On the number of faces of centrally-symmetric simplicial polytopes

I. Bárány and L. Lovász [Acta Math. Acad. Sci. Hung.40, 323–329 (1982)] showed that ad-dimensional centrally-symmetric simplicial polytopeP has at least 2 ^d facets, and conjectured a lower bound for the numberf _i ofi-dimensional faces ofP in terms ofd and the numberf ₀ =2n of vertices. Define integers A. Björner conjectured (unpublished) that (which generalizes the result of Bárány-Lovász sincef _d–1 = h _i ), and more strongly that , which is easily seen to imply the conjecture of Bárány-Lovász. In this paper the conjectures of Björner are proved.Partially supported by NSF grant MCS-8104855. The research was performed when the author was a Sherman Fairchild Distinguished Scholar at Caltech.     

Multidimensional random walks in random environments with subclassical limiting behavior

In this paper we will describe and analyze a class of multidimensional random walks in random environments which contain the one dimensional nearest neighbor situation as a special case and have the pleasant feature that quite a lot can be said about them. Our results make rigorous a heuristic argument of Marinari et al. (1983), and show that in anyd< we can have (a)X _n is recurrent and (b)X _n (logn)².AMS Mid Career Fellowship 1984–1986. Research also partially supported by NSF Grant MCS 83-00836     

Determination of organic carbon in water with a silver-catalyzed peroxydisulfate wet chemical oxidation method

The application of Ag(I) catalysis of S₂O₈^2? to the oxidation of organic carbon to CO₂ for determination of dissolved organic carbon in aqueous samples is described. The resulting method combines to a significant degree the speed of high-temperature combustion methods and the sensitivity of wet chemical oxidation. For some samples, a higher oxidation efficiency has been observed than with an uncatalyzed wet chemical oxidation method.     

Fluorimetric determination of zirconium with morin

Zirconium can be determination fluorimctrically with morin in 2M hydrochloric acid in the presence of such elements as Al, Be, Ga, Sb, Sn, Th and U, which fluorcsce much less strongly under the conditions, by measuring the fluorescence intensity before and after adding ethylenediaminetetraacetic acid. This substance destroys the fluorescence of zirconium only and the difference in fluorescence intensities corresponds to the concentration of zirconium in solution. The determination of zirconium in the presence of aluminum has especially been studied. Satisfactory accuracy can be obtained even when Al/Zr = 10,000, if the proper morin concentration is used. Iron docs not interfere if reduced to the ferrous state with mercap oacetic acid, Zirconium can be determined in silicate rocks without any separations except those made automatically in tlie sodium carbonate decomposition. Niobium and tantalum should not exceed 0.05%.     

Isomerisation in the chemistry of platinacyclobutane complexes

The platinacyclobutane complexes PtCl₂L₂(C₃H₅Me)], L  pyridine, CD₃CN, or tetrahydrofuran, exist as mixtures of isomers containing P$\text{tCH}{}_2\text{CHMeC}$H₂ or P$\text{tCHMeCH}{}_2\text{CH}{}_2$ groups in rapid equilibrium. Decomposition occurs in some cases to give [PtCl₂L(CH₃CH₂CHCH₂)]. Stereospecific skeletal isomerisation also occurs in metallocyclobutanes containing the groups P$\text{tCHRCHRC}$H₂  P$\text{tCHRCH}{}_2\text{C}$HR, when R  aryl further decomposition gives ν-allylplatinum complexes.     

Optically detected zero-field triplet state magnetic resonance in photosynthetic bacteria

Triplet state transitions of the photosynthetic bacteria Rhodospirillum Rubrum, Rhodopseudomonas Spheroides and Chromatium Vinosum in chemically reduced preparations have been observed by zero-field optical detection of magnetic resonance at 2 K. For each bacterial preparation two sharp, structureless, zero-field EPR transitions were observed as microwave-induced decreases in the fluorescence intensity of the frozen cellular preparations. The depopulating rate constants for the spin sublevels of the triplet states observed in R Rubrum and R Spheroides were also measured. The similarities of the triplet state frequencies, spectral features and intersystem crossing rates suggest a common structure for the reaction centers in the photosynthetic bacteria.     

Trapped electrons in substoichiometric MoO3 observed by X-ray electron spectroscopy

Substoichiometric amorphous thin films of MoO₃ in both the transparent and absorptive forms have been studied by X-ray electron spectroscopy. The transparent films can be colored blue (absorptive) electrically or by UV irradiation. The electron distribution curve of the blue film exhibits a small band near the Fermi edge which is absent in the transparent sample. This new band is attributed to electrons trapped in positively charged anion vacancies in the substoichiometric MoO₃ lattice. This model provides an interpretation of the electrical conductivity and color of the films.     

PHYCOBILIPROTEINS: COMPARISON OF SOLUTION AND SINGLE CRYSTAL FLUORESCENCE FOR C-PHYCOCYANIN AND B-PHYCOERYTHRIN*

Abstract— Trimeric and hexameric solution forms of C-phycocyanin (CPC) from the cyanophyte Agme-nellum quadruplicatum have been isolated and their spectral properties compared to those obtained from single crystals. Although the absorbance peak of a suspension of small C-phycocyanin crystals is red-shifted only 7 nm relative to the solution forms, the single crystal fluorescence is red-shifted 60 nm relative to the solution forms. The crystal fluorescence spectrum exhibits a single peak at LD_max= 708 nm when excited at 514.5 or 530.9 nm and two peaks (LD_max= 661 and 708 nm) when excitation occurs at 568.2 nm. Fluorescence depolarization measurements indicate that extensive energy transfer could occur for both solution and crystal forms with the latter being dependent upon the relative orientation of the crystal with respect to the excitation dipole. Similar results were obtained with B-phycoerythrin (BPE) from the red alga Porphyridium cruentum where the single crystal fluorescence is red-shifted =50nm relative to the solution spectra with two peaks (LD_max= 583 and 617 nm) observed whose relative intensities are dependent on the excitation wavelength (LD_max– 514.5 and 530.9 nm). Single crystal fluorescent lifetimes exhibited considerable shortening relative to that observed for the solution forms. The implications of these results are discussed with respect to the possible relationships of the crystalline structures to the assembly forms present within phycobilisomes.     

Synthesis of the ladybug alkaloids (±)-propyleine and (±)-isopropyleine. Modification of the published structure of propyleine

The total syntheses of the ladybug alkaloids (±)-propyleine and (±)-isopropyleine are described. Evidence that the alkaloid propyleine is actually a rapidly interconverting mixture of propyleine and a previously unknown isomer isopropyleine is presented.     

Beitrag zur Kenntnis des Systems Vanadin—Chrom—Stickstoff

The System V–Cr–N has been investigated at 1100 and 1400 °C and at nitrogen pressures between 1 and 1000 atmospheres by X-ray techniques. VN and CrN on the one hand and V₂N and Cr₂N on the other are forming complete series of solid solutions. The phase field of the mononitride solid solution is dependent on nitrogen pressure and temperature conditions.

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Auszug aus der Diplomarbeit des Herrn Dipl.-Ing. Dr.W. Schebesta.