Synthesis of nonlinear control systems invariant under perturbations

For nonlinear control systems with perturbations, we consider the problem of synthesis of perturbation-invariant characteristics (invariant functions) with the use of feedbacks. The existence of invariant functions is related to a decomposition of the control system for which the quotient system is independent of perturbations. We present conditions for the existence of such quotient systems, which are certain systems of partial differential equations. The synthesizing controls are found from these equations.     

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Ohne Zusammenfassung     

Polyalkoxybenzenes from plant raw materials 1. Isolation of polyalkoxybenzenes from CO2 extracts of Umbelliferae plant seeds

For the search for a domestic natural source of allylpolyalkoxybenzenes and development of an effective process for their isolation, CO₂ extracts of several varieties of parsley, dill, celery, caraway, and nutmeg were analyzed systematically for the first time by GC/MS and GLC techniques. The varieties with high contents of myristicin, elemicin, allyltetramethoxybenzene, apiol, and dillapiol were identified. The conditions of CO₂ extraction for obtaining concentrates with minimum contents of the distillation residues were selected. Using high performance fractional distillation, polyalkoxyallylbenzenes with 98–99% purity were isolated from the concentrates on a pilot unit. By isomerization of some allylbenzenes followed by ozonolysis under specially selected conditions, apiol-and dillapiolaldehydes were obtained in 75–80% yields. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2364–2371, December, 2007.     

Isolation of the Trivial Part of a Nonlinear Control System by Factorization: II

The problem of constructing aggregated systems (quotient systems) of the simplest form for nonlinear control systems is considered. This factorization reduces the original control system to a decomposition, which permits one to reduce the dimension of control problems.     

Simulation of Itraconazole Encapsulation by Novel Biocampatible Dendritic Compounds

Summary: To enhance the dissolution rate of itraconazole, the novel macromolecular biocompatible dendritic compounds were selected. The possible drug encapsulation was evaluated by the calculated difference between potential energies of the individual dendrimers and structures having one itraconazole molecule near the dendrimer core. The structures with the decanediol spacers and with the core presented by 1,2,3,4-butanetetracarboxylic acid demonstrated better energetic effects to be good candidates as a drug delivery carrier for itraconazole pharmaceutical applications. Additional simulations with the less bulky modeling structures with different cores, using molecular dynamic procedure, allowed us to obtain the best results with the tetracarboxy benzene core.     

On the Circumference of 3-Connected Quasi-Claw-Free Graphs

A graph G is quasi-claw-free if it satisfies the property: d(x,y)=2 ⇒ there exists such that . In the paper, we prove that the circumference of a 3-connected quasi-claw-free graph G on n vertices is at least min{4δ−2,n} and G is hamiltonian if n≤5δ−5.     

Mode competition in multi-core fiber amplifier

3D beam propagation numerical code and a newly developed optical mode solver were implemented for studies on the recently experimentally realized Yb fiber amplifier with 7-core hexagonal structure. It was found that the launched seven single-frequency beams matched with the cores converge to a wave field with permanently diminishing space beating patterns, but the result is sensitive to phases of separate beams. Namely, at a spread of phases of individual beams within a few tenths of radian, the convergence of the wave field to the in-phase mode is observed, while at phases random spread on the order of π the out-of-phase mode is dominating. Such behavior is observed at strong gain saturation in the cores. Both effects take place even if the guiding index of the cores fluctuates within a limited range. The mode solver predicts that the in-phase mode has the minimal small signal gain, and the gain of the out-of-phase mode is maximal one. This fact proves that there is no strict correlation between modal gains and amplification in strong saturated multi-core fiber. The smaller core index step significantly improves the convergence of the amplified radiation to the in-phase mode. An approach to the waveguide structure tailoring is described which assures the single in-phase mode stability.