Shodhganga Collection:
http://hdl.handle.net/10603/101276
2019-10-18T03:44:55ZExistence and Uniqueness Results for Random Differential Equations
http://hdl.handle.net/10603/253827
Title: Existence and Uniqueness Results for Random Differential Equations
Abstract: The nondeterministic nature of phenomena in the general areas of
newlinebiological, engineering, oceanographic and Physical Sciences the
newlinemathematical descriptions of such phenomena frequently result in random
newlineequations. It is to present theoretical results concerning certain classes of
newlinerandom equations and then to apply those results to problems that arise in
newlinethe general areas. Usually, the mathematical models or the equations that
newlinehave been used to describe a particular phenomenon or process of the
newlineuniverse contains a parameter, which has some specific physically
newlineinterpretations but whose values is not known. If any such phenomena
newlineinvolving mentioned parameters and which satisfy certain probabilistic
newlineand measure theoretic behavior with respect to this parameter, then we
newlinesay it is a random phenomena. For example, in the theory of diffusion
newlineor heat conduction, we have the diffusion coefficient or the coefficient
newlineof conductivity that play the prominent role. Similarly in the case of
newlinewave theory, the propagation coefficient and in the theory of
newlineelasticity, the modulus of elasticity play the significant role in the
newlinebehavior of the underlined processes. Thus, the coefficients or parameters
newlinethat have an important role to play in the natural and physical phenomena
newlinelike above are called random parameters .
newlineThe mathematical equations are solved using as the value of the parameter
newlineor coefficients, the mean value of the set of observations experimentally
newlineobtained. However, if the experiment is performed repeatedly, then the mean
newlinevalues found will vary ,and if the variation is large. The mean value actually
newlineused may be quite unsatisfactory. Thus, in practice the physical constant is
newlinenot really a constant, but a random variable whose behavior is governed by
newlinesome probability distribution. It is thus advantegeous to view these equations
newline(iii)
newlineas being random rather than deterministic ,to search random solution and to
newlinestudy its statistical properties. we take about some parameters or
newlinecoefficients, the random analysis of the random equaA Study of Fuzzy Topological Ordered Spaces
http://hdl.handle.net/10603/251120
Title: A Study of Fuzzy Topological Ordered Spaces
Abstract: newlineSome aspects of Coding Theory
http://hdl.handle.net/10603/230080
Title: Some aspects of Coding Theory
Abstract: The problem we would like to work on revolve primarily around the two areas, Algebraic
newlineGeometry and Coding Theory. Linear error correcting codes associated to higher dimen
newlinesional algebraic varieties deand#64257;ned over and#64257;nite and#64257;elds have been a topic of recent interest. Linear
newlinecodes associated with Grassmann varieties, Schubert varieties have been studied extensively
newline([36, 38, 41]).
newlineIn this thesis, we reviewed the linear codes and their parameters such as length, dimension,
newlinebounds, higher weights. LCD codes is a topic of recent interest to many researchers[3, 4,
newline24, 42]. In this thesis, we have given new proof of Massey s theorem[21], which is one of the
newlinemost important characterization of LCD codes. We also have given one new construction
newlineof ternary LCD codes. Besides this, we constructed some ternary LCD codes attaining one
newlinespeciand#64257;c kind of bound. We then focused on algebraic varieties and their connection with
newlinelinear codes. Our main interest lies in the two projective varieties called Grassmann variety
newlineand Schubert variety. We have concentrated our attention on error correcting capabilities
newlineof Schubert codes. We explain the Grassmann and Schubert codes and the known results
newlineof these codes. These codes have been studied by C. T. Ryan and K. M. Ryan [8], Nogin
newline[12], and Ghorpade and Lachaud [38], Hansen, Johnsen, Ranestad [22], Ghorpade, Patil,
newlinePillai [40]. We have found out generator matrices of Schubert codes in some special cases,
newlinefurther computed GrÂ¨obner bases of ideals associated with such codes and their decoding
newlineand error-correction in accordance with [15, 28, 29]. Finally, we propose our future plan of
newlineresearch.
newline
newlineStudy of Abstract Measure Integro differential Equations and its applications
http://hdl.handle.net/10603/230064
Title: Study of Abstract Measure Integro differential Equations and its applications
Abstract: newline