Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Vibrational and 1H NMR spectra of N-(2-pyridyl)-thioformamide and N-(2-pyridyl)thioacetamide

The Raman and infrared spectra of N-(2-pyridyl) thioformamide and N-(2-pyridyl)-thioacetamide have been measured. The assignment of the bands is aided by the complete normal coordinate treatment for all the vibrations of N-(2-pyridyl)thioformamide and its N-deuterated molecule using a Urey—Bradley force function for the in-plane vibrations and a valence force function for the out of plane vibrations. Variable temperature 1H NMR study of the two pyridylthionamides has also been performed. It is inferred that while N-(2-pyridyl)thioformamide favours a cis —CSNH— group, the other compound favours a trans —CSNH— grouping at ambient temperature.

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

Raman and polarized infrared spectra of pyridine-2-thione

Polarized i.r. spectra of oriented polycrystals and the i.r. and Raman spectra of polycrystalline samples of pyridine-2-thione have been obtained. The Raman spectra of a solution of pyridine-2-thione has also been measured and the polarization of many lines determined. The i.r. spectra of S-methyl and N-deuterated compounds have also been investigated. A complete assignment of all the observed peaks has been possible. The results are correlated with the assignments available for related systems.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter λ which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when λ is small, whereas the effect of the dissipation parameter is more pronounced when λ is comparatively large.

Molecular vibrations, electronic structure and conformation of diprotonated thiocarbohydrazide

The infrared spectra of diprotonated species of thiocarbohydrazide and its perdeuterated derivative have been examined in the crystalline state. A complete vibrational assignment with a full normal coordinate treatment based on a Urey—Bradley type intramolecular potential Function supplemented with a valence force function for the out of plane and torsional modes is proposed and the origin of the amide II band splittings is explained. A CNDO/2 study of diprotonated thiocarbohydrazide and its neutral molecule is undertaken and the changes in the molecular electronic structures and conformations consequent to protonation are determined and briefly discussed. The magnitude of the N—N+H3 torsional barrier is estimated to be 21 kJ mol− (5.0 kcal mol−1) whereas the barrier for the C—N group is found to be 92 kJ mol−1 (22.0 kcal mol−1).

1H and 13C NMR spectral studies of C-2 substituted isomeric exo- and endo-5-methyl-bicyclo[3.2.1]octane-6,8-diones

A detailed analysis of the 1H and 13C NMR spectra of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones is presented. The chemical shift of the C-5 angular methyl, the C-2 alkyl/olefinic (C-10)/C-2 methine protons, the aromatic proton shieldings and the characteristic AMX and ABX spectral pattern of the ketomethylene and bridgehead protons were found to be sensitive to the phenyl ring orientation (anisotropy). These distinctive features could be used for configurational distinction for this class of compounds. With increasing ortho-methoxy substitution on the phenyl ring, considerable deshilelding of the bridgehead proton was observed (ca. 0.6 ppm). Absence of the C-2 alkyl group in the desalkyl isomers resulted in substantial changes in the chemical shifts of different protons. A study of the NMR spectra of the corresponding bicyclic compounds with C-2 methoxy/hydroxy substitution instead of the aryl group revealed that the anisotropy of the phenyl ring and the electronegative oxygen substituents have opposite effects. The 13C NMR spectral assignment of each carbon resonance of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones and the corresponding C-2 methoxy/hydroxy/chloro and methyl bicyclic compounds are reported. Additional ortho-methoxy substitution on the phenyl ring was found to produce considerable high field shifts of the C-10 and C-1 carbon resonances. A high-field shift was observed for the C-6 and C-8 carbonyl carbons, presumably due to 1,3-dicarbonyl interactions. The chemical shifts of C-1 aromatic, C-10 alkyl and C-2 carbons, which are sensitive to exo/endo isomerism, could be utilized in differentiating a pair of isomers.

Gauge hierarchy in a supersymmetric model

In a globally supersymmetric gauge theory with two distinct mass scales, the possible limitation on the gauge hierarchy due to the structure of the loop-corrected Higgs potential is shown to be absent. Also it has been demonstrated that the supersymmetry forces the large corrections to the two-point Greens functions of the light fields from the quadratic divergences and the logarithmic divergences with large coefficients to be zeroseparately. This would, therefore, allow a gauge hierarchy as large as desired.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

Infrared spectra of some oxides of K2NiF4 and related structures

The i.r. spectra of some Ln2BO4 and LnSrBO4 compounds (Ln = La, Pr, Nd, Sm or Gd;B = Fe, Al, Co or Cu) with K2NiF4 or related structures have been studied in the range 800-300 cm−1. The BO6 octahedra in compounds with K2NiF4 structure are elongated. The assignment of the bands in terms of internal modes of sheets of bridged BO6 octahedra or square-planar BO4 sheets has been considered. The observed spectra are correlated with those of solid solutions of these oxides and of LnBO3 perovskites. Unusually high stretching frequencies found in some of the oxides are discussed in terms of the short B---O bonds in the basal plane and the Ln---O bonds along the c axis.

Infrared spectra of some oxides of K2NiF4 and related structures

The i.r. spectra of some Ln2BO4 and LnSrBO4 compounds (Ln = La, Pr, Nd, Sm or Gd;B = Fe, Al, Co or Cu) with K2NiF4 or related structures have been studied in the range 800-300 cm−1. The BO6 octahedra in compounds with K2NiF4 structure are elongated. The assignment of the bands in terms of internal modes of sheets of bridged BO6 octahedra or square-planar BO4 sheets has been considered. The observed spectra are correlated with those of solid solutions of these oxides and of LnBO3 perovskites. Unusually high stretching frequencies found in some of the oxides are discussed in terms of the short B---O bonds in the basal plane and the Ln---O bonds along the c axis.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

Spectroscopic and Coordination Behavior of α-Cyanothioacetamide

α-Cyanothioacetamide (CTAM) complexes of cuprous chloride CuCl–2CTAM and cuprous bromide CuBr–2CTAM have been prepared. The infrared spectra of CTAM and its complexes, and the laser Raman spectrum of CTAM have been recorded. Assignment of the frequencies of the ligand has been made on the basis of a normal coordinate analysis using the Urey-Bradley force field. The copper (I) complexes are inferred to have thiocarbonyl sulfur and amide nitrogen bonded CTAM as evidenced from infrared and electronic spectra.

Single network adaptive critic design for power system stabilisers

The recently developed single network adaptive critic (SNAC) design has been used in this study to design a power system stabiliser (PSS) for enhancing the small-signal stability of power systems over a wide range of operating conditions. PSS design is formulated as a discrete non-linear quadratic regulator problem. SNAC is then used to solve the resulting discrete-time optimal control problem. SNAC uses only a single critic neural network instead of the action-critic dual network architecture of typical adaptive critic designs. SNAC eliminates the iterative training loops between the action and critic networks and greatly simplifies the training procedure. The performance of the proposed PSS has been tested on a single machine infinite bus test system for various system and loading conditions. The proposed stabiliser, which is relatively easier to synthesise, consistently outperformed stabilisers based on conventional lead-lag and linear quadratic regulator designs.

Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.