Abstract:
The
modified Emden-type is being investigated by mathematicians as well as
physicists for about a century. However, there exist no exact explicit solution
of this equation, ẍ + αxẋ + βx^{3} = 0for arbitrary values of α and β. In this work,
the exact analytical explicit solution of modified Emden-type (MEE) equation is
derived for arbitrary values of α and β. The Lagrangian and Hamiltonian of
MEE are also
worked out. The solution is also utilized to find exact explicit analytical
solution of Force-free Duffing oscillator-type equation. And exact explicit
analytical solution of two-dimensional Lotka-Volterra System is
also worked out.

Abstract:
In the Starobinsky inflationary model inflation is driven by quantum corrections to the vacuum Einstein equation. We reduce the Wheeler-DeWitt equation corresponding to the Starobinsky model to a Schroedinger form containing time. The Schroedinger equation is solved with a Gaussian ansatz. Using the prescription for the normalization constant of the wavefunction given in our previous work, we show that the Gaussian ansatz demands Hawking type initial conditions for the wavefunction of the universe. The wormholes induce randomness in initial states suggesting a basis for time-contained description of the Wheeler-DeWitt equation.

Abstract:
We study multidimensional cosmology to obtain the wavefunction of the universe using wormhole dominance proposal. Using a prescription for time we obtain the Schroedinger-Wheeler-DeWitt equation without any reference to WD equation and WKB ansatz for WD wavefunction. It is found that the Hartle-Hawking or wormhole-dominated boundary conditions serve as a seed for inflation as well as for Gaussian type ansatz to Schroedinger-Wheeler-DeWitt equation.

Abstract:
This paper is based on a comparative study between different watermarking techniques such as LSB hiding algorithm, (2, 2) visual cryptography based watermarking for color images [3,4] and Randomized LSB-MSB hiding algorithm [1]. Here, we embed the secret image in a host or original image, by using these bit-wise pixel manipulation algorithms. This is followed by a comparative study of the resultantimages through Peak Signal to Noise Ratio (PSNR) calculation. The property wise variation of differenttypes of secret images that are embedded into the host image plays an important role in this context. The calculation of the Peak Signal to Noise Ratio is done for different color levels (red, green, blue) and also for their equivalent gray level images. From the results, we are trying to predict which technique is more suitable to which type of secret image.

Abstract:
We discuss an inverse approach for atomistic modeling of glassy materials. The focus is on structural modeling and electronic properties of hydrogenated amorphous silicon and glassy GeSe2 alloy. The work is based upon a new approach "experimentally constrained molecular relaxation (ECMR)". Unlike conventional approaches (such as molecular dynamics (MD) and Monte Carlo simulations(MC), where a potential function is specified and the system evolves either deterministically (MD) or stochastically (MC), we develop a novel scheme to model structural configurations using experimental data in association with density functional calculations. We have applied this approach to model hydrogenated amorphous silicon and glassy GeSe2. The electronic and structural properties of these models are compared with experimental data and models obtained from conventional molecular dynamics simulation.

Abstract:
Are geometrical summaries of the CMB and LSS sufficient for estimating cosmological parameters? And how does our choice of a dark energy model impact the current constraints on standard cosmological parameters? We address these questions in the context of the widely used CPL parametrization of a time varying equation of state w in a cosmology allowing spatial curvature. We study examples of different behavior allowed in a CPL parametrization in a phase diagram, and relate these to effects on the observables. We examine parameter constraints in such a cosmology by combining WMAP5, SDSS, SNe, HST data sets by comparing the power spectra. We carefully quantify the differences of these constraints to those obtained by using geometrical summaries for the same data sets. We find that (a) using summary parameters instead of the full data sets give parameter constraints that are similar, but with discernible differences, (b) due to degeneracies, the constraints on the standard parameters broaden significantly for the same data sets. In particular, we find that in the context of CPL dark energy, (i) a Harrison-Zeldovich spectrum cannot be ruled out at $2\sigma$ levels with our current data sets. and (ii) the SNe IA, HST, and WMAP 5 data are not sufficient to constrain spatial curvature; we additionally require the SDSS DR4 data to achieve this.

Abstract:
Let $C$ be an irreducible smooth complex projective curve, and let $E$ be an algebraic vector bundle of rank $r$ on $C$. Associated to $E$, there are vector bundles ${\mathcal F}_n(E)$ of rank $nr$ on $S^n(C)$, where $S^n(C)$ is $ $n$-th symmetric power of $C$. We prove the following: Let $E_1$ and $E_2$ be two semistable vector bundles on $C$, with ${\rm genus}(C)\, \geq\, 2$. If ${\mathcal F}_n(E_1)\,= \, {\mathcal F}_n(E_2)$ for a fixed $n$, then $E_1 \,=\, E_2$.

Abstract:
Cyber-physical systems (CPS) represent a
class of complex engineered systems where functionality and behavior emerge
through the interaction between the computational and physical domains.
Simulation provides design engineers with quick and accurate feedback on the
behaviors generated by their designs. However, as systems become more complex,
simulating their behaviors becomes computation all complex. But, most modern
simulation environments still execute on a single thread, which does not take
advantage of the processing power available on modern multi-core CPUs. This
paper investigates methods to partition and simulate differential
equation-based models of cyber-physical systems using multiple threads on
multi-core CPUs that can share data across threads. We describe model
partitioning methods using fixed step and variable step numerical in-tegration
methods that consider the multi-layer cache structure of these CPUs to avoid
simulation performance degradation due to cache conflicts. We study the
effectiveness of each parallel simu-lation algorithm by calculating the
relative speedup compared to a serial simulation applied to a series of large
electric circuit models. We also develop a series of guidelines for maximizing
performance when developing parallel simulation software intended for use on
multi-core CPUs.

Abstract:
We start from classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schroedinger equation. Without any reference to the Wheeler-DeWitt equation and without invoking the expansion of exponent in WKB wavefunction in powers of Planck mass, we obtain an equation for quantum gravity in Schroedinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler-DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler-DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.