Second-order subdifferentials of C1,1 functions and optimality conditions

We present second-order subdifferentials of Clarke's type of C ^1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ⁿ , considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C ^1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.     

Complexometric titrations controlled by anodic-stripping methods-I Voltammetric stripping

Anodic-stripping voltammetry is used to perform automatic complexometric titrations of metal ions, with high precision. The stripping peaks are converted into corresponding titrant volume increments which are added consecutively during stripping. In analysis of samples containing about 1 mmole, each of lead, indium and gallium, relative standard deviations of 0.008-0.03% were attained.     

Preparative Separation and Analysis of Complex Mixtures of Leucomycins and Desmycarosyl Leucomycins Using HPLC and Mass Spectrometry

Composition and hydrolysis products of a biotechnical available complex of macrolides were analyzed by HPLC and ESI-CID-MSⁿ. Major components are leucomycin-type antibiotics (leucomycins A₁ (5), A₇ (3), A₉ (2), 9-desoxy-9-oxo-turimycin H₃ (4) and niddamycin B (6). Hydrolysis of the complex mixture yielded 9-, 13-isoforocidins (7, 8, 9, 11) and 9-oxo-forocidin (10). A preparative separation procedure was elaborated furnishing compounds 3 - 11 for semisynthetic experiments.Prof. Dr. Udo Gräfe deceased on 14.2.2003. For obituarity see: Schlegel B (2003) J Peptide Sci 9: 661–661.     

Proton bound homodimers and heterodimers of amides and amines in the gas phase. Equilibrium studies by Fourier transform ion cyclotron resonance spectrometry

By injection of the proton bound homodimer [DMF.H+.DMF] of N,N-dimethylformamide (DMF) generated in an external ion source into a mixture of DMF and a second base within the cell of a Fourier transform ion cyclotron resonance (FT-ICR) spectrometer the equilibria between [DMF.H+.DMF] and the other possible proton bound dimers [DMF.H+.base] and [base.H+.base] have been studied for 13 different bases. Strongly polar bases like aliphatic amides and dimethyl sulfoxide (DMSO) exchange both DMF in [DMF.H+.DMF] by a two step process, while the almost non-polar amines exchange only one DMF. If the base is a primary or secondary amine, the proton bound heterodimer [DMF.H+.amine] reacts further by the addition of one DMF to create a proton bound trimer [(DMF)2.H+.amine]. The affinity deltaG(DMFH+) of the bases towards protonated DMF relative to neutral DMF depends linearly on the difference deltaGB of the gas phase basicity of DMF and the other base, but different correlation lines are obtained for polar and non-polar ligands (deltaGDMFH+ = 0.44GB(base)-375 [kJ/mol] (r = 0.97) and deltaGDMFH+ = 0.46GB(base)-397 [kJ/mol] (r = 0.99), respectively). This different behavior is explained by a different character of the proton bridge in the heterodimers containing only polar ligands and those incorporating a non-polar ligand besides DMF. The former dimers contain a more or less symmetric proton bridge while the latter can be viewed as a protonated base solvated by DMF. The available data have been used to calculate the molecular pair gas phase basicity of DMF and the 13 bases used and to estimate the dissociation energies of the bonds of the proton bridge in various proton bound heterodimers.     

Modifying the thermosensitivity of copolymers of sodium styrene sulfonate and<Emphasis Type="Italic"> N</Emphasis>-isopropylacrylamide with dodecyltrimethylammonium chloride

The interactions between copolymers of sodium styrene sulfonate (SSS) and N-isopropylacrylamide (NIPAM), anionic polyelectrolytes, and dodecyltrimethylammonium chloride (DTAC), a cationic surfactant, were studied in aqueous solutions of various ionic strengths. The copolymers were found to be thermoresponsive, showing a lower critical solution temperature (LCST). The influence of the polymer composition, the surfactant concentration, and the ionic strength on the LCST was studied. The surfactant was found to interact strongly with the polymer, forming mixed polymer-surfactant micelles. The critical aggregation concentration (cac) of the polymer-surfactant system was found from fluorescence spectroscopy using pyrene as a fluorescent probe. A strong dependence of the anionic polyelectrolyte-cationic surfactant interactions on the structure of the ionic comonomer was observed.     

Almost constant sequences and well-distribution in compact groups

We study the properties of sequences (c _n ) in a compact groupG such that (x _n ) being (weakly) well-distributed implies (c _n x _n ) being (weakly) well-distributed and give a complete characterisation in terms of almost constant sequences as well as a generalisation to non-compact locally compact groups.     

An investigation of the complete post-buckling behavior of axisymmetric spherical shells

Summary The post-buckling behavior of an elastic spherical shell is studied for large axisymmetric deformations. The complete post-buckling path is given for the experimentally confirmed single dimple solution in a load-deformation diagram, making use of the methods of local bifurcation theory, singular perturbation analysis and numerical analysis. From the specific form of the post-buckling path with its predominating unstable part follows the strong imperfection sensitivity of the shell structure.

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Zusammenfassung Es wird das Nachbeulverhalten einer elastischen Kugelschale für große achsensymmetrische Deformationen untersucht. Der gesamte Nachbeulpfad wird für die experimentell bestätigte single dimple Lösung, die eine starke lokale Eindellung darstellt, angegeben, wobei Methoden der lokalen Verzweigungstheorie, der singulären Störungsrechnung und der numerischen Analysis verwendet wurden. Aus der besonderen Form des Nachbeulpfades mit seinem überwiegend instabilen Teil ist die starke Imperfektionsempfindlichkeit dieser Konstruktion deutlich erkennbar.