On Minimum Average Stretch Spanning Trees in Polygonal 2-trees

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on $n$ vertices, we present an algorithm to compute a minimum average stretch spanning tree in $O(n \log n)$ time. This algorithm also finds a minimum fundamental cycle basis in polygonal 2-trees.Comment: 17 pages, 12 figure

Distribution of the delay time and the dwell time for wave reflection from a long random potential

We re-examine and correct an earlier derivation of the distribution of the Wigner phase delay time for wave reflection from a long one-dimensional disordered conductor treated in the continuum limit. We then numerically compare the distributions of the Wigner phase delay time and the dwell time, the latter being obtained by the use of an infinitesimal imaginary potential as a clock, and investigate the effects of strong disorder and a periodic (discrete) lattice background. We find that the two distributions coincide even for strong disorder, but only for energies well away from the band-edges.Comment: Final version with minor corrections in text, 4 pages, 2 PS figure

Diffusion at constant speed in a model phase space

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the equations for the probability density function using the ``formulae of differentiation'' of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media in that it results in a true diffusion at constant speed in the limit of large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur

Novel magnetic properties of graphene: Presence of both ferromagnetic and antiferromagnetic features and other aspects

Investigations of the magnetic properties of graphenes prepared by different methods reveal that dominant ferromagnetic interactions coexist along with antiferromagnetic interactions in all the samples. Thus, all the graphene samples exhibit room-temperature magnetic hysteresis. The magnetic properties depend on the number of layers and the sample area, small values of both favoring larger magnetization. Molecular charge-transfer affects the magnetic properties of graphene, interaction with a donor molecule such as tetrathiafulvalene having greater effect than an electron-withdrawing molecule such as tetracyanoethyleneComment: 16 pges, 5 figure

Complete controllability of quantum systems

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio

Design and Analysis of Multiplexer based Approximate Adder for Low Power Applications

Low power consumption is crucial for error-acceptable multimedia devices, with picture compression approaches leveraging various digital processing architectures and algorithms. Humans can assemble useful information from partially inaccurate outputs in many multimedia applications. As a result, producing exact outputs is not required. The demand for an exact outcome is fading because new innovative systems are forgiving of faults. In the domain where error-tolerance is accepted, approximate computing is a new paradigm that relaxes the requirement for an accurate modeling while offering power, time, and delay benefits. Adders are an essential arithmetic module for regulating power and memory usage in digital systems. The recent implementation and use of approximate adders have been supported by trade-off characteristics such as delay, lower power consumption. This study examines the delay and power consumption of conventional and approximate adders. Also, a simple, fast, and power-efficient multiplexer-based approximate adder is proposed, and its performance outperforms the adders compared with existing adders. The proposed adder can be utilized in error-tolerant and various digital signal processing applications where exact results are not required. The proposed and existing adders are designed using EDA software for the performance calculations. With a delay of 81 pS, the proposed adder circuit reduces power consumption compared to the exact one. The experiment shows that the designed approximate adder can be used to implement circuits for image processing systems because it has a smaller delay and uses less energy

A spherical perfect lens

It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the sub-wavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with $\epsilon(r) \sim 1/r$ and $\mu(r)\sim 1/r$. We concentrate on lens-like solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of $\mu$ and $\epsilon$ respectively.Comment: Revtex4, 9 pages, 2 figures (eps

Sub-wavelength imaging at optical frequencies using canalization regime

Imaging with sub-wavelength resolution using a lens formed by periodic metal-dielectric layered structure is demonstrated. The lens operates in canalization regime as a transmission device and it does not involve negative refraction and amplification of evanescent modes. The thickness of the lens have to be an integer number of half-wavelengths and can be made as large as required for ceratin applications, in contrast to the other sub-wavelength lenses formed by metallic slabs which have to be much smaller than the wavelength. Resolution of $\lambda/20$ at 600 nm wavelength is confirmed by numerical simulation for a 300 nm thick structure formed by a periodic stack of 10 nm layers of glass with $\epsilon=2$ and 5 nm layers of metal-dielectric composite with $\epsilon=-1$. Resolution of $\lambda/60$ is predicted for a structure with same thickness, period and operating frequency, but formed by 7.76 nm layers of silicon with $\epsilon=15$ and 7.24 nm layers of silver with $\epsilon=-14$.Comment: 4 pages, 4 figures, submitted to PR

Vague Cosets

In this paper we study the vague cosets and their properties.These conceptsnbsp are used in the development of some important results and theorems about vague groups and vague normalgroups.Also some of their important properties havenbspbeen investigated