Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

Popular matchings with variable item copies

We consider the problem of matching people to items, where each person ranks a subset of items in an order of preference, possibly involving ties. There are several notions of optimality about how to best match a person to an item; in particular, popularity is a natural and appealing notion of optimality. A matching M* is popular if there is no matching M such that the number of people who prefer M to M* exceeds the number who prefer M* to M. However, popular matchings do not always provide an answer to the problem of determining an optimal matching since there are simple instances that do not admit popular matchings. This motivates the following extension of the popular matchings problem: Given a graph G = (A U 3, E) where A is the set of people and 2 is the set of items, and a list < c(1),...., c(vertical bar B vertical bar)> denoting upper bounds on the number of copies of each item, does there exist < x(1),...., x(vertical bar B vertical bar)> such that for each i, having x(i) copies of the i-th item, where 1 <= xi <= c(i), enables the resulting graph to admit a popular matching? In this paper we show that the above problem is NP-hard. We show that the problem is NP-hard even when each c(i) is 1 or 2. We show a polynomial time algorithm for a variant of the above problem where the total increase in copies is bounded by an integer k. (C) 2011 Elsevier B.V. All rights reserved.

Cooperative Spectrum Sensing Algorithms For OFDM Systems with Frequency Selective Channels

This paper considers the problem of spectrum sensing in cognitive radio networks when the primary user employs Orthogonal Frequency Division Multiplexing (OFDM). We specifically consider the scenario when the channel between the primary and a secondary user is frequency selective. We develop cooperative sequential detection algorithms based on energy detectors. We modify the detectors to mitigate the effects of some common model uncertainties such as timing and frequency offset, IQ-imbalance and uncertainty in noise and transmit power. The performance of the proposed algorithms are studied via simulations. We show that the performance of the energy detector is not affected by the frequency selective channel. We also provide a theoretical analysis for some of our algorithms.

Variable Elimination in Linear Constraints

Gauss and Fourier have together provided us with the essential techniques for symbolic computation with linear arithmetic constraints over the reals and the rationals. These variable elimination techniques for linear constraints have particular significance in the context of constraint logic programming languages that have been developed in recent years. Variable elimination in linear equations (Guassian Elimination) is a fundamental technique in computational linear algebra and is therefore quite familiar to most of us. Elimination in linear inequalities (Fourier Elimination), on the other hand, is intimately related to polyhedral theory and aspects of linear programming that are not quite as familiar. In addition, the high complexity of elimination in inequalities has forces the consideration of intricate specializations of Fourier's original method. The intent of this survey article is to acquaint the reader with these connections and developments. The latter part of the article dwells on the thesis that variable elimination in linear constraints over the reals extends quite naturally to constraints in certain discrete domains.

Identification of Local Conformational Similarity in Structurally Variable Regions of Homologous Proteins Using Protein Blocks

Structure comparison tools can be used to align related protein structures to identify structurally conserved and variable regions and to infer functional and evolutionary relationships. While the conserved regions often superimpose well, the variable regions appear non superimposable. Differences in homologous protein structures are thought to be due to evolutionary plasticity to accommodate diverged sequences during evolution. One of the kinds of differences between 3-D structures of homologous proteins is rigid body displacement. A glaring example is not well superimposed equivalent regions of homologous proteins corresponding to a-helical conformation with different spatial orientations. In a rigid body superimposition, these regions would appear variable although they may contain local similarity. Also, due to high spatial deviation in the variable region, one-to-one correspondence at the residue level cannot be determined accurately. Another kind of difference is conformational variability and the most common example is topologically equivalent loops of two homologues but with different conformations. In the current study, we present a refined view of the ``structurally variable'' regions which may contain local similarity obscured in global alignment of homologous protein structures. As structural alphabet is able to describe local structures of proteins precisely through Protein Blocks approach, conformational similarity has been identified in a substantial number of `variable' regions in a large data set of protein structural alignments; optimal residue-residue equivalences could be achieved on the basis of Protein Blocks which led to improved local alignments. Also, through an example, we have demonstrated how the additional information on local backbone structures through protein blocks can aid in comparative modeling of a loop region. In addition, understanding on sequence-structure relationships can be enhanced through our approach. This has been illustrated through examples where the equivalent regions in homologous protein structures share sequence similarity to varied extent but do not preserve local structure.

Unsteady nonsimilar two-dimensional and axisymmetric water boundary layers with variable viscosity and prandtl number

The influence of temperature-dependent viscosity and Prandtl number on the unsteady laminar nonsimilar forced convection flow over two-dimensional and axisymmetric bodies has been examined where the unsteadiness and (or) nonsimilarity are (is) due to the free stream velocity, mass transfer, and transverse curvature. The partial differential equations governing the flow which involve three independent variables have been solved numerically using an implicit finite-difference scheme along with a quasilinearization technique. It is found that both the skin friction and heat transfer strongly respond to the unsteady free stream velocity distributions. The unsteadiness and injection cause the location of zero skin friction to move upstream. However, the effect of variable viscosity and Prandtl number is to move it downstream. The heat transfer is found to depend strongly on viscous dissipation, but the skin friction is little affected by it. In general, the results pertaining to variable fluid properties differ significantly, from those of constant fluid properties.

Variable density approach for rotating shallow shell of variable thickness

A new approach based on variable density in conjunction with shallow shell theory is proposed to analyse rotating shallow shell of variable thickness. Coupled non-linear ordinary differential equations governing shallows shells of variable thickness are first derived before applying the variable density approach. Results obtained from the new approach compare well with FEM calculation for a wide range of profiles considered in this paper.

Structural and electrical properties of radio frequency magnetron sputtered tantalum oxide films: Influence of post-deposition annealing

The as-deposited and annealed radio frequency reactive magnetron sputtered tantalum oxide (Ta2O5) films were characterized by studying the chemical binding configuration, structural and electrical properties. X-ray photoelectron spectroscopy and X-ray diffraction analysis of the films elucidate that the film annealed at 673 K was stoichiometric with orthorhombic beta-phase Ta2O5. The dielectric constant values of the tantalum oxide capacitors with the sandwich structure of Al/Ta2O5/Si were in the range from 14 to 26 depending on the post-deposition annealing temperature. The leakage current density was < 20 nA cm(-2) at the gate bias voltage of 0.04 MV/cm for the annealed films. The electrical conduction mechanism observed in the films was Poole-Frenkel. (C) 2010 Elsevier Ltd. All rights reserved.

Spectral Sensing of Adaptive Frequency Hopping Signal for Cognitive Radio

The issue of dynamic spectrum scene analysis in any cognitive radio network becomes extremely complex when low probability of intercept, spread spectrum systems are present in environment. The detection and estimation become more complex if frequency hopping spread spectrum is adaptive in nature. In this paper, we propose two phase approach for detection and estimation of frequency hoping signals. Polyphase filter bank has been proposed as the architecture of choice for detection phase to efficiently detect the presence of frequency hopping signal. Based on the modeling of frequency hopping signal it can be shown that parametric methods of line spectral analysis are well suited for estimation of frequency hopping signals if the issues of order estimation and time localization are resolved. An algorithm using line spectra parameter estimation and wavelet based transient detection has been proposed which resolves above issues in computationally efficient manner suitable for implementation in cognitive radio. The simulations show promising results proving that adaptive frequency hopping signals can be detected and demodulated in a non cooperative context, even at a very low signal to noise ratio in real time.

Experimental validation of the 1-D acoustical model for conical concentric tube resonators with moving medium

Variable cross-sectional area ducts are often used for attenuation at lower frequencies (of the order of firing frequency), whereas concentric tube resonators provide attenuation at relatively higher frequencies. In this paper, analysis of one dimensional control volume approach of conical concentric tube resonators is validated experimentally. The effects of mean flow and taper are investigated. The experimental setup is specially designed to measure the pressure transfer function in the form of Level Difference or Noise Reduction across the test muffler. It is shown that there is a reasonably good agreement between the predicted values of the Noise Reduction and the measured ones for incompressible mean flow as well as stationary medium. (C) 2011 Institute of Noise Control Engineering.

Variable Sparsity Kernel Learning

This paper(1) presents novel algorithms and applications for a particular class of mixed-norm regularization based Multiple Kernel Learning (MKL) formulations. The formulations assume that the given kernels are grouped and employ l(1) norm regularization for promoting sparsity within RKHS norms of each group and l(s), s >= 2 norm regularization for promoting non-sparse combinations across groups. Various sparsity levels in combining the kernels can be achieved by varying the grouping of kernels-hence we name the formulations as Variable Sparsity Kernel Learning (VSKL) formulations. While previous attempts have a non-convex formulation, here we present a convex formulation which admits efficient Mirror-Descent (MD) based solving techniques. The proposed MD based algorithm optimizes over product of simplices and has a computational complexity of O (m(2)n(tot) log n(max)/epsilon(2)) where m is no. training data points, n(max), n(tot) are the maximum no. kernels in any group, total no. kernels respectively and epsilon is the error in approximating the objective. A detailed proof of convergence of the algorithm is also presented. Experimental results show that the VSKL formulations are well-suited for multi-modal learning tasks like object categorization. Results also show that the MD based algorithm outperforms state-of-the-art MKL solvers in terms of computational efficiency.

Electron transfer reaction in the marcus inverted region: role of high frequency vibrational modes

A theoretical study of the dynamics of photo-electron transfer reactions in the Marcus inverted regime is presented. This study is motivated partly by the recent proposal of Barbara et al. (J. Phys. Chem. 96, 3728, 1991) that a minimal model of an electron transfer reaction should consist of a polar solvent mode (X), a low frequency vibrational mode (Q) and one high frequency mode (q). Interplay between these modes may be responsible for the crossover observed in the dynamics from a solvent controlled to a vibrational controlled electron transfer. The following results have been obtained. (i) In the case of slowly relaxing solvents, the proximity of the point of excitation to an effective sink on the excited surface is critical in determining the decay of the reactant population. This is because the Franck-Condon overlap between the reactant ground and the product excited states decreases rapidly with increase in the quantum number of the product vibrational state. (ii) Non-exponential solvation dynamics has an important effect in determining the rates of electron transfer. Especially, a biphasic solvation and a large coupling between the reactant and the product states both may be needed to explain the experimental results. ©1996 American Institute of Physics

Low-frequency variability and the galactic distribution of electron-density fluctuation

A sample of 96 compact flat-spectrum extragalactic sources, spread evenly over all galactic latitudes, has been studied at 327 MHz for variability over a time interval of about 15 yr. The variability shows a dependence on galactic latitude being less both at low and high latitudes and peaking around absolute value of b approximately 15-degrees. The latitude dependence is surprisingly similar in both the galactic centre and anticentre directions. Assuming various single and multi-component distributions for the ionized, irregular interstellar plasma, we have tried to generate the observed dependence using a semi-qualitative treatment of refractive interstellar scintillations. We find that it is difficult to fit our data with any single or double component cylindrical distribution. Our data suggests that the observed variability could be influenced by the spiral structure of our Galaxy.

Multi frequency interrogation of polypyrrole based gas sensors for organic vapors

Polypyrrole exhibits reversible changes in their direct current resistance on exposure to organic volatiles. However, one needs to employ an array of such sensors to discriminate organic volatiles present in a mixture. Hence, polypyrrole based gas sensor is designed for the detection and discrimination of different organic volatiles. Multi frequency impedance measurement technique is used to detect the organic vapors, such as acetone, ethanol and Isopropyl alcohol, in the gas phase, over a frequency range 10 Hz to 2 MHz. The sensor response is monitored by measuring the changes in its capacitance, resistance and the dissipation factor upon exposure to organic volatiles. It is observed that the capacitive property of the sensor is more sensitive to these volatiles than its resistive property. Each volatile responds to the sensor in terms of dissipation factor at specific frequency and found that the peak magnitude has a linear relationship with their concentrations.

Spatially dependent zero-frequency response functions and correlation functions in the Kondo model

We present the details of a formalism for calculating spatially varying zero-frequency response functions and equal-time correlation functions in models of magnetic and mixed-valence impurities of metals. The method is based on a combination of perturbative, thermodynamic scaling theory [H. R. Krishna-murthy and C. Jayaprakash, Phys. Rev. B 30, 2806 (1984)] and a nonperturbative technique such as the Wilson renormalization group. We illustrate the formalism for the spin-1/2 Kondo problem and present results for the conduction-spin-density�impurity-spin correlation function and conduction-electron charge density near the impurity. We also discuss qualitative features that emerge from our calculations and discuss how they can be carried over to the case of realistic models for transition-metal impurities.