Conjugate addition of pyrroles to α,β-unsaturated ketones using copper bromide as a catalyst

Copper bromide was used as a catalyst for the addition of pyrroles to enones. When both the reactants were used in equimolar amounts, mono and dialkylated products were obtained. However, the use of excess enone furnished only dialkylated products. Thus, copper bromide was shown to be an efficient catalyst for the dialkylation of pyrroles.     

Illumination dependence of I-V and C-V characterization of Au/InSb/InP(1 0 0) Schottky structure

The effects of surface preparation and illumination on electric parameters of Au/InSb/InP(100) Schottky diode were investigated, in the later diode InSb forms a fine restructuration layer allowing to block In atoms migration to surface. In order to study the electric characteristics under illumination, we make use of an He-Ne laser of 1 mW power and 632.8 nm wavelength. The current-voltage I(V_G), the capacitance-voltage C(V_G) measurements were plotted and analysed. The saturation current I_s, the serial resistance R_s and the mean ideality factor n are, respectively, equal to 2.03 × 10⁻⁵ A, 85 Ω, 1.7 under dark and to 3.97 × 10⁻⁵ A, 67 Ω, 1.59 under illumination. The analysis of I(V_G) and C(V_G) characteristics allows us to determine the mean interfacial state density N_ss and the transmission coefficient θ_n equal, respectively, to 4.33 × 10¹² eV⁻¹ cm⁻², 4.08 × 10⁻³ under dark and 3.79 × 10¹² eV⁻¹ cm⁻² and 5.65 × 10⁻³ under illumination. The deep discrete donor levels presence in the semiconductor bulk under dark and under illumination are responsible for the non-linearity of the C⁻²(V_G) characteristic.     

Balancing a Rotor with Two Coupled Perfectly Rigid Bodies

The steady motions of a vertical rotor balanced by two coupled perfectly rigid bodies (PRBs) are analyzed for stability. The rotor executes plane-parallel motions. The PRBs can rotate together about the rotor axis and about its transverse axes through equal angles but in opposite directions. It is established that when the mass of the PRBs is much less than that of the rotor and the rotor spins with a superresonant speed, only the basic steady motions, which are those of the best-balanced rotor, are asymptotically stable.     

Expansion of monomer units in poly(ethylene terephthalate) molecules under conditions of thermal and zero-point atomic vibrations

The temperature dependence of the expansion ?_C of trans conformers of the carbon skeleton of macromolecules in crystallized and amorphous poly(ethylene terephthalate) (PET) due to zero-point and thermal atomic vibrations is investigated by IR spectroscopy. It is found that the thermal expansion coefficient β_C jumpwise increases at the characteristic temperatures T _t and T _b. This increase is associated with the crossover from the quantum to classical statistics of torsional and bending vibration modes. The quantum and classical contributions to the expansion ?_C are determined for each mode. The quantum and classical contributions of the torsional vibrational mode in the amorphous polymer are approximately 1.5 times larger than those in the crystallized polymer. This effect is caused by an increase in the anharmonicity of torsional vibrations in the amorphous polymer.     

Nonlinear Theory of Spectra of Thermally Stimulated Currents in Complex Crystals with Hydrogen Bonds

The nonlinear theory of thermally stimulated depolarization currents is developed. The theory explains the processes of hetero- and homocharge relaxation in complex crystals with hydrogen bonds and allows the relaxation oscillator parameters to be calculated using the quadratic approximation for the external electric field.     

Time delay as a key to apoptosis induction in the p53 network

A feedback mechanism that involves the proteins p53 and mdm2, induces cell death as a controlled response to severe DNA damage. A minimal model for this mechanism demonstrates that the response may be dynamic and connected with the time needed to translate the mdm2 protein. The response takes place if the dissociation constant k between p53 and mdm2 varies from its normal value. Although it is widely believed that it is an increase in k that triggers the response, we show that the experimental behaviour is better described by a decrease in the dissociation constant. The response is quite robust upon changes in the parameters of the system, as required by any control mechanism, except for few weak points, which could be connected with the onset of cancer. Received 8 May 2002 / Received in final form 9 July 2002 Published online 17 September 2002     

Segregation in the Falicov--Kimball Model

The Falicov–Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov–Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two regions with a positive and a negative magnetization. Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with a small boundary. For the Falicov- Kimball model, this corresponds to having a single “compact” domain that has no heavy particles. Received: 21 June 2001 / Accepted: 4 January 2002     

Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps

We consider Markov processes built from pasting together pieces of strong Markov processes which are killed at a position dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood ratio process. The main tool is the consideration of the process between successive jumps – what we call ‘elementary experiments’ – and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions with interactions and immigrations. This revised version was published online in June 2006 with corrections to the Cover Date.