Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Performance of a pipelined ring algorithm for Fast Fourier Transform on transputer arrays

In this paper a pipelined ring algorithm is presented for efficient computation of one and two dimensional Fast Fourier Transform (FFT) on a message passing multiprocessor. The algorithm has been implemented on a transputer based system and experiments reveal that the algorithm is very efficient. A model for analysing the performance of the algorithm is developed from its computation-communication characteristics. Expressions for execution time, speedup and efficiency are obtained and these expressions are validated with experimental results obtained on a four transputer system. The analytical model is then used to estimate the performance of the algorithm for different number of processors, and for different sizes of the input data.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Fourier descriptors for morphological analysis of vectorcardiograms

The use of Fourier shape descriptors for morphological studies of vectorcardio-grams (VCGs) is p resented . The FDs can effectively be used as features for classf-fication of VCGs of different clinical categories . In addition , they provide cli-nically significant qualitative shape information for use by the Cardiologist. The initial result sofanalysisof nwrmal and abnormal VCGs areencouraging.

Influence of Si-C bond density on the properties of a-Si(1-x)C(x) thin films

Amorphous silicon carbide (a-Si(1-x)C(x)) films were deposited on silicon (100) and quartz substrates by pulsed DC reactive magnetron sputtering of silicon in methane (CH(4))-Argon (Ar) atmosphere. The influence of substrate temperature and target power on the composition, carbon bonding configuration, band gap, refractive index and hardness of a-SiC films has been investigated. Increase in substrate temperature results in slightly decreasing the carbon concentration in the films but favors silicon-carbon (Si-C) bonding. Also lower target powers were favorable towards Si-C bonding. X-ray photoelectron spectroscopy (XPS) results agree with the Fourier Transform Infrared (FTIR), UV-vis spectroscopy results. Increase in substrate temperature resulted in increased hardness of the thin films from 13 to 17 GPa and the corresponding bandgap varied from 2.1 to 1.8 eV. (C) 2011 Elsevier B.V. All rights reserved.

Wavelet transform analysis of truncated fringe patterns in 3-D surface profilometry

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe images do not satisfy periodicity. Three specific cases that give raise to non-periodicity of fringe image are simulated and leakage effects caused by each one of them are analyzed with continuous complex Morlet wavelet transform. Same images are analyzed with FFT method to make a comparison of the reconstructed profiles with both methods. Simulation results revealed a significant advantage of wavelet transform profilometry (WTP), that the distortions that arise due to leakage are confined to the locations of discontinuity and do not spread out over the entire projection as in the case of Fourier transform profilometry (FTP).

Fourier transform infrared microspectroscopy identifies protein propionylation in histone deacetylase inhibitor treated glioma cells

Histone deacetylase inhibitors (HDIs) have attracted considerable attention as potential drug molecules in tumour biology. In order to optimise chemotherapy, it is important to understand the mechanisms of regulation of histone deacetylase (HDAC) enzymes and modifications brought by various HDIs. In the present study, we have employed Fourier transform infrared microspectroscopy (FT-IRMS) to evaluate modifications in cellular macromolecules subsequent to treatment with various HDIs. In addition to CH3 (methyl) stretching bands at 2872 and 2960 cm1, which arises due to acetylation, we also found major changes in bands at 2851 and 2922 cm1, which originates from stretching vibrations of CH2 (methylene) groups, in valproic acid treated cells. We further demonstrate that the changes in CH2 stretching are concentration-dependent and also induced by several other HDIs. Recently, HDIs have been shown to induce propionylation besides acetylation [1]. Since propionylation involves CH2 groups, we hypothesized that CH2 vibrational frequency changes seen in HDI treated cells could arise due to propionylation. As verification, pre-treatment of cells with propionyl CoA synthetase inhibitor resulted in loss of CH2 vibrational changes in histones, purified from valproic acid treated cells. This was further proved by western blot using propionyl-lysine specific antibody. Thus we demonstrate for the first time that propionylation could be monitored by studying CH2 stretching using IR spectroscopy and further provide a platform for monitoring HDI induced multiple changes in cells. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A pseudo-time EnKF incorporating shape based reconstruction for diffuse optical tomography

Purpose: The authors aim at developing a pseudo-time, sub-optimal stochastic filtering approach based on a derivative free variant of the ensemble Kalman filter (EnKF) for solving the inverse problem of diffuse optical tomography (DOT) while making use of a shape based reconstruction strategy that enables representing a cross section of an inhomogeneous tumor boundary by a general closed curve. Methods: The optical parameter fields to be recovered are approximated via an expansion based on the circular harmonics (CH) (Fourier basis functions) and the EnKF is used to recover the coefficients in the expansion with both simulated and experimentally obtained photon fluence data on phantoms with inhomogeneous inclusions. The process and measurement equations in the pseudo-dynamic EnKF (PD-EnKF) presently yield a parsimonious representation of the filter variables, which consist of only the Fourier coefficients and the constant scalar parameter value within the inclusion. Using fictitious, low-intensity Wiener noise processes in suitably constructed ``measurement'' equations, the filter variables are treated as pseudo-stochastic processes so that their recovery within a stochastic filtering framework is made possible. Results: In our numerical simulations, we have considered both elliptical inclusions (two inhomogeneities) and those with more complex shapes (such as an annular ring and a dumbbell) in 2-D objects which are cross-sections of a cylinder with background absorption and (reduced) scattering coefficient chosen as mu(b)(a)=0.01mm(-1) and mu('b)(s)=1.0mm(-1), respectively. We also assume mu(a) = 0.02 mm(-1) within the inhomogeneity (for the single inhomogeneity case) and mu(a) = 0.02 and 0.03 mm(-1) (for the two inhomogeneities case). The reconstruction results by the PD-EnKF are shown to be consistently superior to those through a deterministic and explicitly regularized Gauss-Newton algorithm. We have also estimated the unknown mu(a) from experimentally gathered fluence data and verified the reconstruction by matching the experimental data with the computed one. Conclusions: The PD-EnKF, which exhibits little sensitivity against variations in the fictitiously introduced noise processes, is also proven to be accurate and robust in recovering a spatial map of the absorption coefficient from DOT data. With the help of shape based representation of the inhomogeneities and an appropriate scaling of the CH expansion coefficients representing the boundary, we have been able to recover inhomogeneities representative of the shape of malignancies in medical diagnostic imaging. (C) 2012 American Association of Physicists in Medicine. [DOI: 10.1118/1.3679855]

The substrate dependent competitive formation of cyclobutanones and cyclopentanones in an intramolecular rhodium carbenoid CH insertion reaction: enantiospecific total synthesis of silphiperfol-6-ene

The enantiospecific total synthesis of silphiperfol-6-ene has been accomplished starting from the readily available monoterpene (R)-limonene, employing a rhodium carbenoid insertion into the CH bond of a tertiary methyl group. A substrate dependent competitive insertion of the rhodium carbenoid in the gamma- and beta-CH bonds to form cyclopentanone and cyclobutanones, respectively, has been described. (C) 2012 Elsevier Ltd. All rights reserved.

Towards a broadband chirped pulse Fourier transform microwave spectrometer

This article gives a brief review of microwave spectroscopy and the experimental techniques used for obtaining microwave spectrum of molecules and complexes since 1950s. It presents a brief summary of the pulsed nozzle Fourier transform microwave (PNFTMW) spectrometer, fabricated in our laboratory, and discusses some of the important results obtained using the spectrometer. The most significant among the results from this spectrometer is the direct structural determination of weakly bound complexes involving H2O/H2S. These have challenged the conventional wisdom on hydrogen bonding leading us to propose a modern definition for the same through IUPAC. The limitations of the PNFTMW spectrometer and the need for the new chirped pulse Fourier transform microwave spectrometer are discussed as well. Moreover, preliminary results from our laboratory on generating a 1 A mu s chirped pulse of 1 GHz bandwidth are given.

Identification of Early Biomarkers during Acetaminophen-Induced Hepatotoxicity by Fourier Transform Infrared Microspectroscopy

Acetaminophen is a widely prescribed drug used to relieve pain and fever; however, it is a leading cause of drug-induced liver injury and a burden on public healthcare. In this study, hepatotoxicity in mice post oral dosing of acetaminophen was investigated using liver and sera samples with Fourier Transform Infrared microspectroscopy. The infrared spectra of acetaminophen treated livers in BALB/ mice show decrease in glycogen, increase in amounts of cholesteryl esters and DNA respectively. Rescue experiments using L-methionine demonstrate that depletion in glycogen and increase in DNA are abrogated with pre-treatment, but not post-treatment, with L-methionine. This indicates that changes in glycogen and DNA are more sensitive to the rapid depletion of glutathione. Importantly, analysis of sera identified lowering of glycogen and increase in DNA and chlolesteryl esters earlier than increase in alanine aminotransferase, which is routinely used to diagnose liver damage. In addition, these changes are also observed in C57BL/6 and Nos2(-/-) mice. There is no difference in the kinetics of expression of these three molecules in both strains of mice, the extent of damage is similar and corroborated with ALT and histological analysis. Quantification of cytokines in sera showed increase upon APAP treatment. Although the levels of Tnf alpha and Ifn gamma in sera are not significantly affected, Nos2(-/-) mice display lower Il6 but higher Il10 levels during this acute model of hepatotoxicity. Overall, this study reinforces the growing potential of Fourier Transform Infrared microspectroscopy as a fast, highly sensitive and label-free technique for non-invasive diagnosis of liver damage. The combination of Fourier Transform Infrared microspectroscopy and cytokine analysis is a powerful tool to identify multiple biomarkers, understand differential host responses and evaluate therapeutic regimens during liver damage and, possibly, other diseases.

A CMOS Gas Sensor Array Platform With Fourier Transform Based Impedance Spectroscopy

A CMOS gas sensor array platform with digital read-out containing 27 sensor pixels and a reference pixel is presented. A signal conditioning circuit at each pixel includes digitally programmable gain stages for sensor signal amplification followed by a second order continuous time delta sigma modulator for digitization. Each sensor pixel can be functionalized with a distinct sensing material that facilitates transduction based on impedance change. Impedance spectrum (up to 10 KHz) of the sensor is obtained off-chip by computing the fast Fourier transform of sensor and reference pixel outputs. The reference pixel also compensates for the phase shift introduced by the signal processing circuits. The chip also contains a temperature sensor with digital readout for ambient temperature measurement. A sensor pixel is functionalized with polycarbazole conducting polymer for sensing volatile organic gases and measurement results are presented. The chip is fabricated in a 0.35 CMOS technology and requires a single step post processing for functionalization. It consumes 57 mW from a 3.3 V supply.

GFT projection NMR for efficient H-1/C-13 sugar spin system identification in nucleic acids

A newly implemented G-matrix Fourier transform (GFT) (4,3)D HC(C)CH experiment is presented in conjunction with (4,3)D HCCH to efficiently identify H-1/C-13 sugar spin systems in C-13 labeled nucleic acids. This experiment enables rapid collection of highly resolved relay 4D HC(C)CH spectral information, that is, shift correlations of C-13-H-1 groups separated by two carbon bonds. For RNA, (4,3)D HC(C)CH takes advantage of the comparably favorable 1'- and 3'-CH signal dispersion for complete spin system identification including 5'-CH. The (4,3)D HC(C)CH/HCCH based strategy is exemplified for the 30-nucleotide 3'-untranslated region of the pre-mRNA of human U1A protein.

Synthesis, structural analysis and solvatochromic behaviour of 4,6-bis (4-butoxyphenyl)-2-methoxynicotinonitrile mesogen

In this communication, we report the synthesis and characterisation of a new luminescent liquid crystalline material, 4,6-bis (4-butoxyphenyl)-2-methoxynicotinonitrile (3). We have confirmed its structure by Fourier transform infrared and 1H nuclear magnetic resonance spectroscopy, elemental analysis and X-ray single crystal diffraction studies. The newly synthesised compound crystallises in a monoclinic system with the space group C2/c and its cell parameters are found to be a?=?25.181(4) angstrom, b?=?15.651(4)angstrom, c?=?12.703(19) angstrom, V?=?4880.4 (16) angstrom, Z?=?8. The results indicate that the presence of weak CH center dot center dot center dot O and CH center dot center dot center dot N hydrogen bonding as short-range intermolecular interactions are responsible for the formation of its crystal assembly. The measured torsion angle shows the existence of a distorted structure for the molecule wherein 4-butoxyphenylene ring substituent at the fourth position of the central pyridine ring forms a torsion angle chiC(4), C(3), C(10), C(19)] of 40.55 degrees. Its liquid crystalline behaviour was investigated with the aid of polarised optical microscopy and differential scanning calorimetry. The study reveals that the compound displays a broad nematic phase in the range of 78112 degrees C. Further, solution phase optical studies indicate that it is a blue light emitter in different non-polar and polar organic solvents at a concentration of 10-5M.