Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model

A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.     

5‐Methyl­sulfanyl‐3H‐1,2,3‐triazolo[4,5‐d]pyrimidin‐7(6H)‐one (2‐methyl­thio‐8‐aza­xanthine) monohydrate

The title compound, C₅H₅N₅OS·H₂O, crystallizes as the monohydrate. Disorder of the H atoms that participate in the hydrogen bonds implies that two different tautomers are present in the crystal structure, one of them with both acidic H atoms attached to the imidazole ring and the other with one acidic H atom on each ring.     

Rigid motions in relativity

Starting with a simple characterization of pairs of rigidly joined straight world lines, successive generalizations are obtained up to the most general case which allows us to establish the various definitions of rigid motions in relativity (both special and general).     

Relaxation of (111) silicon surface atoms from studies of Si4H9 clusters

Self-consistent Hartree-Fock and generalized valence bond calculations have been performed on clusters modeling the (111) silicon surface. We find that the surface state is accurately described as a dangling bond surface orbital with 93% p character. We determined the optimum relaxation of the surface layer to be 0.08 Å toward the second layer. In the positive ion, the surface atom relaxes toward the second layer by an additional 0.30 Å and for the negative ion the surface atom moves toward the vacuum 0.25 Å. The vertical ionization potential was found to be 5.78 eV (experimental values are 5.6 – 5.9 eV) while the calculated adiabatic electron affinity is 3.02 eV.     

Relaxation of (111) silicon surface atoms from studies of Si4H9 clusters

Self-consistent Hartree-Fock and generalized valence bond calculations have been performed on clusters modeling the (111) silicon surface. We find that the surface state is accurately described as a dangling bond surface orbital with 93% p character. We determined the optimum relaxation of the surface layer to be 0.08 Å toward the second layer. In the positive ion, the surface atom relaxes toward the second layer by an additional 0.30 Å, and for the negative ion the surface atom moves toward the vacuum 0.25 Å. The vertical ionization potential was found to be 5.78 eV (experimental values are 5.6 – 5.9 eV) while the calculated adiabatic electron affinity is 3.02 eV.     

A Structure Theorem for Free Temporal Algebras

In this paper an algebraic version for temporal algebras of the logical filtrations for modal and temporal logics is analysed. A structure theorem for free temporal algebras and also some results with regard to the variety of temporal algebras are obtained.     

Rates of desorption from solid surfaces: Coverage dependence

The recently developed Classical Stochastic Diffusion Theory is applied to obtain the coverage dependence of desorption rates for Xe on W(111). Using the attractive Xe-Xe potential from gas phase experiments, we find a strong coverage dependence in the desorption rates and calculate Temperature Programmed Desorption Spectra (for a potential with reduced attractiveness) that are in excellent qualitative agreement with experimental results. We also investigated the effect of purely repulsive adsorbate-adsorbate interactions where we find, for some coverage ranges, that two different adsorption configurations can be stable (at different temperatures) leading to a marked change in the corresponding desorption rates and to distinct non-Arrhenius behavior.     

Tangent algebraic subvarieties of vector fields

An algebraic commutative group is associated to any vector field on a complete algebraic variety . The group acts on and its orbits are the minimal subvarieties of which are tangent to . This group is computed in the case of a vector field on .

     

Flexible contracting theory and case examples

When companies or governmental agencies arrange for contracts that call for deliveries over extended periods of time, arrangements are often made to adjust the final prices for exogenous changes in the costs of production. This paper shows, under specified conditions, how contracts can be devised which allow for price changes but at the same time still provide incentives for the producing unit to be efficient. For example, only under very specific conditions will a “pass-through” arrangement be acceptable. We show how the techniques of Geometric Programming applied to the economic theory of production can be used to analyze such problems.