The Tetrablock as a Spectral Set

The tetrablock, roughly speaking, is the set of all linear fractional maps that map the open unit disc to itself. A formal definition of this inhomogeneous domain is given below. This paper considers triples of commuting bounded operators (A,B,P) that have the tetrablock as a spectral set. Such a triple is named a tetrablock contraction. The motivation comes from the success of model theory in another inhomogeneous domain, namely, the symmetrized bidisc F. A pair of commuting bounded operators (S,P) with Gamma as a spectral set is called a Gamma-contraction, and always has a dilation. The two domains are related intricately as the Lemma 3.2 below shows. Given a triple (A, B, P) as above, we associate with it a pair (F-1, F-2), called its fundamental operators. We show that (A,B,P) dilates if the fundamental operators F-1 and F-2 satisfy certain commutativity conditions. Moreover, the dilation space is no bigger than the minimal isometric dilation space of the contraction P. Whether these commutativity conditions are necessary, too, is not known. what we have shown is that if there is a tetrablock isometric dilation on the minimal isometric dilation space of P. then those commutativity conditions necessarily get imposed on the fundamental operators. En route, we decipher the structure of a tetrablock unitary (this is the candidate as the dilation triple) and a tertrablock isometry (the restriction of a tetrablock unitary to a joint invariant sub-space). We derive new results about r-contractions and apply them to tetrablock contractions. The methods applied are motivated by 11]. Although the calculations are lengthy and more complicated, they beautifully reveal that the dilation depends on the mutual relationship of the two fundamental operators, so that certain conditions need to be satisfied. The question of whether all tetrablock contractions dilate or not is unresolved.

Wave propagation analysis in adhesively bonded composite joints using the wavelet spectral finite element method

A wavelet spectral finite element (WSFE) model is developed for studying transient dynamics and wave propagation in adhesively bonded composite joints. The adherands are formulated as shear deformable beams using the first order shear deformation theory (FSDT) to obtain accurate results for high frequency wave propagation. Equations of motion governing wave motion in the bonded beams are derived using Hamilton's principle. The adhesive layer is modeled as a line of continuously distributed tension/compression and shear springs. Daubechies compactly supported wavelet scaling functions are used to transform the governing partial differential equations from time domain to frequency domain. The dynamic stiffness matrix is derived under the spectral finite element framework relating the nodal forces and displacements in the transformed frequency domain. Time domain results for wave propagation in a lap joint are validated with conventional finite element simulations using Abaqus. Frequency domain spectrum and dispersion relation results are presented and discussed. The developed WSFE model yields efficient and accurate analysis of wave propagation in adhesively-bonded composite joints. (C) 2014 Elsevier Ltd. All rights reserved.

Estimates of site response based on spectral ratio between horizontal and vertical components of ambient vibrations in the source zone of 2001 Bhuj earthquake

We investigated the site response characteristics of Kachchh rift basin over the meizoseismal area of the 2001, Mw 7.6, Bhuj (NW India) earthquake using the spectral ratio of the horizontal and vertical components of ambient vibrations. Using the available knowledge on the regional geology of Kachchh and well documented ground responses from the earthquake, we evaluated the H/V curves pattern across sediment filled valleys and uplifted areas generally characterized by weathered sandstones. Although our HIV curves showed a largely fuzzy nature, we found that the hierarchical clustering method was useful for comparing large numbers of response curves and identifying the areas with similar responses. Broad and plateau shaped peaks of a cluster of curves within the valley region suggests the possibility of basin effects within valley. Fundamental resonance frequencies (f(0)) are found in the narrow range of 0.1-2.3 Hz and their spatial distribution demarcated the uplifted regions from the valleys. In contrary, low HIV peak amplitudes (A(0) = 2-4) were observed on the uplifted areas and varying values (2-9) were found within valleys. Compared to the amplification factors, the liquefaction indices (kg) were able to effectively indicate the areas which experienced severe liquefaction. The amplification ranges obtained in the current study were found to be comparable to those obtained from earthquake data for a limited number of seismic stations located on uplifted areas; however the values on the valley region may not reflect their true amplification potential due to basin effects. Our study highlights the practical usefulness as well as limitations of the HIV method to study complex geological settings as Kachchh. (C) 2014 Elsevier Ltd. All rights reserved.

CH-RES-TOCSY: Enantiomers spectral resolution and measurement of heteronuclear residual dipolar couplings

A new 2D NMR technique cited as CH-RES-TOCSY, for complete unraveling the spectra of enantiomers and for the measurement of structurally important C-HRDC sis reported. The spectral overlap and complexity of peaks were reduced by the blend of selective excitation and homo-decoupling. Differential values of C-H RDCs of enantiomers (R and S) are exploited to separate the enantiomeric peaks. The complete unraveling of the spectra of both the enantiomers is achieved by incorporating a TOCSY mixing blockprior to signal acquisition. The additional application of the method is demonstrated for the assignment of symmetric isomers. (C) 2015 Elsevier B.V. All rights reserved.

A spectral element for wave propagation in honeycomb sandwich construction considering core flexibility

Spectral elements are found to be extremely resourceful to study the wave propagation characteristics of structures at high frequencies. Most of the aerospace structures use honeycomb sandwich constructions. The existing spectral elements use single layer theories for a sandwich construction wherein the two face sheets vibrate together and this model is sufficient for low frequency excitations. At high frequencies, the two face sheets vibrate independently. The Extended Higher order SAndwich Plate theory (EHSaPT) is suitable for representing the independent motion of the face sheets. A 1D spectral element based on EHSaPT is developed in this work. The wave number and the wave speed characteristics are obtained using the developed spectral element. It is shown that the developed spectral element is capable of representing independent wave motions of the face sheets. The propagation speeds of a high frequency modulated pulse in the face sheets and the core of a honeycomb sandwich are demonstrated. Responses of a typical honeycomb sandwich beam to high frequency shock loads are obtained using the developed spectral element and the response match very well with the finite element results. It is shown that the developed spectral element is able to represent the flexibility of the core resulting into independent wave motions in the face sheets, for which a finite element method needs huge degrees of freedom. (C) 2015 Elsevier Ltd. All rights reserved.

Spectral Zero-Crossings: Localization Properties and Applications

We present an analysis of the rate of sign changes in the discrete Fourier spectrum of a sequence. The sign changes of either the real or imaginary parts of the spectrum are considered, and the rate of sign changes is termed as the spectral zero-crossing rate (SZCR). We show that SZCR carries information pertaining to the locations of transients within the temporal observation window. We show duality with temporal zero-crossing rate analysis by expressing the spectrum of a signal as a sum of sinusoids with random phases. This extension leads to spectral-domain iterative filtering approaches to stabilize the spectral zero-crossing rate and to improve upon the location estimates. The localization properties are compared with group-delay-based localization metrics in a stylized signal setting well-known in speech processing literature. We show applications to epoch estimation in voiced speech signals using the SZCR on the integrated linear prediction residue. The performance of the SZCR-based epoch localization technique is competitive with the state-of-the-art epoch estimation techniques that are based on average pitch period.

Multi-transform based spectral element to include first order shear deformation in plates

For obtaining dynamic response of structure to high frequency shock excitation spectral elements have several advantages over conventional methods. At higher frequencies transverse shear and rotary inertia have a predominant role. These are represented by the First order Shear Deformation Theory (FSDT). But not much work is reported on spectral elements with FSDT. This work presents a new spectral element based on the FSDT/Mindlin Plate Theory which is essential for wave propagation analysis of sandwich plates. Multi-transformation method is used to solve the coupled partial differential equations, i.e., Laplace transforms for temporal approximation and wavelet transforms for spatial approximation. The formulation takes into account the axial-flexure and shear coupling. The ability of the element to represent different modes of wave motion is demonstrated. Impact on the derived wave motion characteristics in the absence of the developed spectral element is discussed. The transient response using the formulated element is validated by the results obtained using Finite Element Method (FEM) which needs significant computational effort. Experimental results are provided which confirms the need to having the developed spectral element for the high frequency response of structures. (C) 2015 Elsevier Ltd. All rights reserved.

An enolato-bridged dinuclear Cu(II) complex with a coumarin-assisted precursor: a spectral, magnetic and biological study

A new, phenoxo-bridged Cu-II dinuclear complex Cu-2(L)(2)(DMF)(2)] (1) has been obtained by employing the coumarin-assisted tridentate precursor, H2L, benzoic acid(7-hydroxy-4-methyl-2-oxo-2H-chromen-8-ylmethylene)-hydrazide]. Complex 1 has been systematically characterized by FTIR, UV-Vis, fluorescence and PR spectrometry. The single crystal X-ray diffraction analysis of 1 shows that the geometry around each copper ion is square pyramidal, comprising two enolato oxygen atoms belonging to different ligands (which assemble the dimer bridging the two metal centers), one imine-N and one phenolic-O atoms of the Schiff base and one oxygen atom from the DMF molecule. The temperature dependent magnetic interpretation agrees with the existence of weak ferromagnetic interactions between the bridging dinuclear Cu(II) ions. Both the ligand and complex 1 exhibit anti-mycobacterial activity and considerable efficacy towards M. tuberculosis H37Rv ATCC 27294 and M. tuberculosis H37Ra ATCC 25177 strains. The cytotoxicity study on human adenocarcinoma cell lines (MCF7) suggests that the ligand and complex 1 have potential anticancer properties. Molecular docking of H2L with the enoyl acyl carrier protein reductase of M. tuberculosis H37R(v) (PDB ID: 4U0K) is examined and the best docked pose of H2L shows one hydrogen bond with Thr196 (1.99 angstrom).

Quantitative metabolic profiling of NMR spectral signatures of branched chain amino acids in blood serum

Branched Chain Amino Acids (BCAAs) are related to different aspects of diseases like pathogenesis, diagnosis and even prognosis. While in some diseases, levels of all the BCAAs are perturbed; in some cases, perturbation occurs in one or two while the rest remain unaltered. In case of ischemic heart disease, there is an enhanced level of plasma leucine and isoleucine but valine level remains unaltered. In `Hypervalinemia', valine is elevated in serum and urine, but not leucine and isoleucine. Therefore, identification of these metabolites and profiling of individual BCAA in a quantitative manner in body-fluid like blood plasma/serum have long been in demand. H-1 NMR resonances of the BCAAs overlap with each other which complicates quantification of individual BCAAs. Further, the situation is limited by the overlap of broad resonances of lipoprotein with the resonances of BCAAs. The widely used commercially available kits cannot differentially estimate the BCAAs. Here, we have achieved proper identification and characterization of these BCAAs in serum in a quantitative manner employing a Nuclear Magnetic Resonance-based technique namely T-2-edited Correlation Spectroscopy (COSY). This approach can easily be extended to other body fluids like bile, follicular fluids, saliva, etc.

Spectral Clustering with Jensen-type kernels and their multi-point extensions

Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multipoint' kernels, and study their applications. We study a class of kernels based on Jensen type divergences and show that these can be extended to measure similarity among multiple points. We study tensor flattening methods and develop a multi-point (kernel) spectral clustering (MSC) method. We further emphasize on a special case of the proposed kernels, which is a multi-point extension of the linear (dot-product) kernel and show the existence of cubic time tensor flattening algorithm in this case. Finally, we illustrate the usefulness of our contributions using standard data sets and image segmentation tasks.

Multiple Spectral Peak Tracking for Heart Rate Monitoring from Photoplethysmography Signal During Intensive Physical Exercise

We propose a multiple initialization based spectral peak tracking (MISPT) technique for heart rate monitoring from photoplethysmography (PPG) signal. MISPT is applied on the PPG signal after removing the motion artifact using an adaptive noise cancellation filter. MISPT yields several estimates of the heart rate trajectory from the spectrogram of the denoised PPG signal which are finally combined using a novel measure called trajectory strength. Multiple initializations help in correcting erroneous heart rate trajectories unlike the typical SPT which uses only single initialization. Experiments on the PPG data from 12 subjects recorded during intensive physical exercise show that the MISPT based heart rate monitoring indeed yields a better heart rate estimate compared to the SPT with single initialization. On the 12 datasets MISPT results in an average absolute error of 1.11 BPM which is lower than 1.28 BPM obtained by the state-of-the-art online heart rate monitoring algorithm.

Spectral characterizations and photophysical properties of one-step synthesized blue fluorescent 4 `-aryl substituted 2,2 `:6 `,2 `'-terpyridine for OLEDs application

We have synthesized a series of 4'-aryl substituted 2,2':6',2 `'-terpyridine (terpy) derivatives, namely 4'-(4-methylphenyl)-2,2':6',2 `'-terpyridine (C-1), 4'-(2-furyl)-2,2':6'2 `'-terpyridine (C-2), and 4'-(3,4,5-trimethoxyphenyl)-2,2':6',2 `'-terpyridine (C-3). The synthesized terpy compounds were characterized by elemental analyses, FTIR, NMR (H-1 and C-13), and ESI-Mass spectrometry. Photophysical, electrochemical and thermal properties of terpy compounds were systematically studied. Maximum excitation band was observed between 240 and 330 nm using UV-visible spectra, and maximum emission peaks from PL spectra were observed at 385, 405 and 440 nm for C-1, C-2 and C-3 respectively. Fluorescence lifetime (tau) of the fluorophores was found to be 035 and 1.55 ns at the excitation wavelength of 406 nm for C-1 and C-2 respectively, and tau value for C-3 was found to be 0.29 ns at the excitation wavelength of 468 nm. We noticed that the calculated values of HOMO energy levels were increased from 5.96 (C-1) to 6.08 (C-3) eV, which confirms that C-3 derivative is more electrons donating in nature. The calculated electrochemical band gaps were 2.95, 2.82 and 3.02 eV for C-1, C-2 and C-3 respectively. These blue fluorescent emitter derivatives can be used as an electron transport and electroluminescent material to design the blue fluorescent organic light emitting diode (OLED) applications. (C) 2015 Elsevier B.V: All rights reserved.

Spectral intensity distribution of trapped

To calculate static response properties of a many-body system, local density approximation (LDA) can be safely applied. But, to obtain dynamical response functions, the applicability of LDA is limited bacause dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin4 fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behaviour of the SIDF at a particular momentum can be explained by noting the behaviour of the density of states (DoS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.

Spectral solutions to the Korteweg-de-Vries and nonlinear Schrodinger equations

In this paper, we present the solutions of 1-D and 2-D non-linear partial differential equations with initial conditions. We approach the solutions in time domain using two methods. We first solve the equations using Fourier spectral approximation in the spatial domain and secondly we compare the results with the approximation in the spatial domain using orthogonal functions such as Legendre or Chebyshev polynomials as their basis functions. The advantages and the applicability of the two different methods for different types of problems are brought out by considering 1-D and 2-D nonlinear partial differential equations namely the Korteweg-de-Vries and nonlinear Schrodinger equation with different potential function. (C) 2015 Elsevier Ltd. All rights reserved.

Differential binding of ppGpp and pppGpp to E-coli RNA polymerase: photo-labeling and mass spectral studies

(p) ppGpp, a secondary messenger, is induced under stress and shows pleiotropic response. It binds to RNA polymerase and regulates transcription in Escherichia coli. More than 25 years have passed since the first discovery was made on the direct interaction of ppGpp with E. coli RNA polymerase. Several lines of evidence suggest different modes of ppGpp binding to the enzyme. Earlier cross-linking experiments suggested that the beta-subunit of RNA polymerase is the preferred site for ppGpp, whereas recent crystallographic studies pinpoint the interface of beta'/omega-subunits as the site of action. With an aim to validate the binding domain and to follow whether tetra-and pentaphosphate guanosines have different location on RNA polymerase, this work was initiated. RNA polymerase was photo-labeled with 8-azido-ppGpp/8-azido-pppGpp, and the product was digested with trypsin and subjected to mass spectrometry analysis. We observed three new peptides in the trypsin digest of the RNA polymerase labeled with 8-azido-ppGpp, of which two peptides correspond to the same pocket on beta'-subunit as predicted by X-ray structural analysis, whereas the third peptide was mapped on the beta-subunit. In the case of 8-azido-pppGpp-labeled RNA polymerase, we have found only one cross-linked peptide from the beta'-subunit. However, we were unable to identify any binding site of pppGpp on the beta-subunit. Interestingly, we observed that pppGpp at high concentration competes out ppGpp bound to RNA polymerase more efficiently, whereas ppGpp cannot titrate out pppGpp. The competition between tetraphosphate guanosine and pentaphosphate guanosine for E. coli RNA polymerase was followed by gel-based assay as well as by a new method known as DRaCALA assay.