Solutions of SPDE’s Associated with a Stochastic Flow

Potential Analysis - We consider the following stochastic partial differential equation, $$\begin{array}{@{}rcl@{}} &&dY_{t} = L^{\ast} Y_{t} dt + A^{\ast} Y_{t} \cdot dB_{t}\\...     

Characterizing Gaussian Flows Arising from Itô’s Stochastic Differential Equations

In order to identify which of the strong solutions of Itô’s stochastic differential equations (SDEs) are Gaussian, we introduce a class of diffusions which ‘depend deterministically on the initial condition’ and then characterize the class. This characterization allows us to show, using the Monotonicity inequality, that the transpose of the flows generated by the SDEs, for an extended class of initial conditions, are the unique solutions of the class of stochastic partial differential equations introduced in Rajeev and Thangavelu (Potential Anal. 28(2), 139–162 2008), ‘Probabilistic Representations of Solutions of the Forward Equations’.     

Exact Solution of a(2+1)-Dimensional Anisotropic Star in Finch and Skea Spacetime

We provide a new class of interior solution of a(2+1)-dimensional anisotropic star in Finch and Skea spacetime corresponding to the BTZ black hole. We develop the model by considering the MIT bag model EOS and a particular ansatz for the metric function grrproposed by Finch and Skea [M.R. Finch and J.E.F. Skea, Class. Quantum.Grav. 6(1989) 467]. Our model is free from central singularity and satisfies all the physical requirements for the acceptability of the model.     

Exact interior solutions in 2+1-dimensional spacetime

An exact formulation of two-dimensional chiral hydrodynamics with diffeomorphism and conformal anomalies is provided. The constitutive relation involving the stress tensor is computed. It reveals a one parameter class of solutions which is a new result. For a particular value of this parameter, the results found in the gradient expansion scheme are reproduced. Moreover, the constitutive relation is analogous to the corresponding relation for an ideal fluid, appropriately modified to include the chirality property, which has also been derived here.     

Natures of Statefinder Parameters and Om Diagnostic for Cardassian Universe in Ho?ava-Lifshitz Gravity

In this work, we have considered Cardassian Universe in Ho?ava-Lifshitz gravity. Four types of Cardassian Universe models i.e., polytropic/power law, modified polytropic, exponential and modified exponential models have been considered for accelerating models. The natures of statefinder parameters, deceleration parameter, Om diagnostic and EoS parameters have been investigated for all types of Cardassian models in Ho?ava-Lifshitz gravity.     

Dynamics of Logamediate and Intermediate Scenarios in the Dark Energy Filled Universe

We have considered a model of two component mixture i.e., mixture of Chaplygin gas and barotropic fluid with tachyonic field. In the case, when they have no interaction then both of them retain their own properties. Let us consider an energy flow between barotropic and tachyonic fluids. In both the cases we find the exact solutions for the tachyonic field and the tachyonic potential and show that the tachyonic potential follows the asymptotic behavior. We have considered an interaction between these two fluids by introducing a coupling term. Finally, we have considered a model of three component mixture i.e., mixture of tachyonic field, Chaplygin gas and barotropic fluid with or without interaction. The coupling functions decays with time indicating a strong energy flow at the initial period and weak stable interaction at later stage. To keep the observational support of recent acceleration we have considered two particular forms (i) Logamediate Scenario and (ii) Intermediate Scenario, of evolution of the Universe. We have examined the natures of the recent developed statefinder parameters and slow-roll parameters in both scenarios with and without interactions in whole evolution of the universe.     

Cu(OTf)2-promoted efficient synthetic route towards glycospiro-pyrrolo[2,1-a]isoquinolines

A simple, convenient and efficient protocol for the construction of an array of glycospiro-pyrroloisoquinolines using isoquinolinium ylide and a carbohydrate-derived exocyclic olefin in the presence of Cu(OTf)₂–Et₃N catalytic system is described. Isoquinoline and alkylbromoacetates/2-bromoacetophenones were employed to generate the azomethine ylides in the presence of Et₃N in refluxing toluene and subsequent exposure to the olefin led to the desired isoquinoline derivatives.     

Surface-Mediated Solid Phase Reaction. IX. A Convenient Procedure for Aldol Reaction of Ketene Silyl Acetals with Aldehydes on the Solid Surface of Alumina

The aldol reaction of ketene silyl acetals with aldehydes proceeds efficiently on the solid surface of alumina impregnated with anhydrous zinc chloride under sonication providing aldol products in high yields and with good stereoselectivity.     

Polycrystalline GaSb films prepared by the coevaporation technique

Gallium antimonide (GaSb) films were deposited onto fused silica and n-Si (100) substrates by coevaporating Ga and Sb from appropriate evaporation sources. The films were polycrystalline in nature. The size and the shape of the grains varied with the change in the substrate temperature during deposition. The average surface roughness of the films was estimated to be 10 nm. Grain boundary trap states varied between 2×10¹² and 2.2×10¹² cm^?2 while barrier height at the grain boundaries varied between 0.09 eV and 0.10 eV for films deposited at higher temperatures. Stress in the films decreased for films deposited at higher temperatures. XPS studies indicated two strong peaks located at ～543 eV and ～1121 eV for Sb 3d_3/2 and Ga 2p_3/2 core-level spectra, respectively. The PL spectra measured at 300 K was dominated by a strong peak located ～0.55 eV followed by two low intensity peaks ～0.63 eV and 0.67 eV. A typical n-Si/GaSb photovoltaic cell fabricated here indicated V _oc～311 mV and J～29.45 mA/cm², the density of donors (N _d)～3.87×10¹⁵ cm^?3, built in potential (V _bi)～0.48 V and carrier life time (τ)～28.5 ms. Impedance spectroscopy measurements indicated a dielectric relaxation time ～100 μs.     

Formation of benzofurans in a stoichiometric annulation reaction between stable Pallada (II) Cycles hypervalent vinyl- and alkynyl(phenyl)iodonium salts

Stable pallada(II)cycles featuring Csp²-Pd and Csp³-Pd bonds reacted with vinyl- and alkynyl(phenyl)iodonium salts to generate two new geminal carbon-carbon bonds to the terminal carbon of the vinyl and alkynyl substituents providing benzofuran and dihydrobenzofuran heterocycles. The new annulation process was rationalized by the involvement of Pd(IV) intermediates arising via an initial oxidative addition of hypervalent iodonium electrophiles to the Pd(II) center. Reaction monitoring via low temperature ¹H NMR spectroscopy was performed, and organopalladium(II) intermediates featuring a new Csp²-Csp² or Csp²-Csp bond were isolated and characterized, providing insights into the regiochemical course of the proposed mechanistic pathway.