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Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

Mixed Ligand Complexes of Ni(II) & Cu(II) with Histidine & Iminodiacetic Acid as Primary Ligands & Glycine, ɑ-Alanine, β-Alanine, Leucine & Isoleucine as Secondary Ligands

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Towards Semantic Fast-Forward and Stabilized Egocentric Videos

The emergence of low-cost personal mobiles devices and wearable cameras and the increasing storage capacity of video-sharing websites have pushed forward a growing interest towards first-person videos. Since most of the recorded videos compose long-running streams with unedited content, they are tedious and unpleasant to watch. The fast-forward state-of-the-art methods are facing challenges of balancing the smoothness of the video and the emphasis in the relevant frames given a speed-up rate. In this work, we present a methodology capable of summarizing and stabilizing egocentric videos by extracting the semantic information from the frames. This paper also describes a dataset collection with several semantically labeled videos and introduces a new smoothness evaluation metric for egocentric videos that is used to test our method.Comment: Accepted for publication and presented in the First International Workshop on Egocentric Perception, Interaction and Computing at European Conference on Computer Vision (EPIC@ECCV) 201

Refractive index of a transparent liquid measured with a concave mirror

This paper describes the spherical concave mirror method for measuring the index of refraction of transparent liquids. We derived the refractive index equation using Snell's law and the small-angle approximation. We also verified the validity of this method using the traditional spherical mirror and thin-lens Gaussian equations.Comment: IOPart, 8 pages, 4 figure

On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust

We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are $\rho_{c}$, the initial central density of the massive body, and $R_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity $\beta$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $\beta$ is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.Comment: Original title changed, numerical range of naked singularity corrected. Plain Tex File. 14 pages. To appear in Physical Review

Prediction of long and short time rheological behavior in soft glassy materials

We present an effective time approach to predict long and short time rheological behavior of soft glassy materials from experiments carried out over practical time scales. Effective time approach takes advantage of relaxation time dependence on aging time that allows time-aging time superposition even when aging occurs over the experimental timescales. Interestingly experiments on variety of soft materials demonstrate that the effective time approach successfully predicts superposition for diverse aging regimes ranging from sub-aging to hyper-aging behaviors. This approach can also be used to predict behavior of any response function in molecular as well as spin glasses.Comment: 13 pages, 4 figure