Input control in nonnegative matrix equations

In this paper we consider the nonnegative matrix system c_iA+u_iB=c_i+1 where the nonnegative matrix A is allowed to vary, within bounds. The cone control problem is to find a nonnegative matrix B such that if C_i is a nonnegative vector in a specified cone, then there is a nonnegative vector u_i such that c_i+1 is in that cone. We extend this problem to input control by finding a B such that the cone, generated by the rows of B, is as small as possible. Thus, the percent distribution of ∣u_iB∣ through the states of the sustem by u_iB is either constant or varies little.     

Phase diagram of multilayer magnetic structures

Multilayer ferromagnet-layered antiferromagnet (Fe/Cr) structures frustrated because of roughness of interlayer boundaries were studied by mathematical modeling methods. The phase diagram of a three-layer system (plotted as film thickness versus the degree of roughness of the interfaces) was obtained, and the order parameter distributions in each phase were determined. The character of phase transitions in this system was studied. The applicability range of the Slonczewski magnetic proximity model was determined.     

Contributions to the synthesis of some ferrocene-containing antibiotics

This Review discusses the synthesis and characterization by our Group of new antibiotics belonging to the class of penicillins, cephalosporins and rifamycins with ferrocenyl and 1, 1′-ferrocenilene residues in the molecule. As reactants for 6-aminopenicillanic acid (6-APA) and 7-aminocephalosporanic acid (7-ACA) the following were used: 1, 1-bis(chlorocarbonyl)ferrocene, ferrocenyl sulfochloride, 1, 1′-ferrocenylenedisulfochloride and thioglycolic acids S-modified with ferrocene. In the synthesis of rifamycins, the hydrazides of the thioglycolic acids, S-modified with ferrocene, were employed as nucleophilic agents. The synthesized intermediates were characterized by elemental analysis, TLC, IR, UV and ¹H NMR spectra. The characterization of new antibiotics was made by TLC, IR and UV spectral analysis. Biological activity was tested on Gram-negative and Gram-positive bacteria. Good activity is reported towards Gram-positive bacteria in the case of derivatives containing residues of thioglycolic acid S-modified with ferrocene, the antibacterial activity being similar to that of amoxicillin, carbenicillin and cephalothin. All compounds are inactive towards Gram-negative bacteria.     

Liquid crystal properties of some substituted pyrazines

A number of biphenyl, terphenyl analogues and ethynes which contain a pyrazine ring have been made and their liquid crystal transition temperatures, together with examples of birefringence measurements, are reported. All the 2,5-disubstituted pyrazine systems are liquid crystalline showing high birefringence values for the biphenyl and terphenyl analogues, whereas the 1,5-disubstituted systems are not liquid crystalline. The pyrazine ethyne systems exhibit very high birefringence values. X-ray diffraction has been used to identify the liquid crystal phases of 2-n-nonyloxy-5-(4'-propylbiphenyl-4-yl)pyrazine.     

Plant polysaccharides I. Polysaccharides ofLagochilus and their biological activity

Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (3712) 89 14 75. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 313–314, March–April, 1995. Original article submitted November 7, 1994.     

Complexes in polymers IV. FTIR microscopic characterization of thin organic polymer films containing embedded transition-metal carbonyl complexes

Thin films of polystyrene (PS), poly(methyl methacrylate) (PMMA) and polystyrene-polyacrylonitrile copolymer (PS-AN), containing various embedded transition-metal complexes, have been studied by FTIR microscopy. The spatial distributions of the transition-metal carbonyl complexes throughout the thin organic polymer films have been determined by a two-dimensional IR mapping procedure. The spectral variations observed in the distribution of the metal carbonyls throughout the different polymer films are discussed. The IR data show that the technique used to prepare the organometallic-embedded thin films (viz. freeze-drying of solutions followed by hot mechanical pressing of the residues) does in general lead to homogeneous films which may eventually find industrial application, e.g. as membrane sensors for small molecules.     

The liquid-crystalline behaviour of amphiphilic ethane-1,2-diol derivatives incorporating a six membered ring in their principal structure

Novel 3-phenyloxy substituted propane-1,2-diol derivatives, 4-(4-n-hexyloxyphenyl)-butane-1,2-diol and 4-(trans-4-n-pyropylcyclohexyl)-butane-1,2-diol have been synthesized and their thermal behaviour has been studied. These compounds exhibit thermotropic and, after addition of water, also lyotropic liquid-crystalline behaviour. The clearing temperatures of the smectic mesophases were found to be strongly dependent on the alkyl chain length and on the structural units that link the aromatic ring to the alkyl chain and to the diol unit. The behaviour of the aromatic compounds is compared with that of the cyclohexane derivative. Thereby it has been realized that the mesophase stability of the amphiphilic diols incorporating a rigid unit is largely determined by both, the molecular geometry (molecular shape and intramolecular flexibility) and the amphiphilic structural pattern.     

The Numerical Differentiation of Probe Characteristic

In the paper new methods of the computation of second-order derivative of probe characteristic are proposed. All methods are tested on testing data as well as on experimental measured probe characteristic.