Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Experimental determination of isotope shifts in Mg I

The isotope shift in the Mg l transitionsλλ 5167, 5172 and 5183Å (3s3p ³ P-3s4s ³ S) andλ 5528 Å (3s3p ¹ P 3s4d ¹ D) has been measured for the isotopes²⁴Mg,²⁵Mg and²⁶Mg. The hyperfine structure of theλ 5167 Å line has been studied and theA andB factors for the 3s4s ³ S ¹ level in²⁵Mg determined. The measurements were made with separated isotopes using a scanning Fabry-Perot interferometer.     

On the fifth forces

We discuss the possibility of fifth forces in relativistic gravitation theories of fourth order. The fifth force may be an analog to the weak forces in the theories of electroweak interactions.     

Symmetric and Rees algebras of Koszul cycles and their Gröbner bases

In this paper we study the symmetric algebra S(E _i ) and Rees algebra R(E _i ) of the modules E _i of i-cycles of the Koszul complex associated with the sequence of indeterminates of a polynomial ring . For i=2 and i=n–2 we show that is a d-sequence on S(E _i ) and R(E _i ) and we determine Gröbner bases and Sagbi bases related to these algebras. Mathematics Subject Classification (2000):13A30, 13D02, 13H10, 13P10The second author is grateful to the National Natural Science Foundation of China for support.Part of this work was made while the third author was visiting the Fachbereich Mathematik und Informatik der Universität Essen, to which he would like to thank for its hospitality.     

Theory of perpendicular arrays

The cryptographical theory of unconditional secrecy and authentication is based on design-like structures called perpendicular arrays in the combinatorial literature. In order to meet the cryptographical requirements some additional and rather natural homogeneity conditions have to be satisfied. We develop a theory of these structures. Topics include bounds on the size, recursive and direct constructions using designs and permutation groups, as well as a link to Room cubes. © 1994 John Wiley & Sons, Inc.     

CO adsorption on Cu(1 1 1) and Cu(0 0 1) surfaces: Improving site preference in DFT calculations

CO adsorption on Cu(1 1 1) and Cu(0 0 1) surfaces has been studied within ab initio density functional theory (DFT). The structural, vibrational and thermodynamic properties of the adsorbate–substrate complex have been calculated. Calculations within the generalized gradient approximation (GGA) predict adsorption in the threefold hollow on Cu(1 1 1) and in the bridge-site on Cu(0 0 1), instead of on-top as found experimentally. It is demonstrated that the correct site preference is achieved if the underestimation of the HOMO–LUMO gap of CO characteristic for DFT is corrected by applying a molecular DFT + U approach. The DFT + U approach also produces good agreement with the experimentally measured adsorption energies, while introducing only small changes in the calculated geometrical and vibrational properties further improving agreement with experiment which is fair already at the GGA level.     

Theoretical estimates for proton-NMR spin–lattice relaxation rates of heterometallic spin rings

Heterometallic molecular chromium wheels are fascinating new magnetic materials. We reexamine the available experimental susceptibility data on MCr₇ wheels in terms of a simple isotropic Heisenberg Hamiltonian for M=Fe, Ni, Cu, and Zn and find in that FeCr₇ needs to be described with an iron–chromium exchange that is different from all other cases. In a second step we model the behavior of the proton spin lattice relaxation rate as a function of applied magnetic field for low temperatures as it is measured in nuclear magnetic resonance (NMR) experiments. It appears that CuCr₇ and NiCr₇ show an unexpectedly reduced relaxation rate at certain level crossings.