http://rulrepository.ru.ac.bd/handle/123456789/119 Tue, 07 Apr 2026 21:43:55 GMT 2026-04-07T21:43:55Z 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 GMT http://rulrepository.ru.ac.bd/handle/123456789/1114 2002-01-01T00:00:00Z 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 GMT http://rulrepository.ru.ac.bd/handle/123456789/1111 2021-01-01T00:00:00Z http://rulrepository.ru.ac.bd/handle/123456789/1060 Investigation of the Soliton and Multi-soliton Solutions of nonlinear evolution equations In Mathematical Physics Hossen, Md. Belal Nonlinear evolution equations (NLEEs) play a noteworthy role in various scientific and engineering fields such as applied mathematics, plasma physics, fluid dynamics, optical fibers, biology, solid state physics, chemical physics, mechanics and geochemistry. Various effective procedure have been developed to solve NLEEs. In this work, we have discussed applications of two types methods: first type is modified double sub-equation (MDSE) method which is apply in the (1+1)-dimensional Burger equation, the (1+1)-dimensional Gardner equation and the (1+1)- dimensional Hirota-Ramani equation and secondly, Hirota’s Bilinear method which is apply in (2+1)-dimensional Breaking Soliton, the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov equations, and (3+1)-D generalized B-type Kadomtsev-Petviashvili equation. Using Modified double sub-equation method, we have presented some complexiton solutions in terms of trigonometric, hyperbolic functions. Finally, the interaction phenomena of the achieved complexiton solutions between solitary waves and/or periodic waves are presented with in depth derivation. Based on the bilinear formalism and with the aid of symbolic computation, we determine multisolitons, breather solutions, rogue wave, lump soliton, lump-kink waves and multi lumps using various ansatze’s function. We notice that multi-lumps in the form of breathers visualize as a straight line. Besides this, the breather wave degenerate into a single lump wave is determined by using parametric limit scheme. Also, we reflect a new interaction solution among lump, kink and periodic waves via ‘rational-cosh-cos’ type test function. To realize dynamics, we commit diverse graphical analysis on the presented solutions. Obtained solutions are reliable in the mathematical physics and engineering.---- This Thesis is Submitted to the Department of Mathematics , University of Rajshahi, Rajshahi, Bangladesh for The Degree of Master of Philosophy (MPhil) Wed, 01 Jan 2020 00:00:00 GMT http://rulrepository.ru.ac.bd/handle/123456789/1060 2020-01-01T00:00:00Z http://rulrepository.ru.ac.bd/handle/123456789/1057 An analytical method for finding exact Traveling wave solutions of some nonlinear Evolution equations (nlees) in biological and Mathematical problems Ullah, Mohammad Safi Most of the natural happenings can be present by nonlinear modeling. The soliton theory is a highly effective section of nonlinear sciences that includes soliton, multi-soliton, rational, breather line, breather kinky, lump and rogue wave solutions. Such solutions are essential to realizing the internal properties of the nonlinear models. This dissertation presents exact traveling wave solutions of the three nonlinear models such as the (2+1) Bogoyavlenskii’s breaking soliton (BBS) equation, the (2+1)-dimensional Benjamin-Bona-Mahony-Burgers (BBMB) equation and the (3+1)-dimensional Sharma–Tasso–Olver-like (STOL) equation by applying Hirota bilinear method. By this method, we construct the bilinear form and find the interaction solutions of the above three models. We determine the multi-soliton and their interaction solutions of the BBS model and STOL model. Various properties of the obtained solutions are illustrated clearly with a number of 3D plot, 2D plot, density plot, curve plot and contour plot by choosing suitable parametric values via the computational software Maple 18. 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 GMT http://rulrepository.ru.ac.bd/handle/123456789/1057 2021-01-01T00:00:00Z