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Full-Text Articles in Physical Sciences and Mathematics
Markov Dilation Of Nonconservative Quantum Dynamical Semigroups And Quantum Boundary Theory., B. V. Rajarama Bhat Dr.
Markov Dilation Of Nonconservative Quantum Dynamical Semigroups And Quantum Boundary Theory., B. V. Rajarama Bhat Dr.
Doctoral Theses
In classical probability theory, based on Kolmogorov consistency theorem, one can associate a Markov process to any one parameter semigroup of stochastic matrices or transition probability operators. It is indeed the foundation for the theory of Markov processes. Here a quantum version of this theorem has been established. This effectively answers some of the questions raised by P. A. Meyer in his book (see page 220 of (Me).It is widely agreed upon that irreversible dynamics in the quantum setting is de- scribed by contractive semigroups of completely positive maps on C" algebras ([Kr). (AL]). In other words these semigroups, known …
Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.
Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.
Doctoral Theses
The main theme of this t hesis is hypergroups. In this thesis the the- ory of hypergroups is applied to study the relation between certain graphs and subfactors of II, factors in the context of principal graphs associated with the inclusions of II, factors. More general classes of hypergroups are iutroduced, new examples of hypergroups associated to certain graphs are coustructed and classification of small order hypergroups is discussed.The text of the thesis is arranged in four chapters. The first chapter is on preliminaries of the theory of hypergroups, the second on the appli- cation of the theory of hyjrrgroups …
Parametric Homotopy Principle Of Some Practical Differential Relations., Mahuya Datta Dr.
Parametric Homotopy Principle Of Some Practical Differential Relations., Mahuya Datta Dr.
Doctoral Theses
A system uf r-th order partial differential inequalities is a subspace in the space of r-jets of CT" maps between manifolds. The problem of homotopy classification of C solutions of such systems is stauliel in this thesis. The text roughly divides into two parts. In the first part, the problem is considered in an equivariant setting when the system is open and invariant under the action of a compact L.ie group, but may not be invariant under the action of the pseudogroup of equivariant local diffeomorphisms. The second part concerns a non-equivariant set-up without the openness condition on the systern. …