Bifurcation for a semilinear elliptic equation on ℛN with radially symmetric coefficients

We consider the semilinear eigenvalue problem on ^N (N 2) (N2) and investigate the question under which conditions on the radially symmetric function q, =0 is a bifurcation point for this equation in H¹, In H² and in L^p for 2p+.     

Infinite time optimal control and periodicity

For smooth nonlinear systems

Goodisman's correction of the Thomas-Fermi-von Weizsäcker theory of atoms

Summary Following a suggestion of J. Goodisman, we substitute the therm by in the Thomas-Fermi-von Weizsäcker energy functional for atoms.f _z³ [0,1] is a function depending on the nuclear chargez.We establish conditions for the functionsf _z such that the ratio of this modified TFW-energyE _kz ^/TFWG (z) (kz is the total number of electrons) and the exact quantum mechanical energy converges to 1 asz. Moreover, we prove thatE _kz ^/TFWG (z)=E _kz ^/TFW (z)+Dz ²+o(z ²) (z) and determineD. Here,E _kz ^/TFW (z) is the unmodified TFW energy.

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Zusammenfassung Einem Vorschlag J. Goodismans folgend, ersetzen wir in dem Thomas-Fermi-von Weizsäcker Energiefunktional für Atome den Term durch .f _z³ [0,1] ist hierbei eine Funktion, die von der Kernladungszahlz abhängt.Wir geben dann Bedingungen für die Funktionenf _z an, unter denen der Quotient der so modifizierten TFW-energieE _kz ^/TFWG (z) (kz=Anzahl der Elektronen) und der exakten quantenmechanischen Energie fürz gegen 1 konvergiert. Darüber hinaus beweisen wir, daßE _kz ^/TFWG (z)=E _kz ^/TFW (z)+D·o(itz) ² (z) gilt und bestimmmenD. E _kz ^/TFW (z) ist hierbei die nicht-modifizierte TFW-Energie.

     

XPS investigations of ink‐jet printed paper

Different ink‐jet printed paper materials were investigated using X‐ray photoelectron spectroscopy (XPS) yielding the elemental composition of the near‐surface region of the papers. We found significant differences with respect to the detected elements and their atomic concentrations in the different inks studied here. Two different groups of inks could be identified by means of a lower ratio of the O and C atomic concentrations and lower concentrations in specific trace elements like Mg, Na and Si. High‐resolution spectra of C 1s and O 1s core levels allowed a detailed determination of the chemical state of the respective elements. On the basis of a detailed deconvolution of these XPS signals, significant differences between all the investigated ink‐jet printed papers were found, thereby allowing their discrimination. The applicability of the measurements and, more generally, the XPS technique for forensic investigations of paper are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Fluorescence quenching by excimer formation: quenching constant approximations for excimer formation-dissociation by classical potential models

Fluorescence quenching by excimer formation is studied on the assumption that the excimer formation and dissociation can be modeled as overdamped motion in an attractive potential (classical potential models). An approach to the zeroth-order, concentration-independent quenching constants is proposed which starts from a mean reaction-time ansatz and reduces the calculation essentially to the solution of the eigenvalue problem for the Smoluchowski operator which describes the excimer equilibration. For a square-well potential model it is shown that a quenching constant expansion in terms of relaxation modes, truncated at the kinetic level, gives a satisfactory approximation of the recently obtained exact zeroth-order result under defined conditions. It is demonstrated how this two-mode approach can be applied for a quenching constant estimation if the excimer formation and dissociation are modeled by more realistic interaction potentials, as for instance, Morse- or Gaussian-type ones.     

From quality inspection to quality assurance

Summary Systematic quality assurance, e.g. in accordance with the provisions of ISO 9000, requires not only the targeted use of quality as a management tool, but also a revised attitude to operational procedures. Although sophisticated checking of the final results of a procedure (e.g. results of analyses, sales products, reports) meets the legal requirements and often also the customers' requirements, this misses the chance of being able to influence the quality of a final result at the earliest possible stage. It is then only possible subsequently to take the uneconomic decision as to whether the result of the work is useable or must be discarded or the object reworked. Within quality assurance, all operations are to be considered as processes with the aim of arriving at a statistically controlled process. The advantages of statistical process control are explained by way of examples from analytical procedures and production. The status of internal audits is explained as it interrelates with process control.     

Luminescence kinetic and association equilibria of lanthanide ions in aqueous solutions. II. Determination of the formation constant of Tb acetato complex by means of luminescence lifetime measurement

The association constant K of mono-acetato complex of Tb³⁺ has been determined at normal p and T conditions by measurement of its luminescence lifetime in aqueous solution containing increasing concentrations of acetate. Two experimental arrangements used for the measurement are described.     

Development of reactive thiol-modified monolithic capillaries and in-column surface functionalization by radical addition of a chromatographic ligand for capillary electrochromatography

Reactive thiol-modified capillary columns for capillary electrochromatography (CEC) were developed by transforming the pendent 2,3-epoxypropyl groups of poly(glycidyl methacrylate-co-ethylene dimethacrylate) (poly(GMA-co-EDMA)) monoliths into 3-mercapto-2-hydroxy-propyl residues by a nucleophilic substitution reaction, employing sodium-hydrogen sulfide as nucleophilic reagent. Conditions for this modification reaction were systematically optimized with respect to different parameters, such as reaction temperature, pH-value, reaction time, type and concentration of organic modifier, and concentration of the sodium-hydrogen sulfide solution. The amount of thiol groups that was generated on the monolith surface was determined directly in the capillaries by a disulfide-exchange reaction employing 2,2'-dipyridyl disulfide (DPDS). This reaction in the capillary liberates pyridine-2-thione in equimolar amount to the surface sulfhydryls, which was collected into a vial and determined photometrically at 343 nm by RP-HPLC. About 17% of the total lateral epoxide moieties of the monolithic substrate could be transformed to reactive sulfhydryl groups, which corresponds to about 0.7 mmol g(-1) monolithic polymer, with a column-to-column repeatability of 3.2% R.S.D. The reactive thiol groups can be utilized to attach any chromatographic ligand with appropriate anchor in a second step, e.g. by radical addition, graft polymerization, nucleophilic substitution, disulfide formation or Michael addition reaction. To demonstrate the feasibility of the concept, we chose an anion exchange type chromatographic ligand based on a quinine derivative, O-9-tert-butylcarbamoylquinine (t-BuCQN) which was attached to the monolith in a radical addition reaction, for a further in-column surface functionalisation. About 78% of the sulfhydryl groups were derivatized with t-BuCQN as determined from differential DPDS assays before and after the selector immobilization reaction. The applicability of these surface-functionalised monolithic capillary columns could be shown by an electrochromatographic separation of the enantiomers of N-3,5-dinitrobenzoyl-leucine, which performed fairly well compared to an analogous capillary that was fabricated by an in situ copolymerization approach.     

Assignment of the 5,6-Double-Bond Configuration in Iloprost and Isoiloprost from 13C-NMR Shifts Determined by 2D Methods

The configurations of the 5,6-double bond in the carbacyclins iloprost ( 3 ; (E)) and isoiloprost ( 4 ; (Z)) are based on a complete assignment of the ¹³C and ¹H resonances determined by 1D and 2D ¹³C-NMR and ¹H-NMR methods.