Algebraic quantization of systems with a gauge degeneracy

Systems with a gauge degeneracy are characterized either by supplementary conditions, or by a set of generators of gauge transformations, or by a set of constraints deriving from Dirac's canonical constraint method. These constraints can be expressed either as conditions on the field algebra , or on the states on . In aC*-algebra framework, we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra . This factor algebra, , is free of state conditions. In this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions. The connection between states on and states on is investigated further within this framework, as is also the set of transformations which are compatible with the set of constraints. It is also shown that not every set of constraints can give rise to a nontrivial system. Finally as an example, the abstract theory is applied to the electromagnetic field, and this treatment can be generalized to all systems of bosons with linear constraints. The question of dynamics is not discussed.     

Trifluoromethylation of non-activated aldimines with trimethyl(trifluoromethyl)silane in the presence of tetramethylammonium fluoride: A closer look into the reaction route

The reactions of non-activated aldimines with trimethyl(trifluoromethyl)silane and 1 equiv. of tetramethylammonium fluoride proceed via the formation of tetramethylammonium amides which were identified by low-temperature ¹⁹F NMR experiments. Consecutive reactions of the salts formed in situ with electrophiles yielded trifluoromethylated amines. Fluoride elimination is observed in the absence of electrophilic substrates leading to the formation of difluoromethylated ketimines.     

An improved criterion for absence of eigenvalues of one-dimensional Schrödinger operators

We study one-dimensional Schrödinger operators with complex measures as potentials and present an improved criterion for absence of eigenvalues which involves a weak local periodicity condition. As an application we consider quasiperiodic measures as potentials. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evaluation of confidence intervals for the kappa statistic when the assumption of marginal homogeneity is violated

This article studies the robustness of confidence interval construction for the intraclass kappa statistic based on a dichotomous response when the assumption of marginal homogeneity across two raters is violated. Two methods of construction are considered: the goodness-of-fit approach and the modified Wald method. Evaluation was done by exact calculation of the confidence interval coverage produced by these approaches. It was found that under mild departures from marginal homogeneity (differences in rater success rates of $<$ 10 %), the goodness- of-fit approach can be recommended. Moreover, under these same conditions, Cohen’s kappa tends to be less biased as a point estimator than the intraclass kappa statistic.     

Vertex opposition in spherical buildings

We study to which extent all pairs of opposite vertices of self-opposite type determine a given building. We provide complete answers in the case of buildings related to projective spaces, to polar spaces and the exceptional buildings, but for the latter we restrict to the vertices whose Grassmannian defines a parapolar space of point diameter 3. Some results about non-self opposite types for buildings of types ${\mathsf{A}_n}$ , ${\mathsf{D}_m}$ (m odd), and ${\mathsf{E}_6}$ are also provided.     

A Convenient,Selective Synthesis of Bis[2,4‐bis(trifluoromethyl)phenyl]phosphane Derivatives Starting from 1,3‐Bis(trifluoromethyl)benzene

The reaction of the sterically shielded phosphane derivative, dichlorodiethylaminophosphane, Cl₂PNEt₂, with an excess of a mixture of 2,6‐bis(trifluoromethyl) and 2,4‐bis(trifluoromethyl)phenyl lithium gives bis[2,4‐bis(trifluoromethyl)phenyl]diethylaminophosphane, [2,4‐(CF₃)₂C₆H₃]₂PNEt₂, in 72 % yield as a colourless solid, while 2,6‐bis(trifluoromethyl)phenyl lithium remains unchanged in solution. The amino derivative crystallizes in the monoclinic space group P2₁/c (a 869.2(1), b 1857.4(1), c 1357.6(1) pm, β 100.57(4)°, Z = 4). Treatment of [2,4‐(CF₃)₂C₆H₃]₂PNEt₂ in CHCl₃ solution with conc. HCl allows the synthesis of [2,4‐(CF₃)₂C₆H₃)]₂PCl. [2,4‐(CF₃)₂C₆H₃]₂PCl reacts with H₂O in THF solution with quantitative formation of the corresponding secondary phosphane oxide. To obtain bis[2,4‐bis(trifluoromethyl)phenyl]phosphinic acid, [2,4‐(CF₃)₂C₆H₃]₂P(O)OH, quantitatively, a CHCl₃ solution of [2,4‐(CF₃)₂C₆H₃]₂P(O)H, has to be stirred in an NO₂ atmosphere. The phosphinic acid crystallizes is the triclinic space group (a 754.2(1), b 927.6(2), c 1305.5(2) pm, α 85.11(2)°, β 75.45(1)°, γ 79.99(2)°, Z = 2). From the reaction of the phosphinic acid with either elemental sodium or with cyanide salts, the corresponding phosphinate salts are obtained in an almost quantitatively yield.     

Self-supporting hydrogel stamps for the microcontact printing of proteins

In this work we explore a new hydrogel stamp material obtained from polymerizing 2-hydroxyethyl acrylate and poly(ethylene glycol) diacrylate in the presence of water for the microcontact printing of proteins directly on gold substrates and by covalent coupling to self-assembled monolayers of alkanethiols. At high cross-link density, the hydrogel is rigid, hydrophilic, and with a high buffer holding capacity to enable the unsupported printing of protein patterns homogeneously and reproducibly, with micrometer-range precision. The stamps were used to print antibodies to human parathyroid hormone, which were shown using immunoassay tests to retain their biological function with binding capacities comparable to those of solution-adsorbed antibodies.     

A "green route" to propene through selective hydrogen oxidation

The pros and cons of oxidative dehydrogenation of propane are outlined and a new catalytic system based on metal-doped cerianite catalysts is introduced. These novel materials catalyze the selective combustion of hydrogen from a mixture of hydrogen, propane, and propene at 550 degrees C. This gives three key advantages: energy is supplied directly where needed, product separation is made easier, and the dehydrogenation equilibrium is shifted to the desired products. A set of eighteen doped cerianites was synthesized in parallel, characterized, and screened for activity, selectivity, and stability in a cyclic redox system. The best results were obtained with Ce(0.89)Cr(0.02)Fe(0.09)O(2), Ce(0.98)Sn(0.02)O(2), and Ce(0.96)Cu(0.02)Zn(0.02)O(2), which gave 98 %, 91 %, and 98 % selectivity, respectively. Ce(0.89)Cr(0.02)Fe(0.09)O(2) also shows excellent stability in over 120 cycles (66 h on stream at 550 degrees C). Importantly, these doped cerias are monophasic crystalline materials. The dopants are incorporated as solid solutions throughout the fluorite lattice. This means that these catalysts are very stable (they do not sinter during reduction) as opposed to traditional supported metal oxides. The results show that both activity and selectivity towards hydrogen combustion can be tuned (increased or decreased) by selecting the appropriate dopant. Furthermore, the trends in selectivity differ from those measured on supported oxides of the same elements, which indicates that these novel materials indeed contain unique active sites. The factors governing selectivity towards hydrogen oxidation and the nature of the active site are discussed.