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.

Reaction of normal and pseudo 2-formylbenzenesulfonyl chlorides with amines:experimental and theoretical studies on the structure of 2-formyl benzenesulfonamides in solid, solution and gas phases

The reaction of 2-formylbenzenesulfonyl chloride 1 and its pseudo isomer 2 with primary amines give either the corresponding sulfonamido Schiff bases or the corresponding 2-formylbenzenesulfonamide depending on the concentration of the amine used. The derivatives exist as an equilibrium mixture of the corresponding sulfonamide and 2-alkyl-3-hydroxy(or 3-aminoalkyl)-benzisothiazole-1,1-dioxide. Spectroscopic studies suggest that 2-formylbenzenesulfonamides exist as benzisothiazole-1,1-dioxides in the solid state, as a mixture of 2-formylbenzenesulfonamide and the corresponding benzisothiazole-1,1-dioxide in solution and as 2-formyl-benzenesulfonamides in the gas phase.

A method for the calculation of the adsorbed phase volume and pseudo-saturation pressure from adsorption isotherm data on activated carbon

We propose a new method for evaluating the adsorbed phase volume during physisorption of several gases on activated carbon specimens. We treat the adsorbed phase as another equilibrium phase which satisfies the Gibbs equation and hence assume that the law of rectilinear diameters is applicable. Since invariably the bulk gas phase densities are known along measured isotherms, the constants of the adsorbed phase volume can be regressed from the experimental data. We take the Dubinin-Astakhov isotherm as the model for verifying our hypothesis since it is one of the few equations that accounts for adsorbed phase volume changes. In addition, the pseudo-saturation pressure in the supercritical region is calculated by letting the index of the temperature term in Dubinin's equation to be temperature dependent. Based on over 50 combinations of activated carbons and adsorbates (nitrogen, oxygen, argon, carbon dioxide, hydrocarbons and halocarbon refrigerants) it is observed that the proposed changes fit experimental data quite well.

Reliability Based Design Optimization for Internal Stability of Reinforced Soil Structures Using Pseudo‐Static Method

Seismic design of reinforced soil structures involves many uncertainties that arise from the backfill soil properties and tensile strength of the reinforcement which is not addressed in current design guidelines. This paper highlights the significance of variability in the internal stability assessment of reinforced soil structures. Reliability analysis is applied to estimate probability of failure and pseudo‐static approach has been used for the calculation of the tensile strength and length of the reinforcement needed to maintain the internal stability against tension and pullout failures. Logarithmic spiral failure surface has been considered in conjunction with the limit equilibrium method. Two modes of failure namely, tension failure and pullout failure have been considered. The influence of variations of the backfill soil friction angle, the tensile strength of reinforcement, horizontal seismic acceleration on the reliability index against tension failure and pullout failure of reinforced earth structure have been discussed.

Channel Precoding for STBCs from Generalized Pseudo Orthogonal Designs

Statistical information about the wireless channel can be used at the transmitter side to enhance the performance of MIMO systems. This paper addresses how the concept of channel precoding can be used to enhance the performance of STBCs from Generalized Pseudo Orthogonal Designs which were first introduced by Zhu and Jafarkhani. Such designs include some important classes of STBCs that are directly derivable from Quasi-Orthogonal Designs and Co-ordinate Interleaved Orthogonal Designs.

Pseudo-time particle filtering for diffuse optical tomography

We recast the reconstruction problem of diffuse optical tomography (DOT) in a pseudo-dynamical framework and develop a method to recover the optical parameters using particle filters, i.e., stochastic filters based on Monte Carlo simulations. In particular, we have implemented two such filters, viz., the bootstrap (BS) filter and the Gaussian-sum (GS) filter and employed them to recover optical absorption coefficient distribution from both numerically simulated and experimentally generated photon fluence data. Using either indicator functions or compactly supported continuous kernels to represent the unknown property distribution within the inhomogeneous inclusions, we have drastically reduced the number of parameters to be recovered and thus brought the overall computation time to within reasonable limits. Even though the GS filter outperformed the BS filter in terms of accuracy of reconstruction, both gave fairly accurate recovery of the height, radius, and location of the inclusions. Since the present filtering algorithms do not use derivatives, we could demonstrate accurate contrast recovery even in the middle of the object where the usual deterministic algorithms perform poorly owing to the poor sensitivity of measurement of the parameters. Consistent with the fact that the DOT recovery, being ill posed, admits multiple solutions, both the filters gave solutions that were verified to be admissible by the closeness of the data computed through them to the data used in the filtering step (either numerically simulated or experimentally generated). (C) 2011 Optical Society of America

Conjugacy invariant pseudo-norms, representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.