Classical solutions to a quadratically nonlinear gauge theory

We present some classical solutions to a gauge theory based on quadratically nonlinear Lie algebras without a central term. We observe that instanton-like and meron-like solutions force the internal fields to behave like solitons.     

Efficient multi and single line atomic fluorine lasers

Intense multi- and single-line laser operation is reported from semiconductively preionised atomic fluorine lasers employing an optimised capacitor transfer excitation circuitry. The performance and spectral characteristics of these lasers are discussed and compared to the characteristics of previously described atomic fluorine lasers. The efficiency of one of these lasers described, at optimum conditions, is reaching a value as high as 0.14%. To the best of our knowledge, this is the highest efficiency reported up date, for an atomic fluorine laser.     

Countably compact topological group topologies on free Abelian groups from selective ultrafilters

Tkachenko showed in 1990 the existence of a countably compact group topology on the free Abelian group of size c using CH. Koszmider, Tomita and Watson showed in 2000 the existence of a countably compact group topology on the free Abelian group of size c² using a forcing model in which CH holds.Wallace's question from 1955, asks whether every both-sided cancellative countably compact semigroup is a topological group. A counterexample to Wallace's question has been called a Wallace semigroup. In 1996, Robbie and Svetlichny constructed a Wallace semigroup under CH. In the same year, Tomita constructed a Wallace semigroup from MAcountable.In this note, we show that the examples of Tkachenko, Robbie and Svetlichny, and Koszmider, Tomita and Watson can be obtained using a family of selective ultrafilters. As a corollary, the constructions presented here are compatible with the total failure of Martin's Axiom.     

一个改进的Hardy-Hilbert不等式

通过建立权系数的不等式,得到一个改进的Hardy-Hilbert不等式.     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping

We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation.     

On Gittins’ index theorem in continuous time

We give a new and comparably short proof of Gittins’ index theorem for dynamic allocation problems of the multi-armed bandit type in continuous time under minimal assumptions. This proof gives a complete characterization of optimal allocation strategies as those policies which follow the current leader among the Gittins indices while ensuring that a Gittins index is at an all-time low whenever the associated project is not worked on exclusively. The main tool is a representation property of Gittins index processes which allows us to show that these processes can be chosen to be pathwise lower semi-continuous from the right and quasi-lower semi-continuous from the left. Both regularity properties turn out to be crucial for our characterization and the construction of optimal allocation policies.     

Über die abstandsverträglichen Abbildungen auf dem Kreis und auf der reellen Geraden

Zusammenfassung. Eine Abbildung zwischen metrischen R?umen hei?t abstandsvertr?glich, wenn der Abstand der Bilder zweier Punkte nur vom Abstand der Punkte selbst abh?ngt. Wir zeigen, dass eine Abbildung genau dann abstandsvertr?glich ist, wenn der Cauchyschen Funktionalgleichung genügt, also ein Endomorphismus der Gruppe ist. Ein entsprechendes Resultat gilt auch für die abstandsvertr?glichen Abbildungen des Kreises (mit der Multiplikation komplexer Zahlen als Gruppenverknüpfung). Damit kann man sowohl alle messbaren abstandsvertr?glichen Abbildungen von bzw. in sich angeben, als auch einen Nachweis für die Existenz nichtmessbarer abstandsvertr?glicher Abbildungen auf und erbringen. Eingegangen am 20. Juni 2001 / Angenommen am 13. September 2001     

A new trigonometric method of summation and its application to the degree of approximation

The object of the present investigation is to introduce a new trigonometric method of summation which is both regular and Fourier effective and determine its status with reference to other methods of summation (see §2-§4) and also give an application of this method to determine the degree of approximation in a new Banach space of functions conceived as a generalized Holder metric (see §5).