Invariant measure for the stochastic Cauchy problem driven by a cylindrical L\'evy process

In this work, we present sufficient conditions for the existence of a stationary solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical L\'evy process, and show that these conditions are also necessary if the semigroup is stable, in which case the invariant measure is unique. For typical situations such as the heat equation, we significantly simplify these conditions without assuming any further restrictions on the driving cylindrical L\'evy process and demonstrate their application in some examples

Study of spin and charge dynamics in one-dimensional cuprates using resonant inelastic x-ray scattering

One-dimensional (1D) antiferromagnetic chains and ladders realized in strongly correlated materials have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and other emergent phenomena. In this thesis, we examine spin and charge dynamics of 1D antiferromagnets revealed by resonant inelastic x-ray scattering (RIXS) using numerical techniques, including exact diagonalization and density matrix renormalization group. One of the major findings of this thesis is the first direct observation of multi-spinon excitations at the oxygen K-edge of Sr2CuO3, a prototype 1D cuprate, establishing RIXS as a complementary probe to inelastic neutron scattering (INS) in search of quantum spin liquids. In another study on 1D doped antiferromagnets, the RIXS spectra are shown to be rich, containing distinct two- and four-spinon excitations, dispersive antiholon excitations, and combinations thereof, further establishing that RIXS can serve as a probe of spin-charge separation in these materials. Finally, a systematic theoretical investigation of the Cu L-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving and spin-conserving channels is presented. The spectra host many exotic excitations, in particular, singlet twotriplon bound state excitations. Furthermore, direct signatures of charge quasiparticle excitations are revealed by RIXS in the doped ladders. This dissertation helps establish RIXS as an important tool for revealing the signatures of spin and charge fractionalization, and other collective excitations in strongly correlated material

Impact of Liquidity on the Futures–Cash Basis: Evidence from the Indian Market

The law of one price relies on enforcement by arbitragers who are expected to eliminate price differentials quickly. Arbitragers’ activities are constrained by liquidity of markets. However, large price differentials attract arbitrage activity enhancing the liquidity of markets. Using daily data on the NYSE index and related futures contracts, Roll, Schwartz, and Subrahmanyam (2007) document two-way Granger causality between the futures-cash basis and bid-ask spreads for stocks. We examine the issue using intra-day data on Indian single stock futures (SSF) contracts on Indian stocks and also consider the spread on the futures contracts. While the spreads in both the futures and cash markets affect futures-cash basis, we find that the futures-cash basis Granger-causes only the bid-ask spreads for SSFs but not the stocks.Futures-cash basis; Single stock futures; Indian stocks.

Simulation and Realization of Some CMOS-Transconductor Vhf Filters

CMOS circuits for integrated analog filters at very high frequencies have been designed through PSPICE based on the Transconductance-C integrator. They have been implemented on the bread board and many filters i.e. LP, BP, Elliptic LP etc. are simulated and realized

Neuropharmacological Profile of Novel Benzopyran-2-One Derivatives in Experimental Mice

The present study was aimed to assess the neuropharmacological properties of the novel Benzopyran-2-one (coumarin) derivatives i.e., 7-(2-(m-nitro)-phenyl thiazolidinyl)-4-methyl benzopyran-2-one (comp-I), 7-(2-(o,p-dichloro)-phenyl thiazolidinyl)-4-methyl-benzopyran-2-one (comp-II) and 7-(2-(p-methyl)-phenyl thiazolidinyl)-4-methyl-benzopyran-2-one (comp-III) by using the various pharmacological activities i.e., anticonvulsant, anxiolytic, spontaneous motor activity, skeletal muscle relaxant and analgesic activities along with assay of serum gamma amino butyric acid (GABA) levels. Methods: Investigation of all neuropharmacological profiles were evaluated by performing the various pharmacological activities using the different screening models, i.e., anticonvulsant activity by pentylenetetrazole (PTZ) induced seizure model, anxiolytic activity (exploratory behaviour) by evasion test, assay of GABA levels after anticonvulsant model was performed by using chromatographic technique, spontaneous motor activity (SMA) by actophotometer test, skeletal muscle relaxation by rotarod test and analgesic activity by Eddy’s hot plate and Haffner’s tail clip methods in Wistar albino mice. Results: All the Benzopyran-2-one derivatives showed significant anticonvulsant activity by prolonging the onset of seizures and reducing the duration of seizures and mortality rate when compared with control group. The test compounds showed significant anxiolytic effect. The serum GABA levels were significantly elevated in the treated groups, when compared with that of control group. The test compounds showed significant decrease in the spontaneous motor activity. The test compounds significantly showed a skeletal muscle relaxation after 30 min of dosing. The test compounds showed significant increase in paw licking time to heat stimuli in hot plate method and increase in the reaction time of mice to dislodge the clip. Conclusion: The present study has revealed that all the Benzopyran-2-one derivatives possess significant neuropharmacological properties confirmed by anticonvulsant, anxiolytic, skeletal muscle relaxant, analgesic effects and decrease in spontaneous motor activity at a dose of 20 mg/kg p.o. in swiss albino mice