Some studies on control system using lie groups

This project related to control systems, Lie groups and Lie algebra. Firstly, we have dis- cussed about control systems with its examples. Then various types of control systems and its applications. Control theory has continued to advance with advancing technology and has emerged in modern times as a highly developed discipline. Lie theory, the theory of Lie groups, Lie algebras and their applications is a fundamental part of mathematics. On this project review Lie groups controllability for left-invariant control systems on Lie groups are addressed

Perturbation Theory for Arbitrary Coupling Strength ?

We present a \emph{new} formulation of perturbation theory for quantum systems, designated here as: `mean field perturbation theory'(MFPT), which is free from power-series-expansion in any physical parameter, including the coupling strength. Its application is thereby extended to deal with interactions of \textit{arbitrary} strength and to compute system-properties having non-analytic dependence on the coupling, thus overcoming the primary limitations of the `standard formulation of perturbation theory' ( SFPT). MFPT is defined by developing perturbation about a chosen input Hamiltonian, which is exactly solvable but which acquires the non-linearity and the analytic structure~(in the coupling-strength)~of the original interaction through a self-consistent, feedback mechanism. We demonstrate Borel-summability of MFPT for the case of the quartic- and sextic-anharmonic oscillators and the quartic double-well oscillator (QDWO) by obtaining uniformly accurate results for the ground state of the above systems for arbitrary physical values of the coupling strength. The results obtained for the QDWO may be of particular significance since `renormalon'-free, unambiguous results are achieved for its spectrum in contrast to the well-known failure of SFPT in this case. \pacs{11.15.Bt,11.10.Jj,11.25.Db,12.38.Cy,03.65.Ge}Comment: 9 Pages, 1-Table, Accepted for for publication (Mod. Phys. Lett. A

Texture Segmentation Using Gabor Filters and Wavelets

The present work deals with image segmentation which results in the subdivision of an image into its constituent regions or objects. The result of image segmentation is a set of segments that collectively cover the entire image or a set of contours extracted from the image. Each of the pixels in a region are similar with respect to some characteristic or computed property, such as color, intensity or texture. Specifically this project deals with texture segmentation of an image to find out the different types of textures present in the image. In this project different type of procedures have been followed to carry out texture segmentation. Procedures starting from fundamental filter transforms till multi-resolution technique using wavelet transform have been considered. Many texture-segmentation schemes are based on a filter-bank model, where the filters called Gabor filters are derived from Gabor elementary functions. Both linear and circular Gabor filters are studied and analyzed in this aspect and how these filters are better in comparison to linear filters is also analyzed. Different types of wavelet transform techniques like Haar transform, S transform, etc. are followed and their performance regarding texture segmentation is being studied