Geometrical interpretation of Inönü-Wigner contractions

The Inönü-Wigner contractions which interrelate the Lie algebras of the isometry groups of metric spaces are discussed with reference to deformations of the absolutes of the spaces. A general formula is derived for the Lie algebra commutation relations of the isometry group for anyN-dimensional metric space. These ideas are illustrated by a discussion of important particular cases, which interrelate the four-dimensional de Sitter, Poincaré, and Galilean groups.

Aspects of tautomerism. 6. Base-catalyzed hydrolysis of pseudo esters of .gamma.-keto acids

The rates of base-catalyzed hydrolysis of pseudo esters derived from y-keto acids show strikingly poor sensitivity to the nature of the leaving group.la The rates vary in the narrow range of about 12-fold as contrasted to a 103-fold spread of the corresponding benzoate esters. The results presented are consistent with a rate-determining formation of a tetrahedral intermediate (11) and i t s rapid collapse, by the cleavage of the lactone ring in a fast step.

Aspects of tautomerism. 8. Solvolysis of some pseudo and normal acid chlorides

Pseudo acid chlorides derived from levulinic acid ando-benzoyl-benzoic acid, solvolyse in aqueous acetone, aqueous dioxane and aqueous dimethylformamide by aS Nl process. Their reaction pattern is distinct from that of typical normal acid chlorides, viz.,p-benzoylbenzoyl chloride and fluorene-9-one-1-carboxylic acid chloride, which solvolyse by aS N2 pathway. No evidence for tautomerism could be obtained either between the normal and pseudo forms of the acid chlorides or the derived ion pairs.

Pseudo-time marching schemes for inverse problems in structural health assessment and medical imaging

We propose a self-regularized pseudo-time marching strategy for ill-posed, nonlinear inverse problems involving recovery of system parameters given partial and noisy measurements of system response. While various regularized Newton methods are popularly employed to solve these problems, resulting solutions are known to sensitively depend upon the noise intensity in the data and on regularization parameters, an optimal choice for which remains a tricky issue. Through limited numerical experiments on a couple of parameter re-construction problems, one involving the identification of a truss bridge and the other related to imaging soft-tissue organs for early detection of cancer, we demonstrate the superior features of the pseudo-time marching schemes.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

Reliability assessment of internal stability of reinforced soil structures: A pseudo-dynamic approach

A methodology for reliability based optimum design of reinforced soil structures subjected to horizontal and vertical sinusoidal excitation based on pseudo-dynamic approach is presented. The tensile strength of reinforcement required to maintain the stability is computed using logarithmic spiral failure mechanism. The backfill soil properties, geometric and strength properties of reinforcement are treated as random variables. Effects of parameters like soil friction angle, horizontal and vertical seismic accelerations, shear and primary wave velocities, amplification factors for seismic acceleration on the component and system probability of failures in relation to tension and pullout capacities of reinforcement have been discussed. In order to evaluate the validity of the present formulation, static and seismic reinforcement force coefficients computed by the present method are compared with those given by other authors. The importance of the shear wave velocity in the estimation of the reliability of the structure is highlighted. The Ditlevsen's bounds of system probability of failure are also computed by taking into account the correlations between three failure modes, which is evaluated using the direction cosines of the tangent planes at the most probable points of failure. (c) 2009 Elsevier Ltd. All rights reserved.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time,recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of thePD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small.

Self-regularized pseudo time-marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non-linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least-square solution is through a regularized Gauss-Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo-dynamical GNM (PD-GNM) update equation addresses the major numerical difficulty associated with the near-zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo-dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through apseudo-dynamic ensemble Kalman filter (PD-EnKF). For multiple sets ofmeasurements involving various load cases, we expedite the speed of the PD-EnKF by proposing an inner iteration within every time step. Results using the pseudo-dynamic strategy obtained through PD-EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD-EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright (C) 2009 John Wiley & Sons, Ltd.

Role of the leaving group in the base-catalysed hydrolysis of pseudo-esters

The relative insensitivity of the rate of hydrolysis of γ-pseudo-esters to the leaving group compared to that of the normal esters emphasises that the conjugative ability is an important factor in determining the rate of hydrolysis of esters

Aspects of tautomerism. Part II. Reactions of the pseudo-acid chloride of o-benzoylbenzoic acid with nucleophiles

Reactions of fourteen nucleophiles with the pseudo-acid chloride of o-benzoylbenzoic acid in two solvents have been studied. The nucleophiles that react primarily at the tetrahedral carbon atom to give pseudo derivatives, are weaker than those that react at the carbonyl carbon atom causing opening of the lactone ring. An explanation for this phenomenon is advanced.

Aspects of tautomerism. Part III. A new dimerisation reaction of pseudo-acid chlorides

Pseudo-acid chlorides of five 4′-substituted o-benzoylbenzoic acids are converted into a mixture of dilactones with sodium iodide in acetone. The meso-isomer is always formed to a larger extent than the (±)-mixture. These results imply that the radicals involved are not planar.

Aspects of tautomerism. Part IV. A kinetic study of the dimerization reaction of pseudo-acid chlorides

The kinetics of dimerization of 4-substituted- and unsubstituted o-benzoylbenzoyl chlorides, with iodide ion can be described by the expression, rate =k2[acid chloride][iodide]. The value for the reaction in dimethylformamide solution is –0·38. The entropy of activation for the reaction is –34·2 cal mol–1 K–1 and the activation energy is 10·7 kcal mol–1. These results have been interpreted as evidence for the formation of pseudo-iodide in the rate-determining step and its fast decomposition to radicals which combine to give a mixture of stereoisomeric dilactones.

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).

Betwixt kinetic and thermodynamic control:'Pseudo-Thermodynamic control'

A third mechanistic category of organic reactions, conceptually in-between kinetic and thermodynamic control, needs to be recognized, in order to obtain a proper mechanistic description of certain highly important organic reactions, but also to avoid controversy. In fact, an instance of debatable conclusions having been reached is already known. The term �pseudo-thermodynamic control� is proposed for this newly-defined category, which would include any reaction in which intermediates along different routes mutually interconvert. The new category would thus encompass a very large number of reactions, many of them of great utility.

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.