Abstract:
Recent interest in problems in higher space di mensions is becoming increasingly important and attracted the attention of many investigators in variety of fields in physics. In this paper, the electrostatic energy of two geometries (a charged spherical shell and a nonconducting sphere) is calculated in higher space dimension, N. It is shown that as the space dimension increases, up to N = 9, the electrostatic energy of the two geometries decreases and beyond N = 9 it increases. Furthermore, we discuss a simple example which illustrates classical renormalization in electrostatics in higher dimensions.

Abstract:
FMCW Radar (Frequency Modulated Continuous Wave Radar) is used for various purposes, such as atmospheric Remote Sensing, inter-vehicle ranging, etc. FMCW radar systems are usually very compact, relatively cheap in purchase as well as in daily use, and consume little power. In this paper, FMCW radar determines a target range by measuring the beat frequency between a transmitted signal and the received signal from the target, and Combines between PO and radar single. The approach based on frequency domain physical optics for the scattering estimation and the linear system modeling for the estimation of time domain response, and FMCW Radar signal processing.

Rectangular reflector antennas have motivated the time-domain analysis of electromagnetic scattering problems. The asymptotic time domain physical-optics (TDPO) is applied to the analysis of a rectangular reflector illuminated by a Gaussian-impulse. The effects of time-delayed mutual coupling between points on the surface will be ignored as a result of utilizing the TDPO method for determining the equivalent surface-current density on the reflector. Finally, in this work the scattered signals at the specular reflection point, at the edges, and at the corners can be clearly distinguished.

Abstract:
We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.

In this work we consider a spring with one end is fixed and the other is connected
to a block of mass M located on a horizontal rough table. The other
side of the block is connected to a massless rope that passes over a frictionless
pulley at the end of the table and a second block of mass m is hanged at the
rope’s other end. For this system, we analyze and discuss its dynamics of motion
as function of time when the second block is released. In particular, the
displacement of the system at the end of each half-cycle of motion, the total
distance, and the work done against friction are derived. An interesting result
is obtained for the case when the table is frictionless. It is found that there is
still a work done by friction whose magnitude is exactly the same as the
stored energy in the spring.

Abstract:
This review on dark energy is intended for a wider audience, beginners as well as experts. It contains important notes on various aspects of dark energy and its alternatives. The section on Newtonian cosmology followed by heuristic arguments to capture the pressure effects allows us to discuss the basic features of physics of cosmic acceleration without actually resorting to the framework of general theory of relativity. The brief discussion on observational aspects of dark energy is followed by a detailed exposition of underlying features of scalar field dynamic relevant to cosmology. The review includes pedagogical presentation of generic features of models of dark energy and its possible alternatives.

Abstract:
We present a brief review of various approaches to late time acceleration of universe. The cosmological relevance of scaling solutions is emphasized in case of scalar field models of dark energy. The underlying features of a variety of scalar field models is highlighted. Various alternatives to dark energy are discussed including the string curvature corrections to Einstein-Hilbert action, higher dimensional effects, non-locally corrected gravity and $f(R)$ theories of gravity. The recent developments related to $f(R)$ models with disappearing cosmological constant are reviewed.

Abstract:
We study the evolution of universe with a single scalar field of constant potential minimally coupled to gravity in the brane world cosmology.We find an exact inflationary solution which is not in slow roll.We discuss the limiting cases of the solution.We show that at late times the solution is asymptotic to the de Sitter solution independently of the brane tension. For $t\to 0$ the solution leads to singularity but the nature of the approach to singularity depends upon the brane tension.

Abstract:
In this paper we investigate the general features of "Oscillatory Inflation". In adiabatic approximation, we derive a general formula for the number of e-foldings $\tilde{N}$ which reduces to the standard expression in case of the slow role approximation and leads to the Damour-Mukhanov type expression for the slowly varying adiabatic index. We apply our result to the logarithmic potential and arrive at a simple and elegant formula for the number of e-foldings. We evolve the field equations numerically and observe a remarkable agreement with the analytical result.

Abstract:
In this presentation prepared for a general audience, we briefly mention the shortcomings of standard model of universe. We then focus on the late time inconsistency of the model dubbed age crisis whose resolution requires the presence of a repulsive effect that could be sourced either by dark energy or by a large scale modification of gravity. By and large, our description is based upon Newtonian cosmology which is simple and elegant despite of its limitations. On heuristic grounds, we explain how a tiny mass of graviton could account for late time cosmic acceleration. We also include a brief discussion on the underlying physics of Type Ia supernovae explosion and the direct confirmation of late time acceleration of Universe by the related observations.