Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.     

R-matrices for elliptic Calogero-Moser models

The classicalR-matrix structure for then-particle Calogero-Moser models with (type IV) elliptic potentials is investigated. We show there is no momentum independentR-matrix (without spectral parameter) whenn 4. The assumption of momentum independence is sufficient to reproduce the dynamicalR-matrices of Avan and Talon for the type I, II, III degenerations of the elliptic potential. The inclusion of a spectral parameter enables us to findR-matrices for the general elliptic potential.     

Tensor products over abelian Walgebras

Tensor products of Calgebras over an abelian Walgebra are studied. The minimal Cnorm on is shown to be just the quotient of the minimal Cnorm on if or is exact.

     

Fractional Power Series and Pairings on Drinfeld Modules

Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing

which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.

     

Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Existence theorems for π/n vortex scattering

The analysis of 90° vortex-vortex scattering is extended to /n scattering in all head-on collisions ofn vortices in the Abelian Higgs model. A Cauchy problem with initial data that describe the scattering ofn vortices is formulated. It is shown that this Cauchy problem has a unique global finite-energy solution. The symmetry of the solution and the form of the local analytic solution then show that /n scattering is realized.     

Structure elucidation of triglycerides by chromatographic techniques. Part 1: Capillary GC of ozonized triglycerides

Structure determination of triglycerides according to their number of unsaturated fatty acids (N.U.F.A.) is more easily achieved after ozonolysis of their mixtures (fats and oils) than by capillary gas chromatographic analysis of the mixture as such. Analyses performed before and after ozonolysis of cocoa buttel, hazelnut oil, and a mixture of both fats illustrate the potential of this approach to the structure elucidation of triglycerides by chromatographic techniques.     

离子交换-原子捕集-火焰原子吸收光谱法测定水中的超痕量镍

在文中所述条件下,镍的原子捕集灵敏度较常规法高320倍,即在离子交换法浓缩仅40倍的情况下,可使镍的测定灵敏度提高12800倍,从而成功实现了ppt级超痕量镍的测定。     

σ,π-acetylido complexes via P---C bond cleavage of phosphinoacetylenes: X-ray structure of Fe2(CO)6(CCPh)(PPh2)

Solutions of Co^II salts of organic acids in primary amines absorb molecular oxygen rapidly and irreversibly forming μ-dioxygen—cobalt complexes. Thermolysis leads to a homopolar cleavage of the OO bond with subsequent radical reactions involving ligand amine. After thermolysis the capacity of oxygen uptake is reestablished (catalysis).     

Potentiometric studies of dithiooxamide with a sulphide-selective membrane electrode

The sulphide-selective electrode is applicable to the determination of dithiooxamide by titration with silver nitrate. The effect of the alkali content of the solutions on the reaction has been studied. The reaction products are silver sulphide, oxalic acid, and nitric acid. If the alkali concentration of the solution is lower than that equivalent to the acid formed during the titration, the amount of sulphide produced by hydrolysis decreases and the equilibrium potential is established more slowly.The determination is rapid and accurate in the presence of 1 M sodium hydroxide.