Expansions for von Mises functionals

Summary Berry-Esseen results and expansions are derived for the distribution function of von Mises functionals of order r under moment conditions and conditions on the smoothness of the limit distribution.The results apply to goodness-of-fit statistics — as well as to the central limit theorem in L ^2p,p2, the rate of convergence being O(n ^–1) for centered balls, provided a fourth moment exists.Research sponsored in part under Office of Naval Research. Contract Number N00014-80-C-0163.     

Analysis of lipoproteins with analytical capillary isotachophoresis

An analytical free flow capillary isotachophoresis procedure, with a discontinuous electrolyte system, for the detailed analysis of lipoproteins in human body fluids has been developed. The technique is based on prestaining whole serum lipoproteins with a lipophilic dye before separation. Human serum lipoproteins are separated into 14 well-characterized subfractions according to their electrophoretic mobility. High density lipoproteins (fraction 1 to 6) are separated into three major subpopulations, the fast migrating high density lipoprotein (HDL) subpopulation, containing mainly apo AI and phosphatidylcholine, the subpopulation with intermediate mobility, consisting of particles rich in apo AII, apo E, and C apolipoproteins, and the slowly migrating HDL subfraction, containing mainly particles rich in apo AI, apo AIV, and lecithin: cholesterol acyltransferase (LCAT) activity. The apo B containing lipoproteins (fraction 7 to 14) can be subdivided into four major functional groups. The first represents chylomicron derived particles and large triglyceride-rich very low density lipoproteins (VLDL). The second group consists of small VLDL and intermediate density lipoprotein (IDL) particles, anf the third and fourth group represent the low density lipoproteins. The isotachophoretic analysis of human serum samples obtained from patients with hyperlipoproteinemias is compatible with the classification according to the Frederickson phenotypes and reflects the respective biochemical abnormalities. Furthermore, several genetic disorders of lipid and lipoprotein metabolism like HDL deficiency syndromes, familial LCAT deficiency, Fish eye disease, hypobetalipoproteinemia and abetalipoproteinemia can be well characterized by analytical capillary iso tachophoresis. In addition to patient analysis we investigated the influence of lipid lowering drugs on the lipoprotein subfraction distribution during therapy with analytical capillary isotachophoresis.     

Synthesis and photophysics of one mononuclear Mn(III) and one dinuclear Mn(III,III) complex covalently linked to a ruthenium(II) tris(bipyridyl) complex

The preparation of donor (D)-photosensitizer (S) arrays, consisting of a manganese complex as D and a ruthenium tris(bipyridyl) complex as S has been pursued. Two new ruthenium complexes containing coordinating sites for one (2a) and two manganese ions (3a) were prepared in order to provide models for the donor side of photosystem II in green plants. The manganese coordinating site consists of bridging and terminal phenolate as well as terminal pyridyl ligands. The corresponding ruthenium-manganese complexes, a manganese monomer 2b and dimer 3b, were obtained. For the dimer 3b, our data suggest that intramolecular electron transfer from manganese to photogenerated ruthenium(III) is fast, k(ET) > 5 x 10(7) s(-)(1).     

A 13C endor study on Copper(II)/Zinc(II) bis-(diethyl-dithiocarbamate) Cu/Zn(et2dtc)2

¹³C ENDOR spectra of Cu(et₂dtc)₂ substituted into a single crystals of Zn(et₂dtc)₂ are reported. The symmetry of the incorporated guest molecule appears to be considerably influenced by the Zn(et₂dtc)₂ host lattice. The unexpectedly large isotropic ¹³C hfs coupling can be understood assuming a “transannular overlap” mechanism.     

High-resolution/higher-order derivative spectrophotometry in microanalytical chemistry

Summary Examples are given of the application of higher-order derivative spectrophotometry to microanalytical problems, including the increase in sensitivity for estimation of Zn and Cd dithizonates and the quantitative detection of arenes, aniline and phenols. We also describe the estimation of saccharin in soft drinks, and the characterization and estimation of dyes in solution and after absorption on a thin layer of alumina. Only ng-g amounts of substance are needed.

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Hochauflösende UV/VIS-Derivativspektrophotometrie höherer Ordnung in der Mikroanalytik

Zusammenfassung Einige Beispiele für die Anwendung der Derivativspektrophotometrie höherer Ordnung in der Mikroanalyse wurden angegeben. Im besonderen wurden die Erhöhung der Empfindlichkeit der Zn- und Cd-Dithizonat-Bestimmung, die quantitative Bestimmung von Arenen, Anilin, Phenol, die Erfassung von Saccharin in Limonaden und sowohl die Charakterisierung als auch die quantitative Bestimmung von Farbstoffen in Lösung oder adsorbiert an einer dünnen Schicht Aluminiumoxid beschrieben. Es werden nur einige Mikrogramm bis Nanogramm Substanz für die Untersuchungen benötigt.

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Presented at the 8th International Microchemical Symposium, Graz, August 25–30, 1980.     

Preparative uv-laser photochemistry of the azoalkane spiro(2,3-diazabicyclo [2.2.1]hept-2-ene-7′,1-cyclopropane): Trapping of the 1,4-Diradical 2-(3-Cyclopentenyl) ethyl by Molecular Oxygen

Photo-extrusion of nitrogen from the azoalkane 1 in the presence of molecular oxygen gave besides the hydrocarbons 3 and 5, the endoperoxide 10 and hydroperoxide 11, the former via trapping of the 1,4-diradical 4 by triplet oxygen, the latter by ene-reaction-6f hydrocarbon 5 with singlet oxygen.     

Trennung und Identifizierung von Bactericiden auf der Basis von halogenierten Aromaten durch Dünnschicht-Chromatographie

Plates coated with silica gel with addition of fluorescence indicator are used for thin-layer chromatography with a solvent mixture of benzene and acetone (8∶2). The substances are made visible with UV-light and by spraying with solutions of 2,6-dibromoquinonechloroimide and sodium carbonate. The R_f-values, the fluorescence, and the colour of the spots allow to detect and to identify the bactericides rapidly and without further chemical techniques.     

Interpolation of operator ideals with an application to eigenvalue distribution problems

We derive results on the interpolation of complete quasinormed operator ideals, mainly for the absolutelyp-summing and thes-number idealsS _p ^s defined by Pietsch. By estimating theK-Functional of Peetre, we get that the interpolation ideal (S _p1 ^s ,S _p2 ^s ),_,p is contained inS _p ^s and is even equal to it in the case of the approximation numbers. A similar fact is proved for absolutely (p, q)-summing operators, interpolating the first index. We show further that the absolutelyp-summing operators onc ₀ are contained in the complex interpolation space ( _p1 (c _o), _p2 (c _o))_[].The previous results are then applied to prove summability properties for the eigenvalues of operators in Banach spaces, which are products ofS _p1 ^s -type and absolutelyp _j -summing operators. Roughly speaking, the summability order is the harmonic sum of thep _i - andp _j -indices, wherep _j 2. In the case of Hilbert spaces, this reduces to the well-known Weyl-inequality. The method uses an abstract interpolation estimate for ideal quasinorms which may be useful also for other operator ideals.     

Approximation numbers of Sobolev imbeddings over unbounded domains

Let Ω ? $\text{R}$^N be an open set with $\text{dist}\text{(x, ?Ω) = O(¦ x ¦}{}^{\mathrm{?l}}\text{)}\text{for}\text{x ? Ω}$ and some l > 0 satisfying an additional regularity condition. We give asymptotic estimates for the approximation numbers α_n of Sobolev imbeddings

over these quasibounded domains Ω. Here

denotes the Sobolev space obtained by completing $\text{C}{}_0{}^{\mathrm{staggered\infty }}\text{(Ω)}$ under the usual Sobolev norm. We prove $\text{α}{}_{\mathrm{n}}\text{(I}{}_{\mathrm{p,q}}{}^{\mathrm{m}}\text{)}\text{\$}\text{?}\text{n}{}^{\mathrm{?\gamma }}$, where

. There are quasibounded domains of this type where γ is the exact order of decay, in the case p ? q under the additional assumption that either 1 ? p ? q ? 2 or 2 ? p ? q ? ∞. This generalizes the known results for bounded domains which correspond to l = ∞. Similar results are indicated for the Kolmogorov and Gelfand numbers of I_p,q^m. As an application we give the rate of growth of the eigenvalues of certain elliptic differential operators with Dirichlet boundary conditions in $\text{L}{}_2\text{(Ω)}$, where Ω is a quasibounded domain of the above type.     

On the zeros of polynomials over arbitrary finite dimensional algebras

In [3] it was shown that a polynomial of degree n with coefficients in an associative division algebra, which is d-dimensional over its center, has either infinitely many or at most n^d zeros. In this paper we raise the same question for arbitrary m-ary F-algebras A which are d-dimensional over the algebraically closed field F. Our main result states that in the affine space of m-ary algebras of dimension d there is a non-empty Zariski-open set whose elements A have the following property: in the space of polynomial of precise degree n with coefficients in A there is a non-empty Zariski-open set whose elements have precisely n^d zeros. It is shown that all simple algebras, all semi-simple associative algebras, all semisimple Jordan algebras (char F2), all semi-simple Lie algebras (char F=0), and the generic algebra possess this property.