On the higher eigenvalues for the \infty-eigenvalue problem

We study the higher eigenvalues and eigenfunctions for the so-called -eigenvalue problem. The problem arises as an asymptotic limit of the nonlinear eigenvalue problems for the p-Laplace operators and is very closely related to the geometry of the underlying domain. We are able to prove several properties that are known in the linear case p = 2 of the Laplacian, but are unknown for other values of p. In particular, we establish the validity of the Payne-Pólya-Weinberger conjecture regarding the ratio of the first two eigenvalues and the Payne nodal conjecture, which deals with the zero set of a second eigenfunction. The limit problem also exhibits phenomena that are not encountered for any .Received: 4 January 2004, Accepted: 9 June 2004, Published online: 3 September 2004Mathematics Subject Classification (2000): 35P30, 35J70, 49R50     

Potentiometrische Titrationen in der Lebensmittelanalytik

Ohne Zusammenfassung     

Bestimmung von Nitrofurazon (5-Nitro-2-furaldehydsemicarbazon)

Ohne Zusammenfassung     

Der Nachweis des Eisens als Tri-n-butylammonium-eisen(III)-rhodanid

Ohne ZusammenfassungHierüber und über die quantitative Bestimmung des Eisens wird in Kürze berichtet.     

Eine colorimetrische Methode zur Bestimmung von Acetyl-(p-nitrophenyl)-sulfanilamid (APNPS) in Futtermitteln

Ohne Zusammenfassung     

Kilohertz Cr:forsterite regenerative amplifier

We report on a tunable regenerative amplifier that is operational in the near-infrared spectral region from 1230 to 1280 nm based on the vibronic laser material Cr:forsterite. Utilizing the technique of chirped-pulse amplification, we generated pulses as short as 150 fs at 1255 nm at a repetition rate of 1 kHz. Pulse amplification of more than 5 x 10(5) times was observed, with recorded output pulse energies of 34 muJ . Implementation of a second-harmonic generator yielded 110-fs-duration pulses of 7-muJ energy at 625 nm.     

Ueber den Nachweis von Mutterkorn im Mehle auf spectroskopischem Wege

Analytical and Bioanalytical Chemistry -     

Lectins and/or xyloglucans/alginate layers as supports for immobilization of dengue virus particles

Formation of stable thin films of mixed xyloglucan (XG) and alginate (ALG) onto Si/SiO(2) wafers was achieved under pH 11.6, 50mM CaCl(2), and at 70 degrees C. XG-ALG films presented mean thickness of (16+/-2)nm and globules rich surface, as evidenced by means of ellipsometry and atomic force microscopy (AFM), respectively. The adsorption of two glucose/mannose-binding seed (Canavalia ensiformis and Dioclea altissima) lectins, coded here as ConA and DAlt, onto XG-ALG surfaces took place under pH 5. Under this condition both lectins present positive net charge. ConA and DAlt adsorbed irreversibly onto XG-ALG forming homogenous monolayers approximately (4+/-1)nm thick. Lectins adsorption was mainly driven by electrostatic interaction between lectins positively charged residues and carboxylated (negatively charged) ALG groups. Adhesion of four serotypes of dengue virus, DENV (1-4), particles to XG-ALG surfaces were observed by ellipsometry and AFM. The attachment of dengue particles onto XG-ALG films might be mediated by (i) H bonding between E protein (located at virus particle surface) polar residues and hydroxyl groups present on XG-ALG surfaces and (ii) electrostatic interaction between E protein positively charged residues and ALG carboxylic groups. DENV-4 serotype presented the weakest adsorption onto XG-ALG surfaces, indicating that E protein on DENV-4 surface presents net charge (amino acid sequence) different from E proteins of other serotypes. All four DENV particles serotypes adsorbed similarly onto lectin films adsorbed. Nevertheless, the addition of 0.005mol/L of mannose prevented dengue particles from adsorbing onto lectin films. XG-ALG and lectin layers serve as potential materials for the development of diagnostic methods for dengue.     

Computational NMR spectroscopy of organoarsenicals and the natural polyarsenic compound arsenicin A

The (1)H and (13)C NMR chemical shifts and coupling constants of a series of organoarsenic compounds were calculated with DFT methods and compared with available experimental spectra. We show that non-relativistic methods successfully model the NMR spectra of these molecules; relativistic spin-orbit effects are small but appreciable for (13)C shifts, and their inclusion is beneficial. Application of the same methods of calculation to the intriguing natural polyarsenic compound arsenicin A allowed several viable alternative structures to be ruled out and thereby confirmed the previously suggested adamantane-like structure of arsenicin A. These results not only reinforce the known predictive power of DFT NMR calculations, but also open the way for the investigation of other naturally occurring molecules with unusual structures outside the scope of empirical methods.     

Synthesis of the C3-C18 fragment of amphidinolides G and H

A synthesis of an amphidinolides G and H C3-C18 subunits is reported. The C10-C18 segment 4 was prepared by a Negishi cross-coupling, whereas the synthesis of the C3-C9 fragment 5 employed an asymmetric cyanosilylation as the key step. The two segments were coupled by lithiation of iodide 4 and trapping of the anion with amide 5. The allylic epoxide moiety could be synthesized from the protected anti- mesylate 22.