E-Collections
http://gyan.iitg.ernet.in/handle/123456789/1
Thu, 14 Nov 2019 03:16:57 GMT2019-11-14T03:16:57ZStrong linearizations of polynomial and rational matrices and recovery of spectral data
http://gyan.iitg.ernet.in/handle/123456789/1386
Strong linearizations of polynomial and rational matrices and recovery of spectral data
Das, Ranjan Kumar
Linearization is a classical technique widely used to deal with matrix polynomial. The main purpose of the thesis is to construct and analyze strong linearizations of polynomial and rational matrices. The first part of the thesis is devoted to construction of strong linearizations of matrix polynomials including structure-preserving strong linearizations and the recovery of eigenvectors, minimal bases and minimal indices of matrix polynomials from those of the linearizations. The second part of the thesis is devoted to construction of strong linearizations of rational matrices including structure-preserving strong linearizations and the recovery of eigenvectors, minimal bases and minimal indices of rational matrices from those of the linearizations.Fiedler pencils (FPs), generalized Fiedler pencils (GFPs), Fiedler pencils with repetition (FPRs) and generalized Fiedler pencils with repetition (GFPRs) are important family of strong linearizations of matrix polynomials which have been studied extensively over the years. It is well known that the family of GFPRs of matrix polynomials subsumes the family of FPRs and is an important source of strong linearizations, especially structure-preserving strong linearizations of structured matrix polynomials. We propose a unified framework for analysis and construction of a family of Fiedler-like pencils, which we refer to as extended GFPRs (EGFPRs), that subsumes all the known classes of Fiedler-like pencils such as FPs, GFPs, FPRs and GFPRs of matrix polynomials.
Supervisor: Rafikul Alam
Tue, 01 Jan 2019 00:00:00 GMThttp://gyan.iitg.ernet.in/handle/123456789/13862019-01-01T00:00:00ZOn the module of derivations of certain rings
http://gyan.iitg.ernet.in/handle/123456789/1385
On the module of derivations of certain rings
Dey, Arindam
The goal of this thesis is to study module of derivations of certain rings of invariants and of certain hypersurface rings. The thesis is divided into two parts.In the rst part we study module of derivarions of ring of invariants under the linear action of cyclic subgroups of GL(n; k). The motivation to study this comes from a result by R. V. Gurjar and V. Wagh. They have proved [2] that for a nite cyclic subgroup G of GL(2;C) the module of derivations of the ring of invariants is minimally generated by 4 elements.
Supervisor: Vinay Wagh
Tue, 01 Jan 2019 00:00:00 GMThttp://gyan.iitg.ernet.in/handle/123456789/13852019-01-01T00:00:00ZAnalysis, design and modeling of approximate adders for error-resilient applications
http://gyan.iitg.ernet.in/handle/123456789/1384
Analysis, design and modeling of approximate adders for error-resilient applications
Dutt, Sunil
Over the decades, Complementary Metal-Oxide-Semiconductor (CMOS) technology scaling has been the fundamental driver for computing. However, we are now in a phase where CMOS technology scaling is becoming less effective in improving the system capability. The consequence is that we must either accept that the computing systems are good enough or look for alternate avenues to advance them without significant technology progress. Recent studies show that there are several promising alternate avenues that jointly can improve the system capability equivalent to 2 − 3 decades of Moore’s law. Approximate computing is one of them and has attracted a lot of attention of researchers. It should be noted that the concept of approximate computing trade-offs computation quality for computation efforts.In recent years, several approximate adders have been proposed in the literature. The key design approach behind these approximate adders is to truncate the carry-chain. The two most commonly used approaches to truncate the carry-chain are: (i) Approximate Full Adder (AFA); and (ii) Equal Segment Adder (ESA). In the first approach, an N-bit adder is segmented into two sub-adders: (i) Accurate sub-adder that includes the higher order k bits; and (ii) Approximate sub-adder that includes the remaining lower order (N − k) bits. For accurate sub-adder, Full Adders (FAs) are used, whereas for approximate subadder, AFAs are used. In the second approach, an N-bit adder is segmented into several smaller disjoint or overlapping equally sized accurate sub-adders. The Carry-in (Cin) of all sub-adders is considered as 0. Consequently, all sub-adders become independent and operate in parallel. This thesis is divided into three parts in which analysis, designing, analytical modeling, optimization and applications of AFAs and ESAs are presented.
Supervisor: Gaurav Trivedi and Sukumar Nandi
Mon, 01 Jan 2018 00:00:00 GMThttp://gyan.iitg.ernet.in/handle/123456789/13842018-01-01T00:00:00ZExploring BSM physics through doublet extensions of the Higgs sector
http://gyan.iitg.ernet.in/handle/123456789/1383
Exploring BSM physics through doublet extensions of the Higgs sector
Sahoo, Shibananda
In the year 2012, two collaborations of LHC, ATLAS and CMS independently observed a new particle known as Standard Model (SM)-like Higgs boson. This discovery confirms Higgs mechanism as the way of Electroweak Symmetry Breaking. The Higgs boson was predicted by Peter Higgs and Francois Englert in 1964 to break the electroweak symmetry spontaneously, for which they received nobel prize in 2013. Although the discovery completes the particle spectrum of the SM, it opens the door for the beyond the SM Higgs sector as the observed particle can be accommodated in a natural way in many attractive multi-Higgs scenarios. But the confirmation of these models depends on observing other scalars of the models. Our main aim in this thesis is to explore the implications of some of the multi-Higgs models.In our first work, we perform a model independent analysis focusing on the cascade decay of a heavy Higgs. In our second work, we consider an inert version of 2HDM, popularly known as inert higgs doublet model (IHDM). Explaining DM and non-zero neutrino mass in a single framework is a pressing task among modern particle physicists. In our final work, we make an attempt in this direction.Summarizing, we focus on the multi-Higgs sector aiming to probe the additional scalars of the models at the LHC, and investigate the DM phenomenology from collider perspective in one of the models. We also make the connection of DM with neutrino mass in a single framework.
Supervisor: Poulose Poulose
Tue, 01 Jan 2019 00:00:00 GMThttp://gyan.iitg.ernet.in/handle/123456789/13832019-01-01T00:00:00Z