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.     

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.     

Optimal orthogonalization processes

Two optimal orthogonalization processes are devised toorthogonalize,possibly approximately,the columns of a very large and possiblysparse matrix A∈C^n×k.Algorithmically the aim is,at each step,to optimallydecrease nonorthogonality of all the columns of A.One process relies on using translated small rank corrections.Another is a polynomial orthogonalization process forperforming the L?wdin orthogonalization.The steps rely on using iterative methods combined,preferably,with preconditioning which can have a dramatic effect on how fast thenonorthogonality decreases.The speed of orthogonalization depends on howbunched the singular values of A are,modulo the number of steps taken.These methods put the steps of the Gram-Schmidt orthogonalizationprocess into perspective regardingtheir(lack of)optimality.The constructions are entirely operatortheoretic and can be extended to infinite dimensional Hilbert spaces.     

Alpha decay of the new isotopes207, 208Ac

Two new neutron-deficient isotopes^207,208Ac have been produced in fusion reactions with 5.2–5.6 MeV/nucleon⁴⁰Ar ions on¹⁷⁵Lu and identified on the basis of genetic correlations. The fusion evaporation products were separated on-line using a gas-filled magnetic recoil separator. The alpha energy and half-life of²⁰⁸Ac were determined to be (7572±15) keV and (95 _?16 ⁺²⁴ ) ms, respectively. A new alpha line with a half-life of (25 _?5 ⁺⁹ ) ms and an energy of (7758±20) keV is assigned to the decay of an isomeric state in²⁰⁸Ac. Another new activity with a half-life of (22 _?9 ⁺⁴⁰ ) ms and an alpha energy of (7712±25) keV is assigned to²⁰⁷Ac.     

Alpha decay studies of neutron-deficient radium isotopes

Neutron-deficient isotopes of radium have been produced in the reactions³⁵Cl+¹⁷⁵Lu,⁴⁰Ar+^170,171Yb, and³⁶Ar+^170,171Yb and separated in-flight with a gas-filled recoil separator. The activities have been identified on the basis of correlated alpha decay chains. The alpha particle energy E_α and the half-life T_1/2 of an isomeric state of the new isotope,^203m Ra, have been determined to be (7615±20) keV and (33 _?10 ⁺²² ) ms, respectively. An assignment of another decay with E_α = (7577±20) keV and T_1/2=(1.1 _?0.5 ^+5.0 ) ms to^203g Ra is made on the basis of one observed three-decay chain. Tentative evidence for the production of the new isotope²⁰²Ra is also given. The values E_α = (7860±60) keV and T_1/2=(0.7 _?0.3 ^+3.3 ) ms were measured. Improved decay data have been obtained for²⁰⁴Ra. The results are E_α = (7484±10) keV and T_1/2=(59 _?9 ⁺¹² ) ms. Earlier findings concerning the decay of two states in²⁰⁵Ra and an isomer in²⁰⁷Ra have been confirmed. Approximate values for cross sections have been determined for²⁰²Ra, produced using the³⁶Ar+¹⁷⁰Yb reaction and for²⁰³Ra,²⁰⁴Ra, and²⁰⁵Ra using the³⁵Cl+¹⁷⁵Lu reaction. The results are 2 nb (²⁰²Ra), 4 nb (²⁰³Ra), 40 nb (²⁰⁴Ra), and 800 nb (²⁰⁵Ra).     

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.     

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.