Numerical approximations and regularizations of Riccati equations arising in hyperbolic dynamics with unbounded control operators

This paper provides an approximation theory for numerical computations of the solutions to algebraic Riccati equations arising in hyperbolic, boundary control problems. One of the difficulties in the approximation theory for Riccati equations is that many attractive numerical methods (such as standard finite elements) do not satisfy a uniform stabilizability condition, which is necessary for the stability of the approximate Riccati solutions. To deal with these problems, a regularizationapproximation technique, based on the introduction of special artificial terms to the dynamics of the original model, is proposed. The need for this regularization appears to be a distinct feature of hyperbolic (hyperbolic-like) equations, rather than parabolic (parabolic-like) problems where the smoothing effect of the dynamics is beneficial for the convergence and stability properties of approximate solutions to the associated Riccati equations (see [14]). The ultimate result demonstrates that the regularized, finite-dimensional feedback control yields near optimal performance and that the corresponding Riccati solution satisfies all the desired convergence properties. The general theory is illustrated by an example of a boundary control problem associated with the Kirchoff plate model. Some numerical results are provided for the given example.     

Calculations of the isotropic hyperfine coupling constants in free radicals

For a number of free radicals the results of non-empirical (ab initio) and semi-empirical (INDO, DEPAC, CNDO/SP) calculations of the isotropic hyperfine coupling constants are compared.     

Investigation of adsorbed polymer layers by flocculation of oppositely charged sols III. Effect of molecular mass of polymers

The stabilizing effect of water-soluble neutral polymers with different chemical structure and relative molecular mass on AgI sol has been studied. It was shown that the stabilizing effect of the polymers used is independent of the relative molecular mass of the polymer when equal amounts of the adsorbed polymers are compared with each other as stabilizers. The high stabilizing effect of polymers with high relative molecular mass is presumably due to the larger adsorbed amount.Among polyvinyl alcohol, polyvinyl pyrrolidone and methylcellulose, polyvinyl pyrrolidone exhibits the smallest stabilizing layer thickness at equal adsorbed amounts. According to our earlier results this is due to the fact that the polyvinyl pyrrolidone shows the strongest affinity for AgI surfaces, forming short loops or tails.     

Effect of H-bond formation on the electronic spectra of some azo compounds derived from 3-amino-1,2,4-triazole

The UV-visible spectra of some azo compounds derived from 3-amino-1,2,4-triazole and various active-methylene or active-hydrogen compounds have been investigated in organic solvents of different polarities. The spectral bands obtained are assigned to the possible electronic transitions. It was found that the azo compounds containing the acetylacetone moiety exist mainly in the hydrazone form, while those containing ethylcyanoacetate, or -naphthol substituents exist in an azo hydrazone tautomeric equilibrium in solution. The extra visible band exhibited in the spectra ofo-hydroxyazo compound is assigned to an intermolecular electronic transition. The spectral shifts observed in the various organic solvents are discussed on the basis of the solute-solvent interaction through the formation of hydrogen bonds with different species. The variation of the absorbance with pH is employed to determine the acid dissociation constants.     

Changes in defect concentration within polymer crystals: annealing of isotropic and drawn polyethylene

An estimation of the changes in the level of chain defects (branches) accommodated within crystals of undrawn and drawn branched polyethylene, subsequently annealed, is carried out in the light of unit cell expansion data. The results reveal that annealing affects the estimated crystalline defect concentration differently depending on whether the material was drawn or undrawn. Thus, annealing of drawn polyethylene with a defect concentration of 3 % results in a healing of crystal defects, due to a preferential rejection of branches from the crystals. In contrast, annealing of melt crystallized branched polyethylene does not influence the average concentration of chain defects within the crystal despite the increase in lamellar thickness. The branches are trapped into the much wider lamellar crystals with fewer grain boundaries available and defect sequences cannot diffuse out of the crystals.Cordially dedicated to Prof. Dr. H.-G. Kilian on the occasion of his 60th birthday.     

Thermodynamic Data for Complex Formation Between Cucurbituril and Alkali and Alkaline Earth Cations in Aqueous Formic Acid Solution

Complex formation, between alkali and alkaline earth cations and the macrocyclic ligands cucurbituril and 18-crown-6, was studied by calorimetric titration in aqueous formic acid solution (50 vol.%). The solubility of cucurbituril strongly depends on the concentration of formic acid. At low and very high formic acid concentrations, the solubility of cucurbituril is low. For both ligands the formation of proton complexes influence the complexation reactions with cations. Thus, the complex formation in most cases is favored by entropic contributions. Only in the case of the Ba²⁺ ion stability constants and reaction enthalpies could be measured at lower formic acid concentrations. Using a highly sensitive calorimeter, the stability constants and reaction enthalpies for the reaction of Na⁺ and Ba²⁺ with cucurbituril in aqueous solution could be determined.     

Cyclodextrine und synthetische Wirthohlräume — Vergleich der Komplexierungseigenschaften

It is shown that the synthetic host compounds described in this study possess higher complexation constants versus 1,8-ANS than -or -cyclodextrin. The attachment of side chains to -cyclodextrin increases the complex formation, whereas the value of -cyclodextrin is not reached. The quaternary ammonium nitrogens of the synthetic hosts may be replaced by amide groups without diminution of the association constants. Bicyclic compounds in general bind more strongly than monocyclic hosts due to tighter inclusion and increased hydrophobic interaction. The influence of side chains attached to synthetic host compounds on the complexation constants is difficult to predict.

     

Lanthanide-daunomycin interactions. Predominance of ML2 at low metal to ligand ratios

Spectroscopic investigations have been undertaken on the effects of lanthanide ions on the spectrum of the anticancer agent, daunomycin. The visible spectral perturbations due to the metal ions resulted in hypochromic effects in the 480 nm region and in shifts towards longer wavelength. The different metal ions investigated did not give any significant difference in the, spectral character. Data analysis according to the methods of molar ratio, continuous variation and graphical approaches based on simplex matrix theory indicated the presence of predominantly a ML₂ species at metal to ligand ratios, less than one. Data also suggested the presence of ML and ML₃ as well.     

分散剂分子结构特征对煤浆流变特性的影响

系统考察了具有不同分子结构特片系列分散剂对高浓度煤浆性质的影响。发现煤的成浆性、浆体的流变特性和稳定化作用与分散剂的分子结构特征密切相关。就本研究所涉及的分散剂种类和煤种而言，分散剂单体结构中多核芳烃结构所占比例较小时易于使浆体呈屈服假塑性，相反，则使浆体呈屈服胀塑性。分散剂单体的侧链结构对煤成浆性和浆体流变性的影响不很突出，而分散剂的第二单体结构的影响却非常显著。结果还同时表明，分散剂的高分散性能是导致浆体呈屈服胀塑性流体和弱化浆体稳定化作用的重要因素。     

A thermodynamic study of the inclusion processes of α- andβ-cyclodextrins with the acid forms of methyl orange and methyl yellow

The effect of temperature on the UV-visible spectra of the acid forms of methyl orange and methyl yellow in the presence of - and-cyclodextrins was analysed in terms of 1 : 1 inclusion processes. Three inclusion processes were considered for each azo dye/cyclodextrin system. The processes are the apparent inclusion process, the ammonium inclusion process, and the azonium inclusion process. The values of H ⁰ and S ⁰ are reported for each process. The inclusion complexes of the ammonium tautomer are more stable than those of the azonium tautomer and -cyclodextrin inclusion complexes are more stable than those of-cyclodextrin. The inclusion processes resulted in a shift in the position of the tautomeric equilibrium of an azo dye. A significant color fading was observed in -cyclodextrin/methyl yellow solutions. No measurable changes in the absorbances were observed in the case of azo dye solutions containing -cyclodextrin.