Extended viologen as a source of electric oscillations

A long organic molecule 1 with five bipyridinium functions separated by benzene rings (extended viologen) undergoes a reversible multi-step electron transfer. Here we show that this decacation accepts electrons at the heterogeneous interface with the occurrence of the periodically changing electric reduction currents. According to the applied bias voltage the observed current-time dependence changes from chaotic through periodic and irregular to sinusoidal and finally to monotonous. A careful choice of the controlling parameters yields the sustained periodic sinusoidal currents lasting for a prolonged time. Oscillations stem from a mutual interplay of the heterogeneous supply of electrons and the homogeneous redox reactions (disproportionation) between the transient redox forms. In difference to many other electrochemical oscillating systems the described oscillations do not require any additional external impedance. The principle of these oscillatory currents may serve as a model of a truly 'molecular oscillator'.     

Preconditioning trace coupled 3d‐1d systems using fractional Laplacian

Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d‐1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominating computational complexity. Preconditioning for a system of two elliptic problems posed, respectively, in a three‐dimensional domain and an embedded one dimensional curve and coupled by the trace constraint is discussed. Investigating numerically the properties of the well‐defined discrete trace operator, it is found that negative fractional Sobolev norms are suitable preconditioners for the Schur complement of the system. The norms are employed to construct a robust block diagonal preconditioner for the coupled problem.     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

Scaling in second order electron correlation calculations of potential energy curves and spectroscopic constants

The determination of potential energy curves and spectroscopic constants using the method of scaling in second order electron correlation calculations is investigated. An application to the ground state of the fluorine molecule is described using full fourth order many-body perturbation theory within two basis sets.     

Some open categorical problems inTop

In this paper, a pendant to a recent survey paper, the authors discuss several open problems in categorical topology. The emphasis is on topology-oriented problems rather than on more general category-oriented ones. In fact, most problems deal with full subconstructs or superconstructs of the constructTop of topological spaces and continuous maps.     

Simultaneous production and purification ofBacillus subtilis α-amylase

Production of α-amylase withB. subtilis CCM 2722 in an aqueous two-phase polyethylene glycol/dextran system integrated with product purification by affinity chromatography on crosslinked starch during cultivation was studied. The medium was drawn from the bioreactor to the external settler during fermentation. After phase separation in the settler the dextran-rich bottom phase with cells was returned to the bioreactor. The PEG-rich top phase was pumped to the column with crosslinked starch and returned to the bioreactor after α-amylase adsorption. The same volumetric productivities, 0.53 U/mL/h, were reached in both batch and described process, but total productivity of the latter method was much higher owing to shortening upstream and downstream processing time. The enzyme of 98% homogenity in 95% yield was obtained after its elution from the column.     

Numerical experiments with two approximate inverse preconditioners

We present the results of numerical experiments aimed at comparing two recently proposed sparse approximate inverse preconditioners from the point of view of robustness, cost, and effectiveness. Results for a standard ILU preconditioner are also included. The numerical experiments were carried out on a Cray C98 vector processor. This work was partially supported by the GA AS CR under grant 2030706 and by the grant GA CR 205/96/0921.     

Progress in Optical Waveguiding Thin Films

Overview of recent activities in the development of active and passive thin film waveguides, waveguide lasers and laser-deposited waveguiding films is given. Published results and parameters are summarized. The focus is on films fabricated by laser deposition.     

S-matrices

A new class of so called S-matrices is introduced which allows investigating links between various known classes of matrices such as Vandermonde matrices, Hankel matrices, companion matrices, etc. For complex S-matrices, the problem of decomposition into a quasidirect sum (a sum for which the sum of the ranks of the summands equals the rank of the given matrix) of indecomposable complex S-matrices is completely solved, and the uniqueness of such a decomposition is proved.