A-optimal designs for an additive cubic model

Chan et al. (1998a) obtained A-optimal designs for an additive quadratic mixture model for q≥3 mixture components. In this paper, we obtain the A-optimal designs for an additive cubic model for q≥3 mixture components using the class of symmetric weighted centroid designs based on barycentres of various depths. We observe that barycentres of depths 0 and 2 are possible support points for an A-optimal design. We have also given the optimal weights of A-optimal designs for 3≤q≤17.     

A molecular dynamics study of the interaction of oleate and dodecylammonium chloride surfactants with complex aluminosilicate minerals

Surface characteristics of complex aluminosilicate minerals like spodumene [LiAl(SiO(3))(2)], jadeite [NaAl(SiO(3))(2)], feldspar [KAlSi(3)O(8)], and muscovite [K(2)Al(4)(Al(2)Si(6)O(20))(OH)(4)]) are modeled. Surface energies are computed for the cleavage planes of these minerals. Adsorption mechanisms of anionic chemisorbing type oleate and cationic physisorbing type dodecylammonium chloride molecules on two different crystal planes, that is (110) and (001), of spodumene and jadeite are studied in terms of the surface-surfactant interaction energies computed using molecular dynamics (MD) simulations. The conclusions drawn from purely theoretical computations match remarkably well with our experimental results.     

Meso-diacylated calix[4]pyrrole: structural diversities and enhanced binding towards dihydrogenphosphate ion

Meso-diacylated calix[4]pyrrole was obtained via acid catalysed condensation of meso-acylated dipyrromethane with acetone. Selective presence of flexible substituents at the calix[4]pyrrole periphery led to interesting structural motifs in the solid state along with enhanced binding towards anions, especially dihydrogenphosphate ion via anchoring.     

Fourth-order finite difference methods for three-dimensional general linear elliptic problems with variable coefficients

In this article, we give a simple method for deriving finite difference schemes on a uniform cubic grid. We consider a general, three-dimensional, second-order, linear, elliptic partial differential equation with variable coefficients. We derive two simple fourth-order schemes. When the coefficients of the second-order mixed derivatives are equal to zero, the fourth-order scheme requires only 19 grid points. When the coefficients of the mixed derivatives are not equal to zero and the coefficients of U_xx, U_yy, and U_zz are equal, we require the 27 points of the cubic grid. Numerical examples are given to demonstrate the performance of the two schemes derived. There does not exist a fourth-order scheme involving 27 grid points for the general case.     

Low temperature elastic behaviour of As-Sb-Se and Ge-Sb-Se glasses

The ternary glasses of arsenic and germanium with antimony and selenium can be prepared in large sizes for optical purposes. The elastic behaviour of eight compositions of each glass has been studied down to 4.2 K using a 10 MHz ultrasonic pulse echo interferometer. The glasses have a normal elastic behaviour, with the velocities gradually increasing as the temperature is lowered. An anharmonic solid model of Lakkad satisfactorily explains the temperature variations. The elastic moduli of Ge _x Sb₁₀Se_90?x glasses increase linearly as the Ge content is increased up to 25 at. % and beyond this the increase is nonlinear. (AsSb)₄₀Se₆₀ glasses show a linear increase in elastic moduli with increasing Sb content. The elastic moduli of As _x Sb₁₅Se_85?x glasses exhibit a drastic change near the stoichiometric composition As₂₅Sb₁₅Se₆₀. These behaviours have been qualitatively explained on the basis of the structural changes in glasses.     

On a theorem of M. Deuring and I. R. Šafarevič

Let F/K be a field of algebraic functions of one variable, K algebraically closed of characteristic p≠0. Let E/K be a cyclic extension of F/K of degree ?, a prime not necessarily different from p. Let ξ, ρ denote the ?-ranks of the null class groups of E and F respectively. If E/F is ramified, Deuring proved that ξ=?ρ+(t?δ)(??1) where t is the number of ramified primes and δ is 1 or 2 according as ? equals p or not. ?afarevi? proved the same relation in the unramified case for ?=p where ξ, ρ denote the ranks of the Hasse-Witt matrices. Subrao gave a unified proof for ?=p. Rosen and Sullivan have proved the theorem in special cases. In this paper, using galois cohomology, Deuring's method of proof is modified so as to give a proof of the theorem in all cases.     

Galois module structure of Tate modules

Dedicated to Professor Peter Roquette Received 1 February 1996; in final form 26 April 1996