THE MITRA‐WAN FORESTRY MODEL: A DISCRETE‐TIME OPTIMAL CONTROL PROBLEM

In this paper, we present some new properties of the Mitra‐Wan forestry model written as a discrete‐time optimal control problem. For this problem, the set of stationary states is characterized. For the optimal long‐run management, we consider the following optimality criteria: average optimality, good control policies, bias optimality, and overtaking optimality. We establish relationships between these criteria and show that the value of average optimal policies is constant and equals the value in the optimal stationary state.     

Self-assembly of an Octa-uranate Cage Complex with a Rigid bis-Catechol Ligand

While the terminally protected tripeptide Boc-Phe-Gly-m-ABA-OMe I (m-ABA, meta-amino benzoic acid) is an excellent gelator of aromatic organic solvents, another similar tripeptide Boc-Leu-Gly-m-ABA-OMe II, where the Phe residue of peptide I is replaced by Leu, cannot form gels with the same solvents. The morphology of the gels of peptide I, characterised by the field-emission scanning electron microscopy and high-resolution transmission electron microscopy, reveals the formation of nanofibrous networks which are known to encapsulate solvent molecules to form gels. The wide-angle X-ray scattering studies of the gels suggest the β-sheet-mediated self-assembly of peptide I in the formation of a nanofibrous network, where π-stacking interactions of Phe play an important role in the self-assembly and gel formation. The dried gel of peptide I observed between crossed polarisers after binding with a physiological dye, Congo red, shows a bluish-green birefringence, a characteristic of amyloid fibrils.     

Mesophase behaviour of binary mixtures of bent-core and calamitic compounds

The mesophase behaviour of binary mixtures of bent-core and calamitic liquid crystals is presented. The nematogenic 4,6-dichloro-1,3-phenylene bis[4′-(10-undecen-1-yloxy)-1,1′-biphenyl-4-carboxylate] (I) was the banana-shaped component. As the calamitic compound ethyl 4′-(9-decen-1-yloxy)-1,1′-biphenyl-4-carboxylate (II), similar to one arm of the bent-core molecule, was used which exhibits smectic phases in a wide temperature range. A total of six mixtures with different compositions were prepared and studied by polarising optical microscopy, differential scanning calorimetry and X-ray diffraction on non-oriented samples. In the mixtures, a nematic phase is not concomitant with smectic A phase, and the temperature range of both phases highly depends on the concentration of the comprising compounds. Lowered melting temperatures have been observed for all mixtures with respect to that of the pure compounds. Unforeseen finding is the induction of a monotropic SmC phase in mixtures with lowest concentration of the bent-core compound. Semi-empirical quantum-chemical calculations have also been performed. Based on the calculated molecular conformation, as well as on collected X-ray diffraction data, a model for a possible self-assembly of the banana-shaped and calamitic compounds is proposed.     

Permeability and release properties of cyclodextrin-containing poly(vinyl chloride) and polyethylene films

In this study poly(vinyl chloride) (PVC) and polyethylene (PE) films with 0%, 1.0%, 1.5% and 2.0% β-cyclodextrin (BCD)-content were prepared and their permeation properties were characterized using model flavours like carvone, vanillin and diacetyl. The complex forming carvone and vanillin could penetrate through the films containing cyclodextrin, while diacetyl, which has poor complex forming ability with β-cyclodextrin could not. The effect of CD-concentration on vanillin permeation was found to depend on CD concentration and on the thickness of the films. The leaching of plasticizers from the polymer matrix to the contacting fluid is a drawback of PVC. The presence of β-cyclodextrin in the film results in slower release of plasticizers.     

Homogenization of the Stokes equations with a random potential

Homogenization of the Stokes equations in a random porous medium is considered. Instead of the homogeneous Dirichlet condition on the boundaries of numerous small pores, used in the existing work on the subject, we insert a term with a positive rapidly oscillating potential into the equations. Physically, this corresponds to porous media whose rigid matrix is slightly permeable to fluid. This relaxation of the boundary value problem permits one to study the asymptotics of the solutions and to justify the Darcy law for the limit functions under much fewer restrictions. Specifically, homogenization becomes possible without any connectedness conditions for the porous domain, whose verification would lead to problems of percolation theory that are insufficiently studied. Translated fromMatematicheskie Zametki, Vol. 59, No. 4, pp. 504–520, April, 1996. The work of the first author was supported by the INTAS under grant No. 93-2716.     

Linear circular dichroism in nonlinear absorption of light in a quantum well

The far infrared absorption spectrum caused by optical transitions of holes between size-quantization subbands is calculated for p-GaAs/AlGaAs(001) quantum-well structures. The selection rules for optical transitions at the center of the two-dimensional Brillouin zone are determined. Allowance is made for resonant saturation of one-photon electronic transitions between size-quantized subbands of light and heavy holes. The linear circular dichroism in one-photon nonlinear (resonant) and two-photon absorption of light in a size-quantized well are investigated. Fiz. Tverd. Tela (St. Petersburg) 40, 1347–1349 (July 1998)     

The nature of isostructural spinodal decomposition in the Al-Zn system

The electronic structure and thermodynamic properties of disordered Al-Zn alloys are investigated in the coherent potential approximation by the KKR-ASA method. Analysis of the electronic density of states and the Fermi surfaces of disordered alloys reveals the presence of eight electronic topological transitions in the concentration interval from 0 to 70 at. % Zn. It is shown that the passage of the Fermi level through two minima of the density of states, which are due to the superposition of different types of electronic topological transitions, gives rise to singularities in the concentration dependence of the second derivative of the thermodynamic potential at points corresponding to the boundaries of the region of isostructural decomposition of the high-temperature solid solution, according to the phase diagram of the Al-Zn system. Fiz. Tverd. Tela (St. Petersburg) 39, 593–596 (April 1997)     

Cu(I) complexes with oligo- and polyarylene phosphites

Monovalent copper complexes with oligo- and polyarylene phosphites were obtained. Complexation takes place due to coordination of copper with the phosphorus atom.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 5, pp. 1198–1201, May, 1991.