Department of Mathematics
http://rulrepository.ru.ac.bd/handle/123456789/76
Wed, 06 Nov 2024 17:39:10 GMT2024-11-06T17:39:10ZStudy of Radicals and Semisimple Classes of Rings
http://rulrepository.ru.ac.bd/handle/123456789/1114
Study of Radicals and Semisimple Classes of Rings
Dey, Kalyan Kumar
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………………….
This Thesis is Submitted to the Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh for The Degree of Master of Philosophy (MPhil)
Tue, 01 Jan 2002 00:00:00 GMThttp://rulrepository.ru.ac.bd/handle/123456789/11142002-01-01T00:00:00ZAnalytical Methods to Investigate Exact Solutions for Space-Time Fractional Differential Equations Arising in the Real Physical Phenomena of Mathematical Physics and Biology
http://rulrepository.ru.ac.bd/handle/123456789/1111
Analytical Methods to Investigate Exact Solutions for Space-Time Fractional Differential Equations Arising in the Real Physical Phenomena of Mathematical Physics and Biology
Rahman, Zillur
Fractional derivatives are most important to accurate nonlinear modeling of various real-world difficulties in applied nonlinear science and engineering incidents especially in the fields of crystal, optics and quantum mechanics even in biological phenomena. The investigation of exact solutions of such nonlinear models has great important to visualize the nonlinear dynamics. We consider the space-time fractional nonlinear differential equations for pulse narrowing transmission lines model, the space-time fractional Equal-width (s-tfEW) and the space-time fractional Wazwaz-Benjamin-Bona-Mahony (s-tfWBBM), complex Schrodinger and biological population models, the complex time fractional Schrodinger equation (FSE) and low-pass electrical transmission lines equation (ETLE) are studied with the effective unified method, Jacobi elliptic expansion function integral technique, generalized Kudryshov technique, modified simple equation (MSE) method respectively. As a result, we get some solitary wave solutions in the form of hyperbolic and combo hyperbolic-trigonometric :functions including both stable and unstable cases. We obtain kink wave, bright bell wave, dark bell wave, combo periodic-rogue waves, combo M-W shaped periodic-rogue waves in stable cases, and singular kink type in unstable solitonic natures. Lastly, we proposed an Improved Kudryashov method for solving any nonlinear fractional differential models. We apply the proposed approach to the nonlinear spacetime fractional model leading wave spread in electrical transmission lines (s-tfETL), the spacetime M-fractional Schrodinger-Hirota (s-tM-fSH) and the time fractional complex Schrodinger (tfcS) models to verify the effectiveness of the propose approach. The implementations of the introduced new technique on the models provide us periodic envelope, exponentially changeable soliton envelope, rational, combo periodic-soliton and combo rational-soliton solutions, which are much interesting phenomena in the nonlinear sciences. Beside the scientific derivation of the analytical findings, we represent the results graphically for clear visualization of the dynamical properties.
This Thesis is Submitted to the Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh for The Degree of Master of Philosophy (MPhil)
Fri, 01 Jan 2021 00:00:00 GMThttp://rulrepository.ru.ac.bd/handle/123456789/11112021-01-01T00:00:00ZOn Generalizations of Separation Properties, Compactness and Connectedness
http://rulrepository.ru.ac.bd/handle/123456789/1102
On Generalizations of Separation Properties, Compactness and Connectedness
Biswas, Sanjoy Kumar
The thesis is concerned with generalizations of some important and interesting properties of separation, compactness and connectedness in a span of seven chapters. In the first chapter pseudo regular and pseudo normal topological spaces have been defined. Their properties have been studied and a number of important theorems regarding these spaces have been established.
In the second chapter strongly pseudo-regular and strongly pseudo-normal topological spaces have been introduced and their properties have been studied. A number of important theorems have been proved in this regard.
This is the third chapter. In this chapter strictly pseudo-regular and strictly pseudo-normal topological spaces have been defined and their properties have been studied. In the former class a compact set can be separated from an external point by a continuous function, while in the latter, two disjoint compact sets can be separated by a continuous function. Many important properties have been proved. The fourth chapter introduces the notions of nearly regular topological spaces of the first kind and the second kind and studies their properties. A number of important theorems regarding these spaces have been established.
In this fifth chapter two new generalizations of normal spaces have been defined and studied. The spaces in these classes have been termed nearly normal topological spaces of the first kind and the second kind respectively. This is the sixth chapter. In this chapter further new generalizations of normal spaces have been made. These have been called slightly normal spaces of the first kind, the second kind and the third kind respectively. A number of important properties of these spaces have been proved.
In this chapter seven compactness has been generalized to pseudo-compactness and c-compactness, and a continuum i.e., a connected compact space has been generalized to pseudo-continuum. Several properties of these three classes of spaces have been studied.
This Thesis is Submitted to the Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh for The Degree of Doctor of Philosophy (PhD)
Tue, 01 Jan 2019 00:00:00 GMThttp://rulrepository.ru.ac.bd/handle/123456789/11022019-01-01T00:00:00ZOn Generalizations of Separation properties, Compactness and Connectedness
http://rulrepository.ru.ac.bd/handle/123456789/1065
On Generalizations of Separation properties, Compactness and Connectedness
Biswas, Sanjoy Kumar
The thesis is concerned with generalizations of some important and
interesting properties of separation, compactness and connectedness in a
span of seven chapters.
In the first chapter pseudo regular and pseudo normal topological
spaces have been defined. Their properties have been studied and a number
of important theorems regarding these spaces have been established.
In the second chapter strongly pseudo-regular and strongly pseudonormal
topological spaces have been introduced and their properties have
been studied. A number of important theorems have been proved in this
regard.
This is the third chapter. In this chapter strictly pseudo-regular and
strictly pseudo-normal topological spaces have been defined and their
properties have been studied. In the former class a compact set can be
separated from an external point by a continuous function, while in the
latter, two disjoint compact sets can be separated by a continuous function.
Many important properties have been proved.
The fourth chapter introduces the notions of nearly regular topological
spaces of the first kind and the second kind and studies their properties. A
number of important theorems regarding these spaces have been established.
In this fifth chapter two new generalizations of normal spaces have
been defined and studied. The spaces in these classes have been termed
nearly normal topological spaces of the first kind and the second kind
respectively.
This Thesis is Submitted to the Department of Mathematics , University of Rajshahi, Rajshahi, Bangladesh for The Degree of Doctor of Philosophy (PhD)
Tue, 01 Jan 2019 00:00:00 GMThttp://rulrepository.ru.ac.bd/handle/123456789/10652019-01-01T00:00:00Z