Abstract:
The Lax pair formulation of the two dimensional induced gravity in the light-cone gauge is extended to the more general $w_N$ theories. After presenting the $w_2$ and $w_3$ gravities, we give a general prescription for an arbitrary $w_N$ case. This is further illustrated with the $w_4$ gravity to point out some peculiarities. The constraints and the possible presence of the cosmological constants are systematically exhibited in the zero-curvature condition, which also yields the relevant Ward identities. The restrictions on the gauge parameters in presence of the constraints are also pointed out and are contrasted with those of the ordinary 2d-gravity.

Abstract:
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\"o}schl-Teller, is given. The method, {\it a priori}, is potential independent and connects with earlier developed ones, including the oscillator based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum mechanical potential problems, like the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states, show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.

Abstract:
A recently developed algebraic approach for constructing coherent states for solvable potentials is used to obtain the displacement operator coherent state of the P\"{o}schl-Teller potential. We establish the connection between this and the annihilation operator coherent state and compare their properties. We study the details of the revival structure arising from different time scales underlying the quadratic energy spectrum of this system.

Abstract:
A mathematical analysis is investigated to obtain an analytic solution of magneto hydrodynamic stagnation-point flow towards permeable stretching surface with viscous dissipation and joule heating. In the presence of uniform suction, a transverse magnetic field normal to the surface is applied when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. The governing nonlinear momentum and energy equations are solved by homotopy analysis method (HAM) to obtain the complete analytic solution and a good agreement is found. The convergence region shows the validity of the HAM solutions. It is observed that the velocity at a point increases/decreases more with increase in the magnetic parameter when the free stream velocity is greater/less than the stretching velocity in presence of suction. An interesting result of the analysis is that, in the presence of suction parameter, the temperature increases with the increase in magnetic parameter at a certain distance from the stretching surface. Near stagnation point on the surface, heat flows from the surface to the fluid and far from the stagnation-point, heat flows from the fluid to surface due to combining effect of ohmic dissipation and strain energy inside the boundary layer.

Abstract:
Reversed phase high performance liquid chromatographic method was developed and validated for the estimation of voriconazole in bulk and formulation using prominence diode array detector. Selected mobile phase was a combination of water:acetonitrile (35:65 % v/v) and wavelength selected was 256 nm. Retention time of voriconazole was 3.95 min. Linearity of the method was found to be 0.1 to 2 μg/ml, with the regression coefficient of 0.999. This method was validated according to ICH guidelines. Quantification was done by calculating area of the peak and the detection limit and quantitation limit ware 0.026 μg/ml and 0.1 μg/ml, respectively. There was no significant difference in the intra day and inter day analysis of voriconazole determined for three different concentrations using this method. Present method can be applied for the determination of voriconazole in quality control of formulation without interference of the excipients.

Abstract:
Cyclin A1 is a male germ cell-specific cell cycle regulator that is essential for spermatogenesis. It is unique among the cyclins by virtue of its highly restricted expression in vivo, being present in pachytene and diplotene spermatocytes and not in earlier or later stages of spermatogenesis. To begin to understand the molecular mechanisms responsible for this narrow window of expression of the mouse cyclin A1 (Ccna1) gene, we carried out a detailed analysis of its promoter. We defined a 170-bp region within the promoter and showed that it is involved in repression of Ccna1 in cultured cells. Within this region we identified known cis-acting transcription factor binding sequences, including an Sp1-binding site and two GATA1-binding sites. Neither Sp1 nor GATA1 is expressed in pachytene spermatocytes and later stages of germ cell differentiation. Sp1 is readily detected at earlier stages of spermatogenesis. Site-directed mutagenesis demonstrated that neither factor alone was sufficient to significantly repress expression driven by the Ccna1 promoter, while concurrent binding of Sp1, and most likely GATA1 and possibly additional factors was inhibitory. Occupancy of Sp1 on the Ccna1 promoter and influence of GATA1-dependent cis-acting elements was confirmed by ChIP analysis in cell lines and most importantly, in spermatogonia. In contrast with many other testis-specific genes, the CpG island methylation status of the Ccna1 promoter was similar among various tissues examined, irrespective of whether Ccna1 was transcriptionally active, suggesting that this regulatory mechanism is not involved in the restricted expression of Ccna1.

Abstract:
We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopicquantum- superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges are specified for observing these features.

Abstract:
A general procedure for constructing coherent states, which are eigenstates of annihilation operators, related to quantum mechanical potential problems, is presented. These coherent states, by construction are not potential specific and rely on the properties of the orthogonal polynomials, for their derivation. The information about a given quantum mechanical potential enters into these states, through the orthogonal polynomials associated with it and also through its ground state wave function. The time evolution of some of these states exhibit fractional revivals, having relevance to the factorization problem.

Abstract:
A system of two dimensional photon gas has recently been realized experimentally. It is pointed out that this setup can be used to observe a universal breathing mode of photon gas. It is shown that a modification in the experimental setup would open up a possibility of observing the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in such a system. It is shown that the universal jump in the superfluid density of light in the output channel can be used as an unambiguous signature for the experimental verification of the BKT transition.