Abstract:
Few quinoline-based synthetic compounds (2, 8 Dicyclopentyl-4-methyl quinoline and 2, 8 Dicyclohexyl-4-methyl quinoline), the synthesis of which have been already shown by our medicinal chemistry group, were found to be potent inhibitor of mycobacterial growth. Based on the results of cell culture-based cell killing assays using DNA gyrase positive E. coli strains, we presumed that bacterial DNA gyrase might be a probable target of quinolines. The resemblance of the basic skeletal structural moiety of quinolone and quinoline inspired us to hypothesize that these quinolines might inhibit DNA gyrase. While the non-gyrase inhibitors like ethambutol and isoniazid did not inhibit the growth of these strains. The genesis of the notion of using E. coli DNA gyrase as an alternative to DNA gyrase from the pathogenic Mycobacterium, stems from the fact that E. coli DNA gyrase is found to be about eighty times more sensitive to the action of quinolones than the Mycobacterium DNA gyrase. Therefore, we had used E. coli DNA gyrase as a model enzyme for studying the action of some synthetic quinoline compounds synthesized by us. In the present work, we have used cell killing assay, gel electrophoresis assay (for DNA supercoiling) and UV spectroscopy-based coupled assay (for ATP hydrolysis) for characterizing the activity of DNA gyrase. Quinolones exhibited low IC50 values as compared to the studied quinolines on DNA gyrase positive E. coli strains We found that although quinolones are the potent inhibitors of supercoiling activity of E. coli DNA gyrase, quinolines are not. We further found that ATPase activity of E. coli DNA gyrase (Non-specific inhibitor) was inhibited to a very minor extent in the presence of very high concentration of these synthetic quinolines. DNA gyrase is not the primary target of these synthetic quinolines (2, 8 Dicyclopentyl-4-methyl quinoline and 2, 8 Dicyclohexyl-4-methyl quinoline).

Abstract:
We find static spherically symmetric monopoles in Einstein-Born-Infeld-Higgs model in 3+1 dimensions. The solutions exist only when a parameter $\a $ (related to the strength of Gravitational interaction) does not exceed certain critical value. We also discuss magnetically charged non Abelian black holes in this model. We analyse these solutions numerically.

Abstract:
We study the supersymmetric extension of the gauged $ O(3) $ sigma model in $ 2+1 $ dimensions and find the supersymmetry algebra. We also discuss soliton solutions in case the Maxwell term is replaced by the Born-Infeld term. We show that by appropriate choice of the potential, the self-dual equations in the Born-Infeld case coincide with those of the Maxwell's case.

Abstract:
We study the domain wall soliton solutions in the relativistic self-dual Maxwell Chern-Simons model in 1+1 dimensions obtained by the dimensional reduction of the 2+1 model. Both topological and nontopological self-dual solutions are found in this case. A la BPS dyons here the Bogomol'ny bound on the energy is expressed in terms of two conserved quantities. We discuss the underlying supersymmetry. Nonrelativistic limit of this model is also considered and static, nonrelativistic self-dual soliton solutions are obtained.

Abstract:
We find static spherically symmetric dyons in Einstein-Born-Infeld-Higgs model in 3+1 dimensions. The solutions share many features with the gravitating monopoles in the same model. In particular, they exist only up to some critical value of a parameter $\a$ related to the strength of the gravitational interaction. We also study dyonic non-Abelian black holes. We analyse these solutions numerically.

Abstract:
An empirical relation based on energy gap and refractive index data has been proposed in the present study to calculate the refractive index of semiconductors. The proposed model is then applied to binary as well as ternary semiconductors for a wide range of energy gap. Using the relation, dielectric constants of some III-V group semiconductors are calculated. The calculated values for different group of binary semiconductors, alkali halides and ternary semiconductors fairly agree with other calculations and known values over a wide range of energy gap. The temperature variation of refractive index for some binary semiconductors have been calculated.

Abstract:
Wepropose to measure the concentration of potassium chloride using photonic crystal fiber having circular air holes of diameter 400 nm. The principle of measurement is based on the linear variation of the transmitted field emerging from the PCF with respect to concentration of potassium chloride. Field distribution in photonic crystal structure is simulated using plane wave expansion (PWE) method. Simulation result reveals that the intensity of transmitted light varies linearly with respect to concentration of potassium chloride filled in the air holes.

Abstract:
We investigate the Hyers-Ulam stability of third order Euler's differential equations of the form on any open interval , or , where , and are complex constants. 1. Introduction In 1940, Ulam gave a wide ranging talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of important unsolved problems [1]. Among such problems is a problem concerning the stability of functional equations: give conditions in order for a linear function near an approximately linear function to exist. In the following year, Hyers [2] gave an answer to the problem of Ulam for additive functions defined on Banach spaces. Let and be two real Banach spaces and let . Then, for every function satisfying there exists a unique additive function with the property Furthermore, the result of Hyers has been generalized by Rassias [3, 4]. Since then, the stability problems of various functional equations have been investigated by many authors (see, e.g., [1, 5–8]). A generalization of Ulam’s problem was recently proposed by replacing functional equations with differential equations. The differential equation has Hyers-Ulam stability; if for given and a function such that then there exists a solution of the differential equation such that and . If the preceding statement is also true when we replace and by and , respectively, where and are appropriate functions not depending on and explicitly, then we say that the corresponding differential equation has the generalized Hyers-Ulam stability. Obloza seems to be the first author who has investigated the Hyers-Ulam stability of linear differential equations (see, e.g., [9, 10]). Thereafter, Alsina and Ger published their work [11], which handles the Hyers-Ulam stability of the linear differential equation . If a differentiable function is a solution of the inequality for any , then there exists a constant such that , for all . In [1], Rezaei et al. have discussed the Hyers-Ulam stability of linear differential equations of first and th order by applying Laplace transform which is comparable with the other methods available in the literature. It is Jung et al. who have investigated the Hyers-Ulam stability of linear differential equations of different classes including the stability of the delay differential equation , where is a constant (see, e.g., [5–7, 12–14]). Among the works, we are motivated by the results of [13], where he has studied the Hyers-Ulam stability of the following Euler’s differential equations: where , , and are complex constants. We may note that the Hyers-Ulam stability of (6) depends

Abstract:
We consider self-duality in a 2+1 dimensional gauge theory containing both the Born-Infeld and the Chern-Simons terms. We introduce a Born-Infeld inspired generalization of the Proca term and show that the corresponding self dual equation is identical to that of the Born-Infeld-Chern-Simons theory.

Abstract:
Anisotropic dark energy model with dynamic pressure anisotropies along different spatial directions is constructed at the backdrop of a spatially homogeneous diagonal Bianchi type $V$ $(BV)$ space-time in the framework of General Relativity. A time varying deceleration parameter generating a hybrid scale factor is considered to simulate a cosmic transition from early deceleration to late time acceleration. We found that the pressure anisotropies along the $y-$ and $z-$ axes evolve dynamically and continue along with the cosmic expansion without being subsided even at late times. The anisotropic pressure along the $x-$axis becomes equal to the mean fluid pressure. At a late phase of cosmic evolution, the model enters into a phantom region. From a state finder diagnosis, it is found that the model overlaps with $\Lambda$CDM at late phase of cosmic time.