The Tate-Voloch conjecture for Drinfeld modules

We study the v-adic distance from the torsion of a Drinfeld module to an affine variety.     

Differential operators on Hilbert modular forms

We investigate differential operators and their compatibility with subgroups of SL₂n(R). In particular, we construct Rankin-Cohen brackets for Hilbert modular forms, and more generally, multilinear differential operators on the space of Hilbert modular forms. As an application, we explicitly determine the Rankin-Cohen bracket of a Hilbert-Eisenstein series and an arbitrary Hilbert modular form. We use this result to compute the Petersson inner product of such a bracket and a Hilbert modular cusp form.     

A Fubini theorem

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I₀ on N² strongly violates the countable chain condition.     

Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

The Nature of Electronic Charge

Advances in gauge theories and unified theories have not thrown light on the meaning of electron. The problem of the origin of electronic charge is made precise, new insights gained from Weyl space are summarized, and the origin of charge in terms of fractional spin is suggested. A new perspective on the abelian Chern-Simons theory is presented to explain charge.     

An explosion point space without the fixed point property

In 1988 A. Gutek proved that there exist one-point connectifications of hereditarily disconnected spaces that do not have the fixed point property. We improve on this result by constructing a one-point connectification of a totally disconnected space without the fixed point property.     

Complete systems, elementary submodels and the tightness of upper hyperspaces

We introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality κ satisfying one of these properties is of type Gκ. Hence, we define several new variants of the ?ech number and use elementary submodels to determine further results. We introduce M-hulls and M-networks, for M elementary submodel. As an application, we give estimates for both the tightness and the Lindelöf number of a generic upper hyperspace. Two recent results of Costantini, Holá and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries.     

The origin of the formation of cavities in galvanized coatings

The role of water‐soluble corrosion products on galvanized wires was examined. The samples used were industrial hot‐dip galvanized wires, which were exposed to the open air under all weather conditions for a relatively short time (6 and 12 months), in an urban environment close to the sea. The samples were studied by different methods, i.e. scanning electron microscopy (SEM), transmission electron microscopy (TEM), X‐ray diffraction (XRD) and optical microscopy (OM). Several phases were detected because of the galvanization procedure and the steel substrate. Furthermore, phases which were formed as a result of the reaction of zinc with the atmosphere were also detected. These were oxides like ZnO, carbonates like ZnCO₃ and hydrated Zn and Fe sulfates. Their presence influences the corrosion resistance of the wires, which finally, strongly depends on the solubility of the wires in water. The SO₄^2? compounds especially are very soluble and consequently are easily removed from the coating surface, leading to its degradation by the formation of cavities. In any case, their presence, even after a short period of exposure, implies that the coating is highly affected by the atmosphere of the modern city. Copyright © 2006 John Wiley & Sons, Ltd.     

二分量高温超导机理

用两种电子态,讨论了金属—绝缘相变、反铁磁性—金属相变,以及相分离、正常态—超导态相变、非费米液体行为、高Tc等 关键词： 两种电子态 格林函数 玻色化 高温超导