On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle

We consider the general problem of determining the maximum possible multiplicity of an eigenvalue in a Hermitian matrix whose graph contains exactly one cycle. For some cases we express that maximum multiplicity in terms of certain parameters associated with the graph.     

Ordered OLPS and CF Nth numerators

Definitions, theorems and examples are established for a general model of Laurent polynomial spaces and ordered orthogonal Laurent polynomial sequences, ordered with respect to ordered bases and orthogonal with respect to inner products ·=L°⊙ decomposed into transition functional ⊙ and strong moment functional, or, more generally, sample functional L couplings. Under this formulation that is shown to subsume those in the existing literature, new fundamental results are produced, including necessary and sufficient conditions for ordered OLPS to be sequences of nth numerators of continued fractions, in contrast to the classical result concerning nth denominators which is shown to hold only in special cases.     

Scalar and axial-vector mesons

Almost thirty years ago, Penny G. Estabrooks asked “Where and what are the scalar mesons?” (P. Estabrooks, Phys. Rev. D 19, 2678 (1979)). The first part of her question can now be confidently responded (E. van Beveren et al., Z. Phys. C 30, 615 (1986)). However, with respect to the “What” many puzzles remain unanswered. Scalar and axial-vector mesons form part of a large family of mesons. Consequently, though it is useful to pay them some extra attention, there is no point in discussing them as isolated phenomena. The particularity of structures in the scattering of --basically-- pions and kaons with zero angular momentum is the absence of the centrifugal barrier, which allows us to “see” strong interactions at short distances. Experimentally observed differences and similarities between scalar and axial-vector mesons on the one hand, and other mesons on the other hand, are very instructive for further studies. Nowadays, there exists an abundance of theoretical approaches towards the mesonic spectrum, ranging from confinement models of all kinds, i.e., glueballs, and quark-antiquark, multiquark and hybrid configurations, to models in which only mesonic degrees of freedom are taken into account. Nature seems to come out somewhere in the middle, neither preferring pure bound states, nor effective meson-meson physics with only coupling constants and possibly form factors. As a matter of fact, apart from a few exceptions, like pions and kaons, Nature does not allow us to study mesonic bound states of any kind, which is equivalent to saying that such states do not really exist. Hence, instead of extrapolating from pions and kaons to the remainder of the meson family, it is more democratic to consider pions and kaons mesonic resonances that happen to come out below the lowest threshold for strong decay. Nevertheless, confinement is an important ingredient for understanding the many regularities observed in mesonic spectra. Therefore, excluding quark degrees of freedom is also not the most obvious way of describing mesons in general, and scalars and axial-vectors in particular.     

The three space problem in topological groups

We study compact, countably compact, pseudocompact, and functionally bounded sets in extensions of topological groups. A property P is said to be a three space property if, for every topological group G and a closed invariant subgroup N of G, the fact that both groups N and G/N have P implies that G also has P. It is shown that if all compact (countably compact) subsets of the groups N and G/N are metrizable, then G has the same property. However, the result cannot be extended to pseudocompact subsets, a counterexample exists under p=c. Another example shows that extensions of groups do not preserve the classes of realcompact, Dieudonné complete and μ-spaces: one can find a pseudocompact, non-compact Abelian topological group G and an infinite, closed, realcompact subgroup N of G such that G/N is compact and all functionally bounded subsets of N are finite. Several examples given in the article destroy a number of tempting conjectures about extensions of topological groups.     

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.     

ℙmax variations related to slaloms

We prove the iteration lemmata, which are the key lemmata to show that extensions by Pmax variations satisfy absoluteness for Π₂-statements in the structure 〈H (ω ₂), ∈, NS_{ω 1}, R 〉 for some set R of reals in L (ℝ), for the following statements: (1) The cofinality of the null ideal is ℵ₁. (2) There exists a good basis of the strong measure zero ideal. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Invariant measures and regularity properties of perturbed Ornstein-Uhlenbeck semigroups

This paper deals with perturbations of the Ornstein-Uhlenbeck operator on L²-spaces with respect to a Gaussian measure μ. We perturb the generator of the Ornstein-Uhlenbeck semigroup by a certain unbounded, non-linear drift, and show various properties of the perturbed semigroup such as compactness and positivity. Strong Feller property, existence and uniqueness of an invariant measure are discussed as well.     

Automorphisms and blocking in simple games

Different (proper as well as improper) simple games may share any nonseparating blocking family. An interesting question is whether all such proper games on one hand, and all improper ones on the other, are isomorphic. The answer is given here and the automorphisms of the blocking family help us to understand the structure and links of all such games.     

板模型中具广义边界条件的迁移算子的谱分析

在LP(1 P<∞)空间研究了板模型中一类带广义边界条件具各向异性、连续能量、均匀介质迁移算子的谱,证明了该迁移算子生成C0半群的D yson—Ph illips展开式的二阶余项在LP(1相似文献   

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.