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.     

On\overline {GL(4,\mathbb{R})}-covariant extensions of the Dirac equation

Infinite component generalizations of both massless and massive Dirac equations are constructed which are covariant with respect to the double covering of the general linear group in four dimensions. These generalized Dirac equations can be made covariant with respect to the full diffeomorphism group of the spacetime manifold by replacing ordinary derivatives by covariant derivatives in the usual way.     

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.     

Tautomeric populations of the charged species of 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) studied with computer simulations and cluster expansions

Correct net charge and protonation pattern in the polyamine backbone is one of the major factors that define the interactions of this class of compounds. 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) is a isosteric charge deficient analogue of naturally occurring spermine (Spm) with different biological features. The tautomeric populations of each SpmTrien charge state were estimated with computer simulations, molecular dynamics (MD) and quantum mechanical calculations, and cluster expansions separately. In the computer simulations, tautomeric populations of each charge state were obtained by constrained least‐squares fitting the theoretically calculated (GIAO B3LYP/6‐311 + G**) ¹⁵ N NMR chemical shieldings of SpmTrien tautomers to the experimentally measured chemical shifts. Theoretical chemical shieldings were calculated for water complexes of SpmTrien obtained from MD simulations in explicit water. Both methods gave highly similar realistic results. SpmTrien has many major populations of tautomers at biologically relevant charge states of three (+3) and four (+4) thus enabling a large variety of structures for specific ionic interactions. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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.     

Electrogenerated chemiluminescence of fluorescein in aqueous alkaline solutions

Fluorescein is shown to emit light when electrolyzed either anodically or cathodically using potential pulses, in aqueous alkaline solutions at a platinum electrode.     

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     

Poly­[[tetra­aqua(μ7‐hydrogen di­chloro­methyl­enebis­phospho­nato)(μ5‐hydro­gen di­chloro­methyl­enebis­phosphon­ato)­tribarium(II)] monohydrate]

The title compound, {[Ba₃(CHCl₂O₆P₂)₂(H₂O)₄]·H₂O}_n or {[Ba₃(Cl₂CP₂O₆H)(H₂O)₄]·H₂O}_n, is two‐dimensional. The asymmetric unit contains three independent Ba²⁺ atoms, two chelating and bridging Cl₂CP₂O₆H³⁻ ligands and four aqua ligands, connected in layers parallel to the (100) plane. There are pores between the layers in the direction of the b axis filled with lattice water mol­ecules.