Cuspidality and the growth of Fourier coefficients of modular forms : A survey

In this paper, we present a survey of the recent results on the characterization of the cuspidality of classical modular forms on various groups by a suitable growth of their Fourier coefficients.

A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS

It is shown that there are infinitely many primitive cusp forms f of weight 2 with the property that for all X large enough, every interval (X, X + cX(1/4)), where c > 0 depends only on the form, contains an integer n such that the n-th Fourier coefficient of f is nonzero.

An analysis of MONTBLEX data on heat and momentum flux at Jodhpur

Parameterization of sensible heat and momentum fluxes as inferred from an analysis of tower observations archived during MONTBLEX-90 at Jodhpur is proposed, both in terms of standard exchange coefficients C-H and C-D respectively and also according to free convection scaling. Both coefficients increase rapidly at low winds (the latter more strongly) and with increasing instability. All the sensible heat flux data at Jodhpur (wind speed at 10m <(U)over bar (10)>, < 8ms(-1)) also obey free convection scaling, with the flux proportional to the '4/3' power of an appropriate temperature difference such as that between 1 and 30 m. Furthermore, for <(U)over bar (10)> < 4 ms(-1) the momentum flux displays a linear dependence on wind speed.

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

Unsteady Compressible Boundary-Layer Flow On The Stagnation Line Of An Infinite Swept Cylinder

Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wail enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.

Photocatalytic and Thermal Degradation of Poly(methyl methacrylate), Poly(butyl acrylate), and Their Copolymers

The photocatalytic and thermal degradations of poly(methyl methacrylate), poly(butyl acrylate), and their copolymers of different compositions were studied. The photocatalytic degradation was investigated in o-dichlorobenzene in the presence of two different catalysts, namely, Degussa P-25 and combustion synthesized nanotitania (CSN-TiO2). The samples were analyzed by using gel permeation chromatography (GPC) to obtain the molecular weight distributions (MWDs) as a function of reaction time. Experimental data indicated that the photodegradation of these polymers occurs by both random and chain end scission. A continuous distribution kinetic model was used to determine the degradation rate coefficients by fitting the experimental data with the model. Both the random and specific rate coefficients of the copolymers decreased with increasing percentage of butyl acrylate (BA). Thermal degradation of the copolymers was investigated by thermo-gravimetry. The normalized weight loss profiles for the copolymers showed that the thermal stability of the copolymers increased with mole percentage of BA in the copolymer (PMMABA). The Czawa method was used to determine the activation energies at different conversions. At low acrylate content in the copolymer, the activation energy depends on conversion, indicating multiple degradation mechanisms. At high acrylate content in the copolymer, the activation energy is independent of conversion, indicating degradation by a one-step mechanism.

Dynamics of a dilute sheared inelastic fluid. II. The effect of correlations

The effect of correlations on the viscosity of a dilute sheared inelastic fluid is analyzed using the ring-kinetic equation for the two-particle correlation function. The leading-order contribution to the stress in an expansion in epsilon=(1-e)(1/2) is calculated, and it is shown that the leading-order viscosity is identical to that obtained from the Green-Kubo formula, provided the stress autocorrelation function in a sheared steady state is used in the Green-Kubo formula. A systemmatic extension of this to higher orders is also formulated, and the higher-order contributions to the stress from the ring-kinetic equation are determined in terms of the terms in the Chapman-Enskog solution for the Boltzmann equation. The series is resummed analytically to obtain a renormalized stress equation. The most dominant contributions to the two-particle correlation function are products of the eigenvectors of the conserved hydrodynamic modes of the two correlated particles. In Part I, it was shown that the long-time tails of the velocity autocorrelation function are not present in a sheared fluid. Using those results, we show that correlations do not cause a divergence in the transport coefficients; the viscosity is not divergent in two dimensions, and the Burnett coefficients are not divergent in three dimensions. The equations for three-particle and higher correlations are analyzed diagrammatically. It is found that the contributions due to the three-particle and higher correlation functions to the renormalized viscosity are smaller than those due to the two-particle distribution function in the limit epsilon -> 0. This implies that the most dominant correlation effects are due to the two-particle correlations.

Ultrasonic Degradation of Poly(acrylic acid)

The ultrasonic degradation of poly(acrylic acid), a water-soluble polymer, was studied in the presence of persulfates at different temperatures in binary solvent Mixtures of methanol and water. The degraded samples were analyzed by gel permeation chromatography for the time evolution of the molecular weight distributions. A continuous distribution kinetics model based on midpoint chain scission was developed, and the degradation rate coefficients were determined. The decline in the rate of degradation of poly(acrylic acid) with increasing temperature and with an increment in the methanol content in the binary solvent mixture of methanol and water was attributed to the increased vapor pressure of the solutions. The experimental data showed an augmentation of the degradation rate of the polymer with increasing oxidizing agent (persulfate) concentrations. Different concentrations of three persulfates-potassium persulfate, ammonium persulfate, and sodium persulfate-were used. It was found that the ratio of the polymer degradation rate coefficient to the dissociation rate constant of the persulfate was constant. This implies that the ultrasonic degradation rate of poly(acrylic acid) can be determined a priori in the presence of any initiator.

Constraining the low-energy pion electromagnetic form factor with space-like and phase of time-like data

The Taylor coefficients c and d of the EM form factor of the pion are constrained using analyticity, knowledge of the phase of the form factor in the time-like region, 4m(pi)(2) <= t <= t(in) and its value at one space-like point, using as input the (g - 2) of the muon. This is achieved using the technique of Lagrange multipliers, which gives a transparent expression for the corresponding bounds. We present a detailed study of the sensitivity of the bounds to the choice of time-like phase and errors present in the space-like data, taken from recent experiments. We find that our results constrain c stringently. We compare our results with those in the literature and find agreement with the chiral perturbation-theory results for c. We obtain d similar to O(10) GeV-6 when c is set to the chiral perturbation-theory values.

CCD: Connected Component Descriptor for Robust Mosaicing of Camera-Captured Document Images

We propose a robust method for mosaicing of document images using features derived from connected components. Each connected component is described using the Angular Radial Tran. form (ART). To ensure geometric consistency during feature matching, the ART coefficients of a connected component are augmented with those of its two nearest neighbors. The proposed method addresses two critical issues often encountered in correspondence matching: (i) The stability of features and (ii) Robustness against false matches due to the multiple instances of characters in a document image. The use of connected components guarantees a stable localization across images. The augmented features ensure a successful correspondence matching even in the presence of multiple similar regions within the page. We illustrate the effectiveness of the proposed method on camera captured document images exhibiting large variations in viewpoint, illumination and scale.

Equivariant Birch-Swinnerton-Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Let E be an elliptic curve defined over Q and let K/Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h(1)(E x(Q) K)(1) viewed as amotive over Q with coefficients in Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S-3-extension of Q.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Hydrodynamic Pressure on a Dam During Earthquakes

A straightforward analysis involving Fourier cosine transforms and the theory of Fourier seies is presented for the approximate calculation of the hydrodynamic pressure exerted on the vertical upstream face of a dam due to constant earthquake ground acceleration. The analysis uses the “Parseval relation” on the Fourier coefficients of square integrable functions, and directly brings out the mathematical nature of the approximate theory involved.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.

Fluidity of mica particle dispersed aluminium alloy

Cast aluminium alloy-mica particle composites were made by dispersing mica particles in a vortex produced by stirring the liquid Al-4 wt% Cu-1.5 wt% Mg alloy and then casting the melt containing the suspended particles into permanent moulds. Spiral fluidity and casting fluidity of the alloy containing mica particles in suspension were determined. Both the spiral fluidity and the casting fluidity of the base alloy were found to decrease with an increase in volume or weight percent of mica particles (of a given size), and with a decrease in particle size (for a given amount of particles). The fluidities of Al-4 wt% Cu-1.5 wt% Mg alloys containing suspended mica particles were found to correlate very well with the surface area of suspended mica particles. The regression equation for spiral fluidity Y (cm) as a function of surface area of mica particles per gram of spiral X (cm2 g–1) at 700° C was found to be Y=42.62–0.42X with a correlation coefficient of 0.9634. The regression equations for casting fluidity Yprime (cm) as a functiono of surface area of mica particles per gram of fluidity test piece Xprime (cm2 g–1) at 710 and 670° C were found to be Yprime=19.71–0.17Xprime and Yprime=13.52–0.105Xprime with correlation coefficients of 0.9194 and 0.9612 respectively. The percentage decrease in casting fluidity of composite melts containing up to 2.5 wt% mica with a drop in temperature is quite similar to the corresponding decrease in the casting fluidity of base alloy melts (without mica). The change in fluidity due to mica dispersions has been discussed in terms of changes in viscosity of the composite melts. However, the fluidities of these composite alloys containing up to 2.5 wt% mica are adequate for making a variety of simple castings including bearings for which these alloys have been developed.