Nonvanishing of Siegel Poincaré series

We prove that, under suitable conditions, certain Siegel Poincaré series of exponential type of even integer weight and degree 2 do not vanish identically. We also find estimates for twisted Kloosterman sums and Salié sums in all generality.     

Effect of open boundary condition on numerical simulation of three-dimensional hydrothermal behavior of Biscayne Bay,Florida

A three-dimensional time dependent free-surface model has been used to simulate the velocity and temperature distributions in Biscayne Bay, an estuarine basin in South Florida. Comparisons with tide gauge data and airborne infrared temperature data have been made. Analyses of three-dimensional velocity structure, phase relationships of velocity with depth and horizontal location have been conducted. One of the major concerns with three-dimensional models is the specification of conditions at open-boundaries, since it is rare that complete time dependent variations of variables at these boundaries are available. Two sets of approximate boundary conditions at the Biscayne Bay-Atlantic Ocean interface have been used for computations. It was found that specification of averaged surface height variation at open boundaries yield significantly better results than specification of estimated values of velocity.     

Magnetic circular dichroism of transition metal ions in solids-I. MgO:Cr3+

Absorption and magnetic circular dichroism (MCD) spectra of MgO: Cr³⁺ have been studied over the temperature range 5–300 °K and with magnetic fields up to 77 kG. A theory for intensity calculation using a weak field coupling scheme is discussed. Spin-forbidden transitions to ²E and ²T₁, are observed in MCD and are interpreted as magnetic dipole zero-phonon lines. The spin allowed bands ⁴T₂ and ⁴T₁ are found to be vibration-induced electric dipole transitions in which the t_1u lattice modes are the dominant contributors to the intensity.     

Goal Programming Approach to a Type of Quality Control Problem

Fixing the levels of inputs and process variables in order to meet a required specification of output is a common quality control problem. However difficulties can arise when the output has a number of characteristics and when each of these characteristics has to satisfy a specification. Such a problem was met in a paper manufacturing factory and the problem was solved using Goal Programming (GP). The method can be applied to other process control problems and this paper gives the GP formulation of the general process control problem. The paper also gives details of the case study from which the method was developed.     

Bounding solutions of systems of equations using interval analysis

We introduce some variations of the interval Newton method for bounding solutions to a set ofn nonlinear equations. It is pointed out that previous implementations of Krawczyk's method are very inefficient and an improved version is given. A superior type of Newton method is introduced.     

A discretized spectral approximation in neutron transport theory. Some numerical considerations

The half-range weight function, orthogonality integrals, and completeness theorems in the theory of kinetic equations are often not known, or when they are, are too complicated to be of much practical use. This suggests the use of full-range relations to solve half-range problems, and in this paper we investigate the adaptability of such an approach in the theory of one-speed neutron transport by a discretized spectral approximation formulated recently.     

A study of the motion in rotating containers using a boundary fitted co-ordinate system

Numerical solutions are often inaccurate because conventional co-ordinate systems do not represent the complex physical boundaries accurately. In the present work, the numerical solution of linear shallow water wave equations has been obtained by transforming the physical domain into a rectangular computational domain using elliptic differential operators. This work is part of a programme to develop three-dimensional body-fit grid systems for environmental flows. Solutions have been obtained for a cylindrical container and also a parabolic container. The initial conditions chosen are the ones for which analytical solutions exist. The numerical solutions compare well with analytical solutions.     

Self-consistent calculation of 1s2s3S state of helium and heliumlike ions

In this paper we present a simple method within the coupled Hartree–Fock framework to calculate the 1s2s ³S state of helium and heliumlike ions. The results are in very good agreement with those obtained by the use of multiterm correlated wave functions. Some interesting observations associated with the wave function are presented.