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| Abstract: | There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H. |
| Description: | Department Of Mathematics and Statistics, Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3394 |
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| Dyuthi-T1371.pdf | (4.002Mb) |
| Abstract: | The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis |
| Description: | Department of Mathematics and Statistics, Cochin University of Science & Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3341 |
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| Dyuthi-T1325.pdf | (3.438Mb) |
| Abstract: | This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also. |
| Description: | Department of Mathematics and Statistics, Cochin University of Science and Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3645 |
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| Dyuthi-T1621.pdf | (9.681Mb) |
| Abstract: | An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions. |
| Description: | Department of Mathematics and Statistics, Cochin University of Science & Technology |
| URI: | http://dyuthi.cusat.ac.in/purl/3345 |
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| Dyuthi-T1327.pdf | (4.010Mb) |
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