MPhil Thesis

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Start date: 2000End date: 2009

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Now showing 1 - 7 of 7
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    Study of Radicals and Semisimple Classes of Rings
    (University of Rajshahi, 2002) Dey, Kalyan Kumar; Majumdar, Subrata
    The concept of the radical of a ring was introduced by Artin for rings with the descending chain condition with a view to obtaining a nice structure theorem for the ring. The idea was to single out the Toblerone part, of a ring, called the radical of the ring, and factor out the original ring with respect to the radical. The resulting ring, termed, semi simple has a nice description. Radica1s for rings without chain conditions were proposed by Koethe, Jacobson, Brown, McCoy, Levitzki and others for a similar purpose in an attempt to generalize Artin 's radical. All these attempts were later further generalized by Kurosh and Amitsur to define the concept of a general radical of a ring and the cones ponding semi simple ring and study these in their generality. Andrunakievic advanced these studies further. The class of rings which are radicals of themselves with respect to some radical is called a radical class, or simply, a radical, and the correponding class of the semisimple rings is called a semisimple class. A class rings may be simultaneously a radical ring with respect to some radical and a semisimple ring with respect to another radical. Such a class of rings is called a semisimple radical class. In this thesis we have studied radical classes, semisimple classes and semisimple radical classes of rings………………….
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    A Study of Characterization of Some Regular Gamma Rings
    (University of Rajshahi, 2003) Nazneen, Ayesha; Paul, Akhil Chandra
    The present thesis entitled, "A Study of Characterization of Some Regular Gamma Rings " is the outcome of researches carried out by me under the close supervision of Dr. Akhil Chandra Paul, Professor, Department of Mathematics, Rajshahi University. The thesis is of six chapters. In the first chapter we have tried to introduce all types of the conceptions of the complete thesis. In the second chapter we have given the definition of r - ring due to Barnes and of the relevant things. Various types of r- rings and their examples are also presented there. Some kinds of radical and corresponding theorems are also stated and important ones are proved. The definition of k - regular r- ring is given in the third chapter. Kyuno defmed this regular r - ring. We have tried to prove that the class of all k - regular r- rings forms a radical. Some of the characterizations of this r- rings are developed. We have also shown that k - regular r- ring without zero divisors is a skew r- field…….
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    A Study on Oxygen Diffusion Through Living Tissues
    (University of Rajshahi, 2009) Malek, Abdul; Hoque, Md. Ashabul
    A theoretical study of oxygen diffusion process through living tissues and its various consequences have been presented. In this aspect we have reviewed some physiological terms and fundamental lows of diffusion. A Mathematical model of the partial pressure of oxygen across the alveolar­pulmonary capillary membrane has been determined and expressed in term of membrane thickness due to the oxyhemoglobin dissociation curve. On the other hand, the effect of partial pressure of carbon dioxide has been found to be the function of partial pressure of oxygen. The partial pressure of oxygen along the pulmonary capillary has also been discussed when deoxygenated blood converts to the oxygenated blood taking Hill's modified oxyhemoglobin dissociation equation and Bohr effect. It is found that the partial pressure of oxygen increases with the increasing of capillary length. The mathematical equations have been developed based on the partial pressure of oxygen in the capillary blood is reached in equilibrium position. It is found that the molar flux decreases exponentially with the increasing of radial thickness of the capillary. Moreover, It is found that the molar flux of oxygen increases linearly with the increasing of diffusion coefficient of oxygen. A mathematical model of molar flux of oxygen has been developed across the capillary-tissue membrane by neglecting the convective transport across the capillary membrane. We have found that the maximum consumption rate of oxygen increases rapidly at initial stages after that it decreases with the increasing of wall thickness. Moreover, the result indicates that the pressure profile of oxygen along the wall is approximately linear with the increasing of the thickness of capillary wall.
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    Eulerian Method for Third Order Linear Systems
    (University of Rajshahi, 2003) Haque, Md. Abdul; Sattar, M. Abdus
    In this thesis, we have studied the solutions of the various types of third order linear systems of ordinary differential equations. In chapter I, we have considered the third order linear homogeneous system with constant coefficients and developed Eulerian methods for all possible cases of the characteristic roots of the variational matrix. In chapter 2, we have considered the third order linear nonhomogeneous system with constant coefficients. The method covers all the cases when the roots of the characteristic equation of the corresponding homogeneous linear system are real and distinct, real and equal and complex. In finding particular solutions for the nonhomogeneous system of equations we have used the method of variation of parameters. Finally, we have obtained solutions of this system with the help of Crammer's rule. In chapter 3, we have considered the generalized form of third order linear nonhomogeneous system with constant coefficients. We have extended the Eulerian method and developed new techniques for obtaining solutions of this system. In chapter 4, we have discussed the third order linear nonhomogeneous system with variable coefficients. This problem is very difficult to solve, so we have examined a special case of this problem. By using a suitabletransformation, we have reduced it to a third order linear nonhomogeneous system with constant coefficients and have found solutions by the method of Chapter 2. We have illustrated all the methods by several suitable examples.
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    On Some Universal Constructions for Fuzzy Topological Spaces
    (University of Rajshahi, 2005) Rashid, Mohammed Harunor; Ali, Dewan Muslim
    In this work, many known universal objects such as products, equalizers, pullbacks and their duals, namely, coproducts, coequalizers and pushouts for fuzzy topological spaces are studied in detail. Another known concept of inverse and direct limits on inverse and direct system of fuzzy topological spaces are also studied in more detail. Besides this, we explored some properties of the singular homology groups of fuzzy topological spaces by using the concepts of direct limits on fuzzy direct systems of fuzzy topological spaces.
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    Some Topics in Fuzzy Topological Spaces
    (University of Rajshahi, 2004) Hossain, Md. Sahadat; Ali, Dewan Muslim
    The concept of fuzzy set was introduced by the American Mathematician L. A. Zadeh for the first time in 1965. This provides a natural framework for generalizing many algebraic and topological concepts in various directions. Accordingly fuzzy groups, fuzzy ideals, fuzzy rings, fuzzy vector space, fuzzy measure, fuzzy topology, fuzzy topological groups, fuzzy topological vector space and many other branches have been developed all over the world during the last four decades. It is still developing in many directions. While reviewing the literature in fuzzy topology, we have seen the gap in separation axiom of fuzzy topological space, the counter part of which in ordinary topological space drew attention of several eminent mathematicians like Azad, K. K.; Chang, C. L.; Ali, D. M.; Wuyts, P.; Srivastava, A. K. and Lowen, R. etc. We aim to develop of theories of Fuzzy To, Fuzzy T1, Fuzzy T2, Fuzzy Ro, Fuzzy R1, Fuzzy Regular and Fuzzy Normal spaces analogous to its counterpart in ordinary topology. The material of the thesis has been divided into six chapters, a brief scenario of which we present as follows. Chapter one incorporates some of the basic definitions and results of fuzzy set, fuzzy topology and mappings. These results are ready references for the work in subsequent chapters. Results are stated without proof and can be seen in the papers referred to.
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    A Theoretical Study on Some Aspects of Turbulent Flow
    (University of Rajshahi, 2003) Sultana, Mst. Shamima; Sarker, M. Shamsul Alam
    The conception of turbulent flow and the accompanying transition from laminar to turbulent flow is of fundamental importance. In everyday life, we recognized three states of matter: solid, liquid and gas. Although different in many respects, liquid and gases have a common characteristic in which they differ from solids: they are fluids, lacking the ability of solids to offer permanent resistance to a deforming force. Fluids flow under the action of such forces, deforming continuously for as long as the force applied. The fluids may be classified into different types depending upon the presence of viscosity. Osborne Reynolds shows that two entirely different types of fluids flow exist. In general words, turbulent flow is a flow, in which the inertia force is dominating over the viscosity. On the other hand, Laminar flow is a flow, in which the viscosity of the fluid is dominating over the inertia force. Osborne Reynolds demonstrated this in 1883 through an experiment. Reynolds’s apparatus consist of a tank, containing water and a small tank containing dye. 0. Reynolds’s [50) was also the first to investigate in greater detail the circumstances of the transition from laminar to turbulent flow. The previously mentioned dye experiment was used by him in this connection, and he discovered the law of similarity which now bears his name, which states…………………………..