Meromorphic functions connected with polylogarithms

M. V. Lomonosov Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 1, pp. 88–91, January–March, 1991.     

Tangent cones and Dini derivatives

We prove a property of the Bouligand tangent cone to the epigraph (or to the graph) of a locally Lipschitz function. It is also shown how this result can be used in determining Dini sequences. Finally, some relationships between such a cone and Dini derivatives are provided.     

Mössbauer studies of iron uptake,ferritin and hemoglobin synthesis and denaturation in erythroid cell cultures

Mössbauer studies in murine (MEL) and human K-562 erythroleukemia cell lines have been utilized to study the fate of iron during intracellular Hb synthesis and denaturation. The results showed that ferritin can serve as an intermediate iron pool for Hb synthesis and for storage of iron released during intracellular Hb denaturation.     

Mathematical problems of liquid crystal flows

This article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius–Duhem inequality.     

The Most Critical Path in a PERT Network

The classical PERT approach uses the path with the largest expected duration as the critical path to estimate the probability of completing a project by a given deadline. However, in general, such a path is not the ‘most critical’ path and does not provide the smallest estimate for the probability of completion time. This paper studies the ‘most critical path’ problem and formulates it as an optimal path problem in a deterministic network with a two-attribute fractional objective function. An exact solution approach is presented for the optimal path problem which also gives the solution to the most critical path problem. The illustrative examples as well as our computational results demonstrate that the proposed algorithm provides estimates for the probabilities of completion time that are much more accurate than those of the classical approach.     

HPLC study of starch hydrolysis products obtained with α-amylase from bacillus amyloliquefaciens and bacillus licheniformis

Two bacterial α-amylases from new industrial strains were studied: α-amylase fromBacillus amyloliquefaciens CCM 3502 (Czechoslovak) and thermostable α-amylase fromBacillus licheniformis 44MB82 (Bulgarian). The thermostable enzyme hydrolyzed starch mainly to dextrins, and after 1 h, 30% of the products were oligosaccharides. TheB. amyloliquefaciens enzyme produced more maltooligosaccharides than the first enzyme (B. licheniformis). Within 1 h, up to 80% of the substrate were hydrolyzed, giving different spectrum of oligosaccharides in comparison with the thermostable one.     

Hamiltonian graph representation of zeolite frameworks and Si,Al ordering in the framework

In the first part, a topological characterization of various zeolite frameworks is performed on the basis of the Hamiltonian graph. It affords a simple representation of the framework connectivity, and presents some possibility of the classification as well as the prediction of unknown frameworks. In the second part, a simple and direct method based on the connectivity matrix is presented, by which all the possible Al distributions in a given framework are derived exhaustively under the restriction of Loewenstein's rule. An example of Al preference site determination is applied for zeolite ZSM-5 and compared with the result by the SCF-MO method.     

Rotation Part of the Dielectric Permittivity of Water Vapor for Different Spectral Line Profiles

We estimate the possible influence of spectral line profile (Lorentz profile, Van Vleck–Weisskopf profile, and profile obtained by solving kinetic equation) on the rotation part of the dielectric permittivity of water-vapor monomers. Spectral regions corresponding to long-wavelength (static) and high-frequency (optical) limiting cases as well as regions in close proximity to resonances of various intensities are considered. The studied effects are compared with the corresponding effects on water-vapor absorption coefficient, which are related to factors determining the line-shape structure.     

Effects of neutron skin on the excitation of isovector modes of neutron-rich nuclei

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.     

Quantum-networks: master equation and local measurements

Based on the SU(n)-algebra the Markoff master equation in discrete product space is reformulated to explicitly deal with composite systems. The resulting local (single node) and nonlocal (multi-node) state parameters allow a systematic approach to non-classical features of the state, like variance and covariance tensors. For local optical driving forces, inter-node interactions, and local damping channels the solution of the master equation is unraveled into stochastic quantum trajectories. Sampling leads to a joint distribution function in terms of those state parameters. Its linear moments define the ensemble-density matrix. The average variance and covariance are in terms of non-linear moments, which should be distinguished from their entirely statistical counterpairs. Non-classicality of the network dynamics is shown to reflect itself in the luminescence-photonstatistics.