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.

Characteristics of Proportional Weirs

A theorem termed the Geometrical Continuity Theorem is enunciated and proven. This theorem throws light on the aspects of the continuity of the proportional portion with the base weir portion. These two portions constitute the profile of a proportional weir. A weir of this type with circular bottom is designed. The theorem is used to establish the continuity at the junction of the proportional and the base weir portions of this weir. The coordinates of the weir profile are obtained by numerical methods and are furnished in tabular form for ready use by designers. The discharge passing through the weir is a linear function of the head. The verification of the assumed linear discharge-head relation is furnished for one of the three weirs with which experiments were conducted. The coefficient of discharge for this typical weir is found to be a constant with a value of 0.59.

Two Stage Transform Vector Quantization of LSFs for Wideband Speech Coding

We investigate the use of a two stage transform vector quantizer (TSTVQ) for coding of line spectral frequency (LSF) parameters in wideband speech coding. The first stage quantizer of TSTVQ, provides better matching of source distribution and the second stage quantizer provides additional coding gain through using an individual cluster specific decorrelating transform and variance normalization. Further coding gain is shown to be achieved by exploiting the slow time-varying nature of speech spectra and thus using inter-frame cluster continuity (ICC) property in the first stage of TSTVQ method. The proposed method saves 3-4 bits and reduces the computational complexity by 58-66%, compared to the traditional split vector quantizer (SVQ), but at the expense of 1.5-2.5 times of memory.

Automatic Path Planning and Control Design for Autonomous Landing of UAVs using Dynamic Inversion

In this paper a nonlinear control has been designed using the dynamic inversion approach for automatic landing of unmanned aerial vehicles (UAVs), along with associated path planning. This is a difficult problem because of light weight of UAVs and strong coupling between longitudinal and lateral modes. The landing maneuver of the UAV is divided into approach, glideslope and flare. In the approach UAV aligns with the centerline of the runway by heading angle correction. In glideslope and flare the UAV follows straight line and exponential curves respectively in the pitch plane with no lateral deviations. The glideslope and flare path are scheduled as a function of approach distance from runway. The trajectory parameters are calculated such that the sink rate at touchdown remains within specified bounds. It is also ensured that the transition from the glideslope to flare path is smooth by ensuring C-1 continuity at the transition. In the outer loop, the roll rate command is generated by assuring a coordinated turn in the alignment segment and by assuring zero bank angle in the glideslope and flare segments. The pitch rate command is generated from the error in altitude to control the deviations from the landing trajectory. The yaw rate command is generated from the required heading correction. In the inner loop, the aileron, elevator and rudder deflections are computed together to track the required body rate commands. Moreover, it is also ensured that the forward velocity of the UAV at the touch down remains close to a desired value by manipulating the thrust of the vehicle. A nonlinear six-DOF model, which has been developed from extensive wind-tunnel testing, is used both for control design as well as to validate it.

On walls of marginal stability in N=2 string theories

We study the properties of walls of marginal stability for BPS decays in a class of N = 2 theories. These theories arise in N = 2 string compactifications obtained as freely acting orbifolds of N = 4 theories, such theories include the STU model and the FHSV model. The cross sections of these walls for a generic decay in the axion-dilaton plane reduce to lines or circles. From the continuity properties of walls of marginal stability we show that central charges of BPS states do not vanish in the interior of the moduli space. Given a charge vector of a BPS state corresponding to a large black hole in these theories, we show that all walls of marginal stability intersect at the same point in the lower half of the axion-dilaton plane. We isolate a class of decays whose walls of marginal stability always lie in a region bounded by walls formed by decays to small black holes. This enables us to isolate a region in moduli space for which no decays occur within this class. We then study entropy enigma decays for such models and show that for generic values of the moduli, that is when moduli are of order one compared to the charges, entropy enigma decays do not occur in these models.

On plane-wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient

A theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented. The temperature variation in the pipe is taken to be a linear temperature gradient along the axis. The theoretical studies include the formulation of a wave equation based on continuity, momentum, and state equation, and derivation of a general four-pole matrix, which is shown to yield the well-known transfer matrices for several other simpler cases.

Spatial correlation in grain misorientation distribution

Grain misorientation was studied in relation to the nearest neighbor's mutual distance using electron back-scattered diffraction measurements. The misorientation correlation function was defined as the probability density for the occurrence of a certain misorientation between pairs of grains separated by a certain distance. Scale-invariant spatial correlation between neighbor grains was manifested by a power law dependence of the preferred misorientation vs. inter-granular distance in various materials after diverse strain paths. The obtained negative scaling exponents were in the range of -2 +/- 0.3 for high-angle grain boundaries. The exponent decreased in the presence of low-angle grain boundaries or dynamic recrystallization, indicating faster decay of correlations. The correlations vanished in annealed materials. The results were interpreted in terms of lattice incompatibility and continuity conditions at the interface between neighboring grains. Grain-size effects on texture development, as well as the implications of such spatial correlations on texture modeling, were discussed.

Modeling of magnetostrictive materials and structures

The constitutive model for a magnetostrictive material and its effect on the structural response is presented in this article. The example of magnetostrictive material considered is the TERFENOL-D. As like the piezoelectric material, this material has two constitutive laws, one of which is the sensing law and the other is the actuation law, both of which are highly coupled and non-linear. For the purpose of analysis, the constitutive laws can be characterized as coupled or uncoupled and linear or non linear. Coupled model is studied without assuming any explicit direct relationship with magnetic field. In the linear coupled model, which is assumed to preserve the magnetic flux line continuity, the elastic modulus, the permeability and magneto-elastic constant are assumed as constant. In the nonlinear-coupled model, the nonlinearity is decoupled and solved separately for the magnetic domain and the mechanical domain using two nonlinear curves, namely the stress vs. strain curve and the magnetic flux density vs. magnetic field curve. This is performed by two different methods. In the first, the magnetic flux density is computed iteratively, while in the second, the artificial neural network is used, where in the trained network will give the necessary strain and magnetic flux density for a given magnetic field and stress level. The effect of nonlinearity is demonstrated on a simple magnetostrictive rod.

Structural plasticity and enzyme action: Crystal structures of Mycobacterium tuberculosis peptidyl-tRNA hydrolase

Peptidyl-tRNA hydrolase cleaves the ester bond between tRNA and the attached peptide in peptidyl-tRNA in order to avoid the toxicity resulting from its accumulation and to free the tRNA available for further rounds in protein synthesis. The structure of the enzyme from Mycobacteritan tuberculosis has been determined in three crystal forms. This structure and the structure of the enzyme frorn Escherichia coli in its crystal differ substantially on account of the binding of the C terminus of the E. coli enzyme to the peptide-binding site of a neighboring molecule in the crystal. A detailed examination of this difference led to an elucidation of the plasticity of the binding site of the enzyme. The peptide-binding site of the enzyme is a cleft between the body, of the molecule and a polypepticle Y stretch involving a loop and a helix. This stretch is in the open conformation when the enzyme is in the free state as in the crystals of M. tuberculosis peptidyl-tRNA hydrolase. Furthermore, there is no physical continuity between the tRNA and the peptide-binding sites. The molecule in the E. coli crystal mimics the peptide-bound enzyme molecule. The peptide stretch referred to earlier now closes on the bound peptide. Concurrently, a channel connecting the tRNA and the peptide-binding site opens primarily through the concerted movement of two residues. Thus, the crystal structure of M. tuberculosis peptidyl-tRNA hydrolase when compared with the crystal structure of the E. coli enzyme, leads to a model of structural changes associated with enzyme action on the basis of the plasticity of the molecule. (c) 2007 Elsevier Ltd. All rights reserved.

Structural plasticity and enzyme action: Crystal structures of Mycobacterium tuberculosis peptidyl-tRNA hydrolase

Peptidyl-tRNA hydrolase cleaves the ester bond between tRNA and the attached peptide in peptidyl-tRNA in order to avoid the toxicity resulting from its accumulation and to free the tRNA available for further rounds in protein synthesis. The structure of the enzyme from Mycobacteritan tuberculosis has been determined in three crystal forms. This structure and the structure of the enzyme frorn Escherichia coli in its crystal differ substantially on account of the binding of the C terminus of the E. coli enzyme to the peptide-binding site of a neighboring molecule in the crystal. A detailed examination of this difference led to an elucidation of the plasticity of the binding site of the enzyme. The peptide-binding site of the enzyme is a cleft between the body, of the molecule and a polypepticle Y stretch involving a loop and a helix. This stretch is in the open conformation when the enzyme is in the free state as in the crystals of M. tuberculosis peptidyl-tRNA hydrolase. Furthermore, there is no physical continuity between the tRNA and the peptide-binding sites. The molecule in the E. coli crystal mimics the peptide-bound enzyme molecule. The peptide stretch referred to earlier now closes on the bound peptide. Concurrently, a channel connecting the tRNA and the peptide-binding site opens primarily through the concerted movement of two residues. Thus, the crystal structure of M. tuberculosis peptidyl-tRNA hydrolase when compared with the crystal structure of the E. coli enzyme, leads to a model of structural changes associated with enzyme action on the basis of the plasticity of the molecule. (c) 2007 Elsevier Ltd. All rights reserved.

On the design of quadratic weirs

This paper considers the problem of the design of the quadratic weir notch, which finds application in the proportionate method of flow measurement in a by-pass, such that the discharge through it is proportional to the square root of the head measured above a certain datum. The weir notch consists of a bottom in the form of a rectangular weir of width 2W and depth a over which a designed curve is fitted. A theorem concerning the flow through compound weirs called the “slope discharge continuity theorem” is discussed and proved. Using this, the problem is reduced to the determination of an exact solution to Volterra's integral equation in Abel's form. It is shown that in the case of a quadratic weir notch, the discharge is proportional to the square root of the head measured above a datum Image a above the crest of the weir. Further, it is observed that the function defining the shape of the weir is rapidly convergent and its value almost approximates to zero at distances of 3a and above from the crest of the weir. This interesting and significant behaviour of the function incidentally provides a very good approximate solution to a particular Fredholm integral equation of the first kind, transforming the notch into a device called a “proportional-orifice”. A new concept of a “notch-orifice” capable of passing a discharge proportional to the square root of the head (above a particular datum) while acting both as a notch, and as an orifice, is given. A typical experiment with one such notch-orifice, having A = 4 in., and W = 6 in., shows a remarkable agreement with the theory and is found to have a constant coefficient of discharge of 0.61 in the ranges of both notch and orifice.

On higher order shear deformation theory of laminated composite panels

In this paper we examine the suitability of higher order shear deformation theory based on cubic inplane displacements and parabolic normal displacements, for stress analysis of laminated composite plates including the interlaminar stresses. An exact solution of a symmetrical four layered infinite strip under static loading has been worked out and the results obtained by the present theory are compared with the exact solution. The present theory provides very good estimates of the deflections, and the inplane stresses and strains. Nevertheless, direct estimates of strains and stresses do not display the required interlaminar stress continuity and strain discontinuity across the interlaminar surface. On the other hand, ‘statically equivalent stresses and strains’ do display the required interlaminar stress continuity and strain discontinuity and agree very closely with the exact solution.

Characterization of unitary processes with independent and stationary increments

This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci. 45 (2009) 745-785) to characterize unitary stationary independent increment Gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson-Parthasarathy equation is proved.

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

A mimetic-based frequency domain technique for automatic generation of EEG reports

This paper describes a novel mimetic technique of using frequency domain approach and digital filters for automatic generation of EEG reports. Digitized EEG data files, transported on a cartridge, have been used for the analysis. The signals are filtered for alpha, beta, theta and delta bands with digital bandpass filters of fourth-order, cascaded, Butterworth, infinite impulse response (IIR) type. The maximum amplitude, mean frequency, continuity index and degree of asymmetry have been computed for a given EEG frequency band. Finally, searches for the presence of artifacts (eye movement or muscle artifacts) in the EEG records have been made.