Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.     

Prox-regular functions in variational analysis

The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not.

     

Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results

This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a pseudo-regular solution which generalizes Robinson's concept of a strongly regular solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.This work was based on research supported by the National Science Foundation under grant ECS-8717968.     

Efficiency of composite vs. conically shaped chromatographic columns

The theory of composite chromatographic columns has been re-examined and general equations relating their efficiency to those of individual columns were derived. The derivations were based on elementary principles without reference to the principle of variance additivity. Derived also, were general equations for the efficiency of columns with continuously varying diameters, HETP and other properties from which formulae for special cases of practical interest were deduced. An example comparing the efficiencies of two columns, one conical and the other composite was given. The calculations show clearly that the conical column is superior in efficiency for the same total length and total retention volume.     

Theoretical studies on the reaction path and dynamics of the reaction CH_3+H_2O→CH_4+OH

The reaction path, the dynamical properties along the reaction path and CVT rate constants are computed by the ab initio MO method, the reaction path Hamiltonian theory and the variational transition state theory. The results show that the effect of the electron correlation energy on activation barrier is large, the recrossing and tunneling effects exist in the reaction.     

On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.     

Radiation: Waves or particles? A quantized approach to time

A fundamental difficulty in theoretical physics is the dual and apparently incompatible interpretations of radiation as showing both continuous and extensive wave properties but also those of discrete atomic or smaller individual particles. Some of these contradictions are outlined. The explanation offered is of a quantized nature of time; units t_o=h/m_oc² for a particle at rest, and of similar interval unit s_o when in relative motion, with conventional relativistic corrections.

For many purposes this form of quantization replaces the need for a wave concept which then appears as a mathematical approach, chosen to avoid the physical concept of an intrinsicc time for any particle, just as we have for its intrinsic mass, spin and electrical charge. t_o and s_o are directly related to its frequency, energy and mass. The uncertainty principle and interference relations follow directly from this model, without any physical wave concept.     

Analysis of the pungent principles of ginger and grains of paradise by high-performance liquid chromatography using electrochemical detection

Summary The pungent principles of ginger and grains of paradise are examined using a reversed-phase HPLC column. An electrochemical detector is used to selectively detect the phenolic gingerols and shogaols. The retention indices of the compounds are compared using methanowater and acetonitrile-water as eluents.Presented at the 14th International Symposium on Chromatography London, September, 1982     

Chemical reaction dynamics of PeCB and TCDD decomposition: A tight‐binding quantum chemical molecular dynamics study with first‐principles parameterization

The decomposition reaction dynamics of 2,3,4,4′,5‐penta‐chlorinated biphenyl (2,3,4,4′,5‐PeCB), 3,3′,4,4′,5‐penta‐chlorinated biphenyl (3,3′,4,4′,5‐PeCB), and 2,3,7,8‐tetra‐chlorinated dibenzo‐p‐dioxin (2,3,7,8‐TCDD) was clarified for the first time at atomic and electronic levels, using our novel tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization. The calculation speed of our new method is over 5000 times faster than that of the conventional first‐principles molecular dynamics method. We confirmed that the structure, energy, and electronic states of the above molecules calculated by our new method are quantitatively consistent with those by first‐principles calculations. After the confirmation of our methodology, we investigated the decomposition reaction dynamics of the above molecules and the calculated dynamic behaviors indicate that the oxidation of the 2,3,4,4′,5‐PeCB, 3,3′,4,4′,5‐PeCB, and 2,3,7,8‐TCDD proceeds through an epoxide intermediate, which is in good agreement with the previous experimental reports and consistent with our static density functional theory calculations. These results proved that our new tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization is an effective tool to clarify the chemical reaction dynamics at reaction temperatures. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The index of ideality of correlation: improvement of models for toxicity to algae

Toxicity to algae is important characteristic of substances from ecologic point of view. The CORAL software (http://www.insilico.eu/coral) gives possibility to build up model of toxicity to algae using data on the molecular architecture and experimental toxicity, without additional data on physicochemical and/or biochemical parameters. Considerable improvement of the model is observed in the case of using the index of ideality of correlation (IIC) in the role of additional criterion of predictive potential. The IIC is calculated with using of the correlation coefficient between experimental and calculated values of endpoint for the calibration set, with taking into account the positive and negative dispersions between experimental and calculated values. The best model calculated with use the IIC is characterized (the validation set) by n?=?50, r²?=?0.947, RMSE?=?0.401 whereas, model calculated without use the IIC is characterized by n?=?50, r²?=?0.805, and RMSE?=?0.539. The suggested models are built up in accordance to five OECD principles.