Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies . As applications, we establish the nonexistence ofsome difference sets and affine difference sets.     

Normsets and determination of unique factorization in rings of algebraic integers

The image of the norm map from to (two rings of algebraic integers) is a multiplicative monoid . We present conditions under which is a UFD if and only if has unique factorization into irreducible elements. From this we derive a bound for checking if is a UFD.

     

Atom-probe field ion microscopy

The atom probe field ion microscope (AP-FIM) is a combination of a field ion microscope and a time-of-flight mass spectrometer with a single ion detection sensivity. With the field ion microscope topology of a surface, surface reactions and surface modifications can be studied in atomic detail. By time-of-flight measurements surface layers and interface layers can be chemically analyzed atom by atom and atomic layer by atomic layer. Compositional variations according to surface or interface segregation, precipitations, or surface changes in corrosion or in electrochemical layer formation etc. can be studied quantitatively on a subnanometer scale. Some of our studies on related problems will be decribed briefly.     

A case study in conformation design: learning by doing

Efforts are described to design simple, fully flexible but conformationally preorganised omega-hydroxy-nonanoic acids that could serve as the conformation controlling unit in analogues of the potent protein-kinase C activator aplysiatoxin. Such analogues are macrodilactones incorporating the designed omega-hydroxy-nonanoic acid and 3,4-dihydroxy-pentanoic acid, which contains the pharmacophoric groups. The design process (replacement of CH(2) groups by an oxygen atom, annelation of a six-membered ring and placement of alkyl substituents) of the omega-hydroxy-nonanoic acids was monitored by force-field calculations. In the end of this process simple analogues of aplysiatoxin are proposed in which the proper disposition of the pharmacophoric groups is secured by a conformationally flexible but preorganised template structure as part of the macrodilactone ring.     

Evaluation of Multicenter Electronic Attraction, Electric Field and Electric Field Gradient Integrals with Screened and Nonscreened Coulomb Potentials over Integer and Noninteger n Slater Orbitals

By the use of complete orthonormal sets of -exponential-type orbitals, where ( = 1, 0, –1, –2,...) the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of nonscreened and Yukawa-like screened Coulomb potentials are expressed through the two-center overlap integrals with the same screening constants and the auxiliary functions introduced in our previous paper (I.I. Guseinov, J. Phys. B, 3 (1970) 1399). The recurrence relations for auxiliary functions are useful for the calculation of multicenter EA, EF and EFG integrals for arbitrary integer and noninteger values of principal quantum numbers, screening constants, and location of slater-type orbitals. The convergence of the series is tested by calculating concrete cases.     

Survey of ligand field parameters of strong field d complexes obtained from the g matrix

Using a newly proposed approach involving an internally consistent set of equations, the ligand field parameters Δ/ξ, V/ξ and k are obtained from literature values of the g matrix for strong field d⁵ systems of various conformations in which |Δ/ξ|≤10. Qualitative analysis of the observed results is done using the Angular Overlap Model, AOM.     

The relaxation field for the general case of electrolyte mixtures

The relaxation field for solutions of mixed electrolytes of any type is calculated. the calculation is based on the well-known treatment due to Fuoss-Onsager with the same distance parameter for all the ions in solution. A general conductance-continuity equation has been established and an improved iterative method of calculation, using Laplace transforms, is proposed. The relaxation-field results are derived to the second iteration in the perturbation method of integration.     

The electronic spectrum of VCr

The electronic spectrum of VCr has been studied using the complete-active-space self-consistent field complete-active-space second-order perturbation theory approach. Potential-energy curves for 12 electronic states have been computed. Transition energies, with respect to the X² ground state, for some of the calculated electronic states are (with possible experimental values within parentheses) 0.53 eV (0.56) for A²⁺, 1.03 eV (1.14) for A⁴, 1.20 eV (1.14) for B², 1.45 eV (1.51) for B⁴, 1.60 eV (1.51, 1.78) for C², and 1.61 eV (1.63) for A^4–. AcknowledgementsThe research reported in this communication was supported by a grant from the Swedish Natural Science Research Council (NFR). S. Alex and D.G. Leopold are acknowledged for providing results from their negative ion photoelectron spectroscopy on VCr.Contribution to Björn Roos Honorary Issue     

Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions

We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in the plane occupy the imaginary axis from –i to –i_c and i_c to i for some _c. They also occupy the diamond shape of four straight lines from ±i_c to _c and from ±i_c to –_c. The fugacity acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented.