On the interlattice displacement of rhombohedral structure

The expressions for the components of the interlattice displacement to the first order in strain and hence the expressions for the SOE constants are obtained for the rhombohedral lattice using the method of homogeneous deformation. Two and three body interactions are considered up to fourth neighbours in the calculations. The special strains that are generally chosen in explaining the temperature variation of thermal expansion of a uniaxial crystal, which make the interlattice displacement zero, are shown to be dependent [$\text{η}{}_{\mathrm{zz}}\text{= ?}\text{3}\text{2p}{}^2\text{C}\text{D}\text{(η}{}_{\mathrm{xx}}\text{+ η}{}_{\mathrm{yy}}\text{)}$]. The internal displacement factors A, B, C and D are calculated for the metals As, Sb and Bi to get an idea on the magnitude of C/D.     

Structure of 3P size resonance in neutron strength functions

Neutron capture cross sections of 21 nuclei have been determined using the activation technique and an antimony-beryllium photoneutron source. The nuclei have been selected in the mass range 60 < A < 140 so as to cover the 3P size resonance region of neutron strength functions. Using the latest available data on the low energy resonance parameters, the P-wave neutron strength functions of the 21 isotopes are extracted, and found to be in general agreement with similar isotopic values reported in literature. The values of experimental P-wave neutron strength functions in the 3P resonance region (60 < A < 140) are compared on the one hand with the theoretical predictions of Fiedeldey and Frahn and on the other with those of Buck and Perey. The shape and structure of the 3P size resonance, as revealed experimentally, are found to agree better with the predictions of Fiedeldey and Frahn, who assumed twice the normal spin-orbit force in their calculations.     

Efficient algorithms for Koblitz curves over fields of characteristic three

The nonadjacent form method of Koblitz [Advances in Cryptology (CRYPTO'98), in: Lecture Notes in Comput. Sci., vol. 1462, 1998, pp. 327–337] is an efficient algorithm for point multiplication on a family of supersingular curves over a finite field of characteristic 3. In this paper, a further discussion of the method is given. A window nonadjacent form method is proposed and its validity is proved. Efficient reduction and pre-computations are given. Analysis shows that more than 30% of saving can be achieved.     

Linear independence of digamma function and a variant of a conjecture of Rohrlich

Let ψ(x) denote the digamma function. We study the linear independence of ψ(x) at rational arguments over algebraic number fields. We also formulate a variant of a conjecture of Rohrlich concerning linear independence of the log gamma function at rational arguments and report on some progress. We relate these conjectures to non-vanishing of certain L-series.     

On the supersingular reduction of elliptic curves

Let a∈Q and denote byE _a the curvey ² = (x ² + l)(x + a). We prove thatE _a(F_p) is cyclic for infinitely many primesp. This fact was known previously only under the assumption of the generalized Riemann hypothesis. Research partially supported by NSERC grant A9418.     

Class Numbers of CM-Fields with Solvable Normal Closure

Stark conjectured that given a positive integer h, there are only a finite number of CM-fields L with class number equal to h. We prove this conjecture for fields L of degree 6 whose normal closure is solvable.