bicarbonates (p<0.01) and sodium levels (p<0.001) were significantly higher in the T2DM subjects where as salivary pH (p<0.01), flow rate (p<0.01) and calcium level (p<0.001) were significantly lower in the T2DM subjects.Conclusions: In our study, we conclude that significant variations were reported in salivary pH, flow rate and electrolyte variables between diabetics and non diabetics. Therefore, we suggested that estimation of salivary variables might be a cost effective and a non invasive choice for screening, diagnosis and monitoring of diabetes instead of blood

Library-An important central point of elementary schooling

A library is an interesting and fascinating space where children make friends with books and construct their knowledge freely. This robust relationship plays an important role in developing their capacities in reading, painting, drama, puzzle-solving, sports, craft and other activities. In our library project, children also get involved in the process of issuing and returning books, their maintenance and several related activities

Non-Conventional Silage for Arid Region

Thar is one of the most heavily populated desert areas in the world and the main occupations of the people living here are agriculture and livestock production. Agriculture is not a dependable proposition in this area due to erratic rains and occurrence of frequent droughts. A large number of farmers in Thar Desert depend on animal husbandry for their livelihood. Animal husbandry, trees and grasses, intercropped with vegetables or fruit trees, is the most viable farming system for arid, drought-prone regions (Anonymous, 2012a,b). Further, livestock sector is expected to emerge as an engine of agricultural growth in the 12th plan and beyond, in view of rapid growth for the demand of animal food products. Achieving growth rate of 5-6 %, however, would require addressing challenges of shortage of feed and fodder (Anonymous, 2012a,b). According to the ministry of agriculture assessment, there is a large gap between demand and supply of feed and fodder for the livestock in the country. The shortage of dry fodder, green fodder and concentrate is as high as 40% (Pawar, 2012). The problem is compounded by the lack of reliable data regarding fodder availability. The scenario appears alarming in case of availability of quality fodder. With the existing shortages of fodder, it would be difficult for India to achieve the target of 160 MT of milk production by 2020. For increasing milk production from the current level of 40 MT to 160 MT by 2020, 494 MT of dry fodder, 825 MT of green fodder and 54 MT concentrates will be required (Das, 2012). There are several crop products potentially used after enriching their quality for animal feeding, but are being wasted. All such bye-products needs to be ensiled and suitable mechanism for their enrichment and ensiling need to be developed. Keeping this in view efforts were made to ensile the dry fodder after enriching their quality by modified process