Kantorovich-type inequalities and the measures of inefficiency of the glse

In this paper we introduce some Kantorovich inequalities for the Euclidean norm of a matrix, that is, the upper bounds to (X'B ^–1 X) ^–1 X'B ^–1 AB ^–1 X(X'B ^–1X)^–1 X' BX(X'AX) ^–1 X'CX² are given, where A²=trace (A'A). In terms of these inequalities the upper bounds to the three measures of inefficiency of the generalized least squares estimator (GLSE) in general Gauss-Markov models are also established.Project supported partially by the Third World Academy of Sciences under contract TWASRG 87-46 and by the National Natural Science Foundation.     

Asymptotic expansions andL ∞-error estimates for mixed finite element methods for second order elliptic problems

Summary Asymptotic expansions for mixed finite element approximations of the second order elliptic problem are derived and Richardson extrapolation can be applied to increase the accuracy of the approximations. A new procedure, which is called the error corrected method, is presented as a further application of the asymptotic error expansion for the first order BDM approximation of the scalar field. The key point in deriving the asymptotic expansions for the error is an establishment ofL ¹-error estimates for mixed finite element approximations for the regularized Green's functions. As another application of theL ¹-error estimates for the regularized Green's functions, we shall present maximum norm error estimates for mixed finite element methods for second order elliptic problems.     

Thermodynamic properties of aqueous mixtures of LiCl and Li2SO4 at different temperatures

Emf measurements were made on the cell without liquid junction: Li?ISE LiCl(m₁), Li₂SO₄(m₂) Ag/AgCl. The performances of the electrode pairs constructed in our laboratory were tested and exhibited near-Nernstian behavior. The mean activity coefficients of LiCl for the system Li⁺?Cl^??SO ₄ ^2? ?H₂O have been investigated by the emf values at temperatures of 0, 15, 35°C and constant total ionic strengths of 0.05, 0.1, 0.5, 1.0, 2.0, 3.0 and 5.0 mol·kg^?1. The activity coefficients decrease with increasing temperature and the ionic strength fraction of Li₂SO₄ in the mixtures. The thermodynamic properties are interpreted by use of Harned's empirical equations and Pitzer's ion interaction approach including the contribution of higher order electrostatic terms. The experimental results obey Harned's rule and are described by using Pitzer equations satisfactorily. The activity coefficients of Li₂SO₄, the osmotic coefficients and the excess free energies of mixing for the system in the experimental temperature range were reported.     

Multiple impulse solutions to McKean's caricature of the nerve equation. I—existence

McKean's caricature of the nerve equation: is considered. The H in (1) is the Heaviside function. We prove the existence of multiple impulse solutions consisting of any finite number of pulses. These solutions are referred to as n-ple impulse solutions, where n is an arbitrary positive integer.     

Essay on gravitation: Present-time variation of Newton's gravitational constant in superstring theories

Superstring theories provide an appropriate framework for studying the time variation of fundamental coupling constants. The present time variation of coupling constants in Superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of internal space. If the potential is almost flat, as in perturbation theory to all orders, the present value of ¦/G¦ for Newton's gravitational constant is calculable and estimated to be 1×10^–11±1yr^–1, which is just at the edge of the present observational bound for/G. If the potential has a minimum with finite curvature due to unknown nonperturbative effects,/G will become unobservably small. The improvement of the measurement of/G of 1 or 2 orders of magnitude would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed.This essay received the fourth award from the Gravity Research Foundation for the year 1987-Ed.     

Bioaccumulation and voltammetry of gold at flower-biomass modified electrodes

The bioaccumulation of gold at antheral cells from flower Datura innoxia is investigated by incorporating these plant cells into a carbon paste matrix. The resulting plant-modified electrode offers a preferential uptake of gold from dilute solutions. The voltammetric behavior of the surface-bound gold is examined under different preconcentration conditions. Scanning electron microscopy offers useful insights into the gold collection process. Convenient measurements of micromolar gold concentrations are possible, with effective self cleaning allowing the use of a single electrode in multiple determinations (R.S.D. of 4.8% for 50 repetitions). The sensitivity and selectivity enhancements associated with the preferential bioaccumulation process, and the convenient surface regeneration, offer the prospect of using the flower-biomass containing electrodes as sensors for gold.