Trace Extensions,Determinant Bundles,and Gauge Group Cocycles

We study the geometry of determinant line bundles associated with Dirac operators on compact odd-dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated nonmultiplicative renormalized determinants.     

Reflection of Long Game Formulas

We study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict-II¹₁ reflection (or ∑₁-compactness). We show that admissible sets such as H(ω₂) and L_ω2 which fail to have strict-II¹₁ reflection, may or may not, depending on set-theoretic hypotheses satisfy one or both of these weaker forms. Mathematics Subject Classification : 03C70, 03C75.     

Novel Thiazole-Containing Complexing Agents and Luminescence of Their Europum(III) and Terbium(III) Chelates

The synthesis of novel thiazole-containing complexing agents and their luminescence properties with Eu^III and Tb^III ions are reported. One of these terpyridine analogues was also tested as an Eu^III labelling reagent, and its luminescence properties as an antibody conjugate were studied.     

Chiral anomalies in even and odd dimensions

Odd dimensional Yang-Mills theories with an extra topological mass term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.     

Determination of naphthodianthrones and phloroglucinols from Hypericum perforatum extracts by liquid chromatography/tandem mass spectrometry

Hypericum perforatum L. (St. John's Wort) has long been known as a medicinal plant, and has been used for the treatment of depression and neuralgic disorders. Its main active constituents are believed to be a naphthodianthrone, hypericin, and a phloroglucinol, hyperforin. A sensitive high performance liquid chromatography (HPLC)/electrospray tandem mass spectrometric method for fast simultaneous determination of six major naphthodianthrones and phloroglucinols of Hypericum perforatum extract has been developed. The method, based on multiple dissociation reaction monitoring (MRM), allows the analysis of hypericin, protohypericin, pseudohypericin, protopseudo-hypericin, hyperforin and adhyperforin from the extract in less than 5 min. Good linearity over the range 0.1-1000 ng/mL for hyperforin and 2-500 ng/mL for hypericin was observed. Intra-assay accuracy and precision varied from 2 to 19% within these ranges. Lower levels of quantitation for hyperforin were 0.5 ng/mL and 2 ng/mL for hypericin.     

The analysis of chromium, cobalt, iron, nickel, niobium, tantalum, titanium and zinc in cemented tungsten carbides with cobalt as a binder by inductively coupled plasma atomic emission spectrometry

 Inductively coupled plasma atomic emission spectrometry (ICP-AES) was applied as a rapid routine method for the analysis of cemented tungsten carbides. Chromium, cobalt, iron, nickel, niobium, tantalum, titanium and zinc were selected as major, minor and trace constituents in the material investigated. In the first step, the sample was treated with hydrochloric and orthophosphoric acid. The second step consisted of the simultaneous addition of hydrofluoric and nitric acids. Cemented tungsten carbides dissolved completely, leaving only minor quantities of carbon in the solution. Multiple linear regression proved to be very effective in the search for interfering elements. Using simple acid based standards, all the elements investigated could be determined individually from the complicated matrix using an appropriate method of calculation. The method described was successfully applied to real type commercial samples. The advantages of the ICP-AES method in comparison with the XRF-method are discussed. Received: 15 February 1996/Revised: 22 April 1996/Accepted: 2 May 1996     

Characteristics and safety of nano-sized cellulose fibrils

A finely ground fibrillated cellulose was fractionated into separate size fractions. The characteristics of the smallest size fractions were studied, and the toxicity to humans was tested as part of a safety assessment. Morphological studies performed with state-of-the-art methods, such as scanning electron microscopy and atomic force microscopy, showed that the fraction obtained consisted of long thin fibrils but also larger fibril agglomerates, and spherical particles were present. The finest fraction did not show any sub-lethal effects as assessed by RNA inhibition test in vitro, nor were there any indications of genotoxicity as tested by the Ames test in vitro. Systemic effects tested in vivo with the nematode were also absent. No cytotoxic effects were seen in the highest tolerated dose test in vitro, but some indication of cytotoxicity was observed in the total protein content test in vitro at the highest sample concentration. The significance of this toxicity test result should be addressed in relation to the other toxicity tests, in which no toxicity was observed, with special emphasis on the in vivo test. Given this, the overall toxicity analyses support the conclusion that nano-scale cellulose fibrils can be considered to be safe towards humans. However, the reason for the positive cytotoxicity test result and, in addition, the effect of the biocide used in sample preservation on the toxicity tests need to be clarified before generalizing these results and declaring nanocellulose to be unambiguously safe.     

Discrete series of lie superalgebras

Let $\text{g}$ denote the Lie superalgebra $\text{sl}\text{(n, 1)}$. Its even part is the Lie algebra $\text{g}{}_0\text{=}\text{gl}\text{(n)}$ of n×n complex matrices. Let

denote the reductive subalgebra $\text{gl}\text{(p)⊕}\text{gl}\text{(q)}$ in $\text{g}{}_0\text{, p+q=n}$. We show that for a certain set Λ⁺₀ of irreducible finite dimensional

-modules there exists, for each λ?Λ⁺₀, an irreducible

-finite g-module (which is unique up to equivalence) with minimal

- type λ.     

One-pot synthesis of 3,4-disubstituted 1H-pyrroles from 2-tropanones

3,4-Disubstituted pyrroles (2, 3) were prepared from 6/7-carboxyethyl-3-phenyl-3-tropen-2-ones (1) regioselectively and with high yields by using tosylmethyl isocyanide (TosMIC). This procedure enables the synthesis of pyrroles substituted with two distinct groups: a phenyl group and a substituted pyrrolidine analogue. The crystal structure of product 2a was determined, and the analogous derivatives were identified by (1)H and (13)C NMR spectroscopy.