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.     

Structural Changes of Cellulose Crystallites Induced by Mercerisation in Different Solvent Systems; Determined by Powder X-ray Diffraction Method

The completeness of mercerisation can be evaluated by investigating the changes in the crystalline regions of cellulose from cellulose I (C-I) to cellulose II (C-II) by the X-ray powder diffraction method. Mercerisation experiments in four different solution systems: ethanol/water, acetone, DMSO and xylene, are reported. Also the effect of some additives, external pressure, treatment time and alkalisation temperature were studied. In two-phase solvent systems, structural changes of cellulose crystallites depended primarily on the distribution and solubility of sodium hydroxide in the solvent phases. The sodium hydroxide concentration in the hydrophilic phase must exceed 7–8 w/w-% before complete crystal change from C-I to C-II can occur. The precipitation of sodium hydroxide due to high concentration prevents the successful use of one-phase ethanol/water system in slurry process. On the contrary, the 2-propanol/water/sodium hydroxide system separates into two layers; to the water-rich lower layer and the 2-propanol-rich upper layer, where the sodium hydroxide remains mainly in the water-rich lower layer. This prevents the precipitation of sodium hydroxide and promotes the alkalisation of cellulose. Ammonium chloride and ammonium hydroxide clearly had a positive effect by promoting the crystal changes, however, the urea concentration used in this study was obviously too small. In the advantageous two-phase 2-propanol/water systems, the alkalisation time was only 15 min when the treatment temperature was kept between 0 and 10 °C. Reduced external pressure was found to have a small but still detectable positive effect on cellulose alkalisation while over-pressure prevented crystal changes.     

Feasibility of low-voltage cathodic electroluminescence at oxide-covered aluminum electrodes for trace metal determinations in aqueous solutions

Metal-catalyzed electroluminescence is generated at an oxide-covered aluminum electrode during the reduction of oxygen, potassium peroxodisulfate, and especially hydrogen peroxide in aqueous solutions. The feasibility of this electroluminescence for the determination of copper (5 × 10^?9 M) and thallium (> 10^?10 M) is demonstrated.     

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.     

A new ionic liquid dimethyldinonylammonium bromide as a flow modifier for the simultaneous determination of eight carboxylates by capillary electrophoresis

Two new methods of capillary zone electrophoresis based on aqueous phosphate running buffers with UV spectrophotometric detection were developed and optimized for the determination of eight carboxylates as copper complexes. Metalcomplexes are negatively charged, so measurements were made as anion analyses with flow reversal in the capillary. Two flow modifiers were used: a common tetradecyltrimethylammonium bromide (TTAB) and a new ionic liquid dimethyldinonylammonium bromide (DMDNAB). The methods were compared to each other. Better separation was achieved with DMDNAB as the flow modifier. Method development was done using a fused silica capillary (61 cm x 50 microm i.d.).Optimization was done using 95 mmol L(-1) phosphate buffer with TTAB or DMDNAB in the concentration 0.5 mmol L(-1) at pH 7.1. A -20 kV voltage and direct UV detection at 254 nm was used in measurements. In both CE methods all the peaks in the electropherograms were properly separated, the calibration plots gave good correlation coefficients and all eight carboxylates were detected in less than 7.5 min. The two methods were tested with natural water samples and a paper mill sample, and proved to be feasible.     

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.     

Cathodic electrochemiluminescence at double barrier Al/Al2O3/Al/Al2O3 tunnel emission electrodes

Double insulating barrier tunnel emission electrodes were fabricated by adding a new pure aluminum layer upon oxidized aluminum electrodes by vacuum evaporation and thermally oxidizing the new aluminum layer in air at room temperature. Resulting Al/Al₂O₃/Al/Al₂O₃ electrodes allow the use of various aluminum alloys in the electrode body necessary for hardness or shaping ability of the electrode while obtaining the luminescence properties of pure aluminum oxide. During electrical excitation of luminescent labels by cathodic hot electron injection into aqueous electrolyte solution, the background noise is mainly based on high-field-induced solid-state electroluminescence and F-center luminescence of the outer aluminum oxide film. The more defect states and/or impurity centers the outer oxide film contains, the higher is the background emission intensity. The present electrode fabrication method provides a considerable improvement in signal-to-noise ratio for time-resolved electrochemiluminescence (TR-ECL) measurements when the original native oxide film of the electrode body contains luminescence centers displaying long-lived luminescence. The excellent performance of the present electrodes is demonstrated by extremely low-level detection of Tb(III) chelates, luminol, Pt(II) coproporphyrin and Tb(III) labels in an immunometric immunoassay by time-resolved electrochemiluminescence.