Spectral Invariance of SG Pseudo-Differential Operators on L-P(R-n)

We prove the spectral invariance of SG pseudo-differential operators on L-P(R-n), 1 < p < infinity, by using the equivalence of ellipticity and Fredholmness of SG pseudo-differential operators on L-p(R-n), 1 < p < infinity. A key ingredient in the proof is the spectral invariance of SC pseudo-differential operators on L-2(R-n).

Constrained Linear Spectral Unmixing Technique for Regional Land Cover Mapping Using MODIS Data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up-to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat-TM/ETM+, IRS-ICID LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (similar to 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 in), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end-members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications. Index Terms-Remote sensing, digital

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

1H and 13C NMR spectra of some unsymmetric N,N-dipyridyl ureas: spectral assignments and molecular conformation

Abstract: The H-1 NMR spectra of N-(2-pyridyl), N'-(3-pyridyl)ureas and N-(2-pyridyl), N'-(4-pyridyl)ureas in CDCl3 and (CD3)(2)CO have been assigned with the aid of COSY and NOE experiments and chemical shift and coupling constant correlations, The C-13 NMR spectra in CDCl3 were analysed utilizing the HETCOR and proton coupled spectra, The H-1 NMR spectra, NOE effects and MINDO/3 calculations have been utilized to show that the molecular conformation of these compounds has the 2-pyridyl ring coplanar with the urea plane with the N-H group hydrogen bonded to the nitrogen of the 2-pyridyl group on the other urea nitrogen while the 3/4-pyridyl group rotates rapidly about the N-C-3/N-C-4 bond.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

A Spectral Iteration Technique For The Analysis Of Yagi-Uda Arrays

The paper present a spectral iteration technique for the analysis of linear arrays of unequally spaced dipoles of unequal lengths. As an example, the Yagi-Uda array is considered for illustration. Analysis is carried out in both the spatial as well as the spectral domains, the two being linked by the Fourier transform. The fast Fourier transform algorithm is employed to obtain an iterative solution to the electric field integral equation and the need for matrix inversion is circumvented. This technique also provides a convenient means for testing the satisfaction of the boundary conditions on the array elements. Numerical comparison of the input impedance and radiation pattern have been made with results deduced elsewhere by other methods. The computational efficency of this technique has been found to be significant for large arrays.

Spectral Sensing for Cognitive Radio: Estimation of Adaptive Frequency Hopping Signal

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.

Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Conformation of some N,N'-arylalkyl thioureas by 1H-NMR and infrared spectral analysis

Several N,N-²-arylalkyl thioureas were examined with 1H-NMR and i.r. spectra in order to study the conformation of the -NHCSNH- group. The influence of temperature and substituents on the chemical shift of the N---H protons has been investigated. Formation of a strong intramolecular hydrogen bond stabilizes the trans-cis conformation for most systems, while for the others the prevalence of different rotational isomers can be postulated. The influence of the steric effect on hydrogen bonding and molecular conformation is discussed.

Spectral analysis of finite section normal integral operators

Some continuity and differentiability properties of the eigenvalues and eigenfunctions of finite section normal integral operators are proved. These are the extension of corresponding results for symmetric operators ([4.], 554–566; K. B. Athreya and R. Vittal Rao, to appear; [10.], 463–471.

1H and 13C NMR spectral studies of C-2 substituted isomeric exo- and endo-5-methyl-bicyclo[3.2.1]octane-6,8-diones

A detailed analysis of the 1H and 13C NMR spectra of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones is presented. The chemical shift of the C-5 angular methyl, the C-2 alkyl/olefinic (C-10)/C-2 methine protons, the aromatic proton shieldings and the characteristic AMX and ABX spectral pattern of the ketomethylene and bridgehead protons were found to be sensitive to the phenyl ring orientation (anisotropy). These distinctive features could be used for configurational distinction for this class of compounds. With increasing ortho-methoxy substitution on the phenyl ring, considerable deshilelding of the bridgehead proton was observed (ca. 0.6 ppm). Absence of the C-2 alkyl group in the desalkyl isomers resulted in substantial changes in the chemical shifts of different protons. A study of the NMR spectra of the corresponding bicyclic compounds with C-2 methoxy/hydroxy substitution instead of the aryl group revealed that the anisotropy of the phenyl ring and the electronegative oxygen substituents have opposite effects. The 13C NMR spectral assignment of each carbon resonance of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones and the corresponding C-2 methoxy/hydroxy/chloro and methyl bicyclic compounds are reported. Additional ortho-methoxy substitution on the phenyl ring was found to produce considerable high field shifts of the C-10 and C-1 carbon resonances. A high-field shift was observed for the C-6 and C-8 carbonyl carbons, presumably due to 1,3-dicarbonyl interactions. The chemical shifts of C-1 aromatic, C-10 alkyl and C-2 carbons, which are sensitive to exo/endo isomerism, could be utilized in differentiating a pair of isomers.

The scale-invariance of spatial patterning in a developing system

Regulating systems, that is, those which exhibit scale-invariant patterns in the adult, are supposed, to do so on account of interactions between cells during development. The nature of these interactions has to be such that the system of positional information (ldquomaprdquo) in the embryo also regulates. To our knowledge, this supposition regarding a regulating map has not been subjected to a direct test in any embryonic system. Here we do so by means of a simple and novel criterion and use it to examine tip regeneration in the mulicellular stage (slug) ofDictyostelium discoideum. When anterior, tip-containing fragments of slugs are amputated, a new tip spontaneously regenerates at the cut surface of the (remaining) posterior fragment. The time needed for regeneration to occur depends on the relative size of the amputated fragment but is independent of the total size of the slug. We conclude from this finding that there is at least one system underlying positional information in the slug which regulates.

Short-window spectral analysis using AMVAR and multitaper methods: a comparison

We compare two popular methods for estimating the power spectrum from short data windows, namely the adaptive multivariate autoregressive (AMVAR) method and the multitaper method. By analyzing a simulated signal (embedded in a background Ornstein-Uhlenbeck noise process) we demonstrate that the AMVAR method performs better at detecting short bursts of oscillations compared to the multitaper method. However, both methods are immune to jitter in the temporal location of the signal. We also show that coherence can still be detected in noisy bivariate time series data by the AMVAR method even if the individual power spectra fail to show any peaks. Finally, using data from two monkeys performing a visuomotor pattern discrimination task, we demonstrate that the AMVAR method is better able to determine the termination of the beta oscillations when compared to the multitaper method.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.