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.

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.

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.

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.

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

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.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Molecular theory for the effects of specific solute-solvent interaction on the diffusion of a solute particle in a molecular liquid

An understanding of the effect of specific solute-solvent interactions on the diffusion of a solute probe is a long standing problem of physical chemistry. In this paper a microscopic treatment of this effect is presented. The theory takes into account the modification of the solvent structure around the solute due to this specific interaction between them. It is found that for strong, attractive interaction, there is an enhanced coupling between the solute and the solvent dynamic modes (in particular, the density mode), which leads to a significant increase in the friction on the solute. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of the attractive interaction. An interesting observation is that specific solute-solvent interaction can induce a crossover from a sliplike to a sticklike diffusion. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. On the other hand, for repulsive interaction, the diffusion coefficient of the solute increases. These results are in qualitative agreement with recent experimental observations.

An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.

New Look at Kirchhoff's Theory of Plates

KIRCHHOFF’S theory [1] and the first-order shear deformation theory (FSDT) [2] of plates in bending are simple theories and continuously used to obtain design information. Within the classical small deformation theory of elasticity, the problem consists of determining three displacements, u, v, and w, that satisfy three equilibrium equations in the interior of the plate and three specified surface conditions. FSDT is a sixth-order theory with a provision to satisfy three edge conditions and maintains, unlike in Kirchhoff’s theory, independent linear thicknesswise distribution of tangential displacement even if the lateral deflection, w, is zero along a supported edge. However, each of the in-plane distributions of the transverse shear stresses that are of a lower order is expressed as a sum of higher-order displacement terms. Kirchhoff’s assumption of zero transverse shear strains is, however, not a limitation of the theory as a first approximation to the exact 3-D solution.

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.

Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

On the shear deformation theory for dynamic analysis of beams

Timoshenko's shear deformation theory is widely used for the dynamical analysis of shear-flexible beams. This paper presents a comparative study of the shear deformation theory with a higher order model, of which Timoshenko's shear deformation model is a special case. Results indicate that while Timoshenko's shear deformation theory gives reasonably accurate information regarding the set of bending natural frequencies, there are considerable discrepancies in the information it gives regarding the mode shapes and dynamic response, and so there is a need to consider higher order models for the dynamical analysis of flexure of beams.