The eigenvalue field is a splitting field

Let K be an algebraically closed field of arbitrary characteristic and F < K a subfield. If is an irreducible semigroup of matrices such that the spectra of all the elements of are contained in F, then is conjugate to a subsemigroup of M _n (F). Research supported in part by the Ministry of Higher Education, Science, and Technology of Slovenia. Received: 6 April 2006     

Fermi-liquid versus non-Fermi-liquid behavior in triple quantum dots

We study the effect of electron hopping in triple quantum dots modeled by the three-impurity Anderson model. We determine the range of hopping parameters where the system exhibits the two-channel Kondo effect and has non-Fermi-liquid properties in a wide temperature interval. As this interval is entered from above, the conductance through the side dots increases to a half of the conductance quantum, while the conductance through the system remains small. At lower temperatures the conductance through the system increases to the unitary limit as the system crosses over to the Fermi-liquid ground state. Measuring the differential conductance in a three-terminal configuration provides an experimental probe into the NFL behavior.     

Car-Parrinello simulation of an O-H stretching envelope and potential of mean force of an intramolecular hydrogen bonded system: application to a Mannich base in solid state and in vacuum

Car-Parrinello molecular dynamics (CPMD) study was performed for an anharmonic system-an intramolecularly hydrogen bonded Mannich-base-type compound, 4,5-dimethyl-2(N,N-dimethylaminemethyl)phenol, to investigate the vibrational spectrum associated with the O-H stretching. Calculations were carried out for the solid state and for an isolated molecule. The classical CPMD simulation was performed and then the proton potential snapshots were extracted from the trajectory. The vibrational Schrodinger equation for the snapshots was solved numerically, and the (O-H) envelope was calculated as a superposition of the 0-->1 transitions. The potential of mean force for the proton stretching mode was calculated from the proton vibrational eigenfunctions and eigenvalues incorporating statistical sampling, nuclear quantum effects, and effects of the environment. Perspectives for application of the presented methodology in the computational support of biocatalysis are given in the study.     

Electrochemical kinetics of porous, carbon-decorated LiFePO4 cathodes: separation of wiring effects from solid state diffusion

We try to identify the rate-determining step of electrochemical kinetics of a LiFePO(4)-carbon composite electrode by varying the mass of electrode and, additionally, by varying the charge-discharge current in a wide range. It is shown that the reversible capacity is almost independent of electrode mass at currents lower than ca. 1 C (170 mAh g(-1)). At higher currents, however, the reversible capacity starts to drop significantly. The electrode resistance determined from the corresponding polarization voltage shows inverse proportionality with mass at currents smaller than 1 C. At higher currents the electrode resistance is almost independent of electrode mass. We conclude that at lower currents (below 1 C) the main transport step is related to the active particles themselves (either to incorporation reaction or solid state diffusion of Li). At higher currents the contribution of electronic and ionic transport towards the active particles becomes substantial and should be taken into account when designing high-rate insertion electrodes.     

Formation and structure elucidation of two novel spiro[2H-indol]-3(1H)-ones

The molecular structures of two byproducts 1,1'-diphenyl-3',4'-dihydrodispiro[indole-2,2'-furan-5',2'-indole]-3,3'(1H, 1'H)-dione (3) and 1,5'-diphenyl-4',5'-dihydro-3'H-spiro[indole-2,2'-pyrano[3,2-b]indol]-3(1H)-one (4), which accompanied the rearrangement of 3-hydroxy-3-methyl-1-phenylquinoline-2,4(1H,3H)-dione (1) to 2-hydroxy-2-methyl-1-phenyl-1,2-dihydro-3H-indol-3-one (2), have been elucidated by NMR, MS, and X-ray diffraction.     

Simulation of slow reaction with quantum character: Neutral hydrolysis of carboxylic ester

By computer simulation, using both quantum and classical dynamics, we determined the rate constant and the kinetic isotope effect of the rate-determining step in the neutral hydrolysis of p-methoxyphenyl dichloroacetate in aqueous solution. This step involves a proton transfer concerted with the formation of a C O bond. A method of biased sampling was used; the Gibbs free energy of the biased configuration from which proton transfer is likely to occur was determined by a combination of semiempirical quantum calculations and thermodynamic integration. The proton dynamics was modeled with the quantum-dynamical density matrix evolution method that includes nonadiabatic pathways. The proton dynamics is driven by a fluctuating proton potential that was derived from a classical molecular dynamics simulation of the system including solvent. The calculated rate constant of 3×10⁻² s⁻¹ agrees within the error of the calculation with the experimentally observed value of 2.78×10⁻³. The calculated pseudo-first-order kinetic isotope effect of 3.9 is in good agreement with the experimentally observed value of 3.2. The results show the feasibility of computational approaches to slow reactions in complex environments, where proton transfer with an essential quantum-dynamical nature is the rate-limiting step. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 886–895, 1999     

Velocity autocorrelation spectra of fluid in porous media measured by the CPMG sequence and constant magnetic field gradient

Carr-Purcell-Meiboom-Gill (CPMG) train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency domain instead of in the time domain as with the two-pulse gradient spin echo. The frequency range of this novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO2) and provides comprehensive information about the molecular restricted motion as well as about the structure of the medium.     

Measurement of temperature and temperature gradient in?millimeter samples by chlorine NQR

A mini-thermometer based on the ³⁵Cl nuclear quadrupole resonance (NQR) frequency temperature dependence in the chlorates KClO₃ and NaClO₃ was built and successfully tested by measuring temperature and temperature gradient at 77 K and higher in about 100 mm³ active volume of a mini Joule–Thomson refrigerator. In the design of the tank-circuit coil, an array of small coils connected in series enabled us (a) to achieve a suitable ratio of inductance to capacity in the NQR spectrometer input tank circuit, (b) to use a single crystal of KClO₃ or NaClO₃ (of 1–2 mm³ size) in one coil as a mini-thermometer with a resolution of 0.03 K and (c) to construct a system for measuring temperature gradients when the spatial coordinates of each chlorate single crystal within an individual coil are known.     

Semidefinite approximations for quadratic programs over orthogonal matrices

Finding global optimum of a non-convex quadratic function is in general a very difficult task even when the feasible set is a polyhedron. We show that when the feasible set of a quadratic problem consists of orthogonal matrices from \mathbbR^n×k{\mathbb{R}^{n\times k}} , then we can transform it into a semidefinite program in matrices of order kn which has the same optimal value. This opens new possibilities to get good lower bounds for several problems from combinatorial optimization, like the Graph partitioning problem (GPP), the Quadratic assignment problem (QAP) etc. In particular we show how to improve significantly the well-known Donath-Hoffman eigenvalue lower bound for GPP by semidefinite programming. In the last part of the paper we show that the copositive strengthening of the semidefinite lower bounds for GPP and QAP yields the exact values.