Optimal control synthesis for the constrained bilinear biquadratic regulator problem

Optimal process control with control constraints is a challenging task related to many real-life problems. In this paper, a single input continuous time constrained linear quadratic regulator problem, is defined and fully solved. The constraints include both bilinear inequality constraints and customary control force bounds. As a first step, the problem is reformulated as an equivalent constrained bilinear biquadratic optimal control problem. Next, Krotov’s method is used to solve it. To this end, a sequence of improving functions suitable to the problem’s new formulation is constructed and the corresponding successive algorithm is derived. The required computational steps are arranged as an algorithm and proof outlines for the convergence and optimality of the solution are given. The efficiency of the suggested method is demonstrated by numerical example.     

Prediction of the activity of β-lactam antibiotics

The pharmacological properties of penam, 3-cepheme, and semisynthetic penicillins were predicted by means of the ORAKUL automated system. A comparative evaluation of the similarity between the structures of these compounds and the structures of 8800 biologically active substances in the data base of the system made it possible to uncover the high probability of the manifestation of anti-inflammatory, analgesic, antitumorigenic, antiallergic, and anticoagulant activity by structural analogs of -lactam antibiotics.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 555–564, April, 1992.     

Rectifiable Curves in Proximally Smooth Sets

Set-Valued and Variational Analysis - In this article we study some geometric properties of proximally smooth sets. First, we introduce a modification of the metric projection and prove its...     

Phase synchronization of chaotic oscillations in terms of periodic orbits

We consider phase synchronization of chaotic continuous-time oscillator by periodic external force. Phase-locking regions are defined for unstable periodic cycles embedded in chaos, and synchronization is described in terms of these regions. A special flow construction is used to derive a simple discrete-time model of the phenomenon. It allows to describe quantitatively the intermittency at the transition to phase synchronization. (c) 1997 American Institute of Physics.     

Palladium and platinum catalyzed hydroselenation of alkynes: SeH vs SeSe addition to CC bond

A mechanistic study of the hydroselenation of alkynes catalyzed by Pd(PPh₃)₄ and Pt(PPh₃)₄ has shown that the palladium complex gives products of both SeH and SeSe bond addition to the triple bond of alkynes, while the platinum complex selectively catalyzes SeH bond addition. The key intermediate of PhSeH addition to the metal center, namely Pt(H)(SePh)(PPh₃)₂, was detected by ¹H-NMR spectroscopy. The analogous palladium complex rapidly decomposes with evolution of molecular hydrogen. A convenient method was developed for the preparation of Markovnikov hydroselenation products H₂CC(SePh)R, and the scope of this reaction was investigated. The first X-ray structure of the Markovnikov product H₂CC(SePh)CH₂N⁺HMe₂·HOOCCOO⁻ is reported.     

2, 4-Dimethyl -5 -nitrofuran -3 -carboxylic acid and its derivatives

It is found that 2, 4-dimethyl-5-nitrofuran-3-carboxylic acid and its methyl ester can give comparatively stable anionic groups, which are prepared electrochemically and investigated by EPR. Their lives (80–100 sec) are 4- 5 times greater than the lives of other anionic groups of the 5-nitrofuran series previously studied. Starting from 2, 4-dimethyl-5-nitrofuran-3-carboxylic acid and 2, 4-dimethylfuran-3-carboxylic acid, two new semisynthetic penicillins are prepared, with activities basically extending to Gram-positive microorganisms, including forms of staphylcocci resistant to benzylpenicillin. Introduction of the nitro group into the furan ring increases the stability of penicillin to acid 79-fold. Low toxicity penicillins are synthesized (LD₅₀ 1000–1500 mg/kg).     

Sensing and fixation of NO2/N2O4 by calix[4]arenes

An approach toward visual detection and chemical utilization of NO(2)/N(2)O(4) is proposed, which employs simple calix[4]arenes. Exposure of tetra-O-alkylated calix[4]arenes 1 and 2, possessing either a cone or a 1,3-alternate conformation, to NO(2)/N(2)O(4), both in chloroform solution and in the solid state, results in deeply colored calixarene-nitrosonium (NO(+)) complexes. In the presence of a Lewis acid, such as SnCl(4), stable calixarene-NO(+) complexes 7 and 8 were isolated in a quantitative yield and characterized by UV-vis, FTIR, high-resolution (1)H NMR spectroscopy and elemental analysis. NO(+) is found encapsulated within the calixarene cavity, and stable charge-transfer complexes result with K(ass) > 10(6) M(-1) (CDCl(3)). The NO(+) encapsulation was also demonstrated in titration experiments with calixarenes 1, 2, and 5 and commercially available NO(+)SbF(6)(-) salt in chloroform. The complexation process is reversible, and the complexes dissociate upon addition of water and alcohol, recovering the parent calixarenes. Attachment of functionalized calix[4]arenes to silica gel was demonstrated, which afforded a solid material 15 capable of visual detection and entrapment of NO(2)/N(2)O(4). Calixarene-NO(+) complexes can be utilized for the NO(+) transfer processes and nitrosation reactions. The NO(+) guest transfer between two calixarene containers 2 and 5 was achieved and studied by UV-vis and (1)H NMR spectroscopy. Chemical fixation of NO(2)/N(2)O(4) was demonstrated through their quantitative transformation into the calixarene-NO(+) complex and its use as a nitrosonium transfer agent in the synthesis of N-nitrosoamides. These results may lead toward novel nitrogen oxides storing materials.     

Asymmetric induction in the reactions of 3-aryl-1,2,4-triazin-5(4H)-ones with C-nucleophiles

3-Aryl-1,2,4-triazin-5(4H)-ones, in the presence of N-protected amino acids, react with C-nucleophiles to form 1-acyl-6-Nu-3-aryl-1,6-dihydro-1,2,4-triazin-5(4H)-ones in high diastereomeric excess. This is the first case of the use of amino acids as chiral auxiliaries in nucleophilic additions to triazinones.     

Synthesis and cytotoxic properties of 7α-chloro-3-methyl-1,1-dioxoceph-3-ems, substituted with amide or keto group at position 4

7α-Chloro-3-methyl-1,1-dioxoceph-3-ems with amide or keto group at position 4 have been synthesized by structural modification of 7α-chloro-3-methyl-1,1-dioxoceph-3-em-4-carboxylic acid. Screening of these compounds for cytotoxic activity revealed compounds with specific activity against cancer cells in vitro, capable of effective inhibition of the growth of sarcoma S-180 in vivo. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, 1849–1859, December 2007.     

A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation;we construct a finite difference scheme on a priori (se-quentially) adapted meshes and study its convergence.The scheme on a priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution,which allows us to find a priori a subdomain where the computed solution requires a further improvement.This subdomain is defined by the perturbation parameterε,the step-size of a uniform mesh in x,and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for im- proving the solution.To solve the discrete problems aimed at the improvement of the solution,we use uniform meshes on the subdomains.The error of the numerical so- lution depends weakly on the parameterε.The scheme converges almostε-uniformly, precisely,under the condition N~(-1)=o(ε~v),where N denotes the number of nodes in the spatial mesh,and the value v=v(K) can be chosen arbitrarily small for suitable K.