An approach to dynkin diagrams associated with KAC-moody superalgebra

In the present project report, a sincere report has been made to construct and study the basic portions related to Simple Lie Algebras, Lie superalgebras and Kac-Moody (super-) algebras and their corresponding Dynkin Diagrams. In chapter-1, I have given the precise definitions of Lie Algebra and some of the terms related to Lie algebra, i.e. subalgebras, ideals, commutativity, solvability, nilpotency etc. Also, I have done the classifications of Classical Lie algebras. In chapter-2, I made a review over the basics of Representation Theory, i.e. structure constants, modules, reflections in a Euclidean space, root systems (simple roots) and their corresponding root diagrams. Then I have discussed the formation of Dynkin Diagrams associated with the roots of the simple lie algebras. After that, in chapter-3, the introductory parts of Lie superalgebras, i.e. Z2 graded algebra, definition of lie superalgebra, modules, the killing form, root systems and simple root systems (distinguished root systems) are addressed. In this section, also the classifications of simple lie superalgebras are plotted and the Dynkin Diagrams related to the Basic Lie superalgebras are presented. In chapter-4, I gave the necessary theory based on Kac-Moody Lie superalgebras and their classifications. Then the definition of the extended Dynkin diagrams for Affinization of Kac-Moody superalgebras and the Dynkin Diagrams associated with the affine Kac-Moody superalgebras are provided

Design and Analysis of Microstrip Filtennas

The Goal of this thesis is to design and analyses the filtenna, also called by name filtering antenna. Designed by integration of the filter and antenna. In modern day wireless devices multiple antennas are required to make sure that it can be used for multiple communication services, this not only make the system bulky but the power loss is also more. In filtenna using active components can replace them making a system with low profile, more light weight, and energy efficient characteristics. In this thesis includes the first part which is an introduction to computational electromagnetics and using this analysis of microstrip antenna and second is the proposed design of two microstrip filtennas. Under computation electromagnetics, the Maxwell equation and antenna parameter are analyzed using finite difference method. The design and simulation of this filtenna have been done in ANSYS-HFSS-15 simulation tool. The first filtenna designed structure is the integration of the band-rejection filter with monopole antenna for UWB and X-Band applications. Where after applying the open stub it only passes the X-Band i.e. 8-12 GHz. The second proposed filtenna is for overlay cognitive radio application. This is design using the bandpass filter which is integrated with the antenna. In bandpass filter, the frequency tuning is done by varactor diode. This filtenna resonates at frequency 2.6 to 3 GHz and gain of 2.7dB. The fabrication of second filtenna using bandpass characteristics is done and analyzed the results

Using time-dependent indirect CPCP asymmetries to measure TT and CPTCPT violation in B0B^0-Bˉ0{\bar B}^0 mixing

Quantum field theory, which is the basis for all of particle physics, requires that all processes respect $CPT$ invariance. It is therefore of paramount importance to test the validity of $CPT$ conservation. In this Letter, we show that the time-dependent, indirect $CP$ asymmetries involving $B$ decays to a $CP$ eigenstate contain enough information to measure $T$ and $CPT$ violation in $B^0$-${\bar B}^0$ mixing, in addition to the standard $CP$-violating weak phases. Entangled $B^0{\bar B}^0$ states are not required (so that this analysis can be carried out at LHCb, as well as at the $B$ factories), penguin pollution need not be neglected, and the measurements can be made even if the $B^0$-${\bar B}^0$ width difference vanishes.Comment: 10 pages, no figures, changes: removed almost all discussion of what can and cannot be done with the method of entangled states; explained that CPT- and T-violating parameters also contribute to CP-violating effects; reorganized the presentation of the paper; added footnotes and reference

The study of multifragmentation around transition energy in intermediate energy heavy-ion collisions

Fragmentation of light charged particles is studied for various systems at different incident energies between 50 and 1000 MeV/nucleon. We analyze fragment production at incident energies above, below and at transition energies using the isospin dependent quantum molecular dynamics(IQMD) model. The trends observed for the fragment production and rapidity distributions depend upon the incident energy, size of the fragments, composite mass of the reacting system as well as on the impact parameter of the reaction. The free nucleons and light charged particles show continous homogeneous changes irrespective of the transition energies indicating that there is no relation between the transition energy and production of the free as well as light charged particles

Temporal Information Processing and Stability Analysis of the MHSN Neuron Model in DDF

Implementation of a neuron like information processing structure at hardware level is a burning research problem. In this article, we analyze the modified hybrid spiking neuron model (the MHSN model) in distributed delay framework (DDF) for hardware level implementation point of view. We investigate its temporal information processing capability in term of inter-spike-interval (ISI) distribution. We also perform the stability analysis of the MHSN model, in which, we compute nullclines, steady state solution, eigenvalues corresponding the MHSN model. During phase plane analysis, we notice that the MHSN model generates limit cycle oscillations which is an important phenomenon in many biological processes. Qualitative behavior of these limit cycle does not changes due to the variation in applied input stimulus, however, delay effect the spiking activity and duration of cycle get altered