A simple proof of Sanov’s theorem*

A simple self-contained proof of Sanov's theorem in τ-topology is given, well suited for a first course on large deviations. *This work was supported by the Hungarian National Foundation for Scientific Research under Grant T046376     

Homology of proof-nets

This work defines homology groups for proof-structures in multiplicative linear logic (see [Gir1], [Gir2], [Dan]). We will show that these groups characterize proof-nets among arbitrary proof-structures, thus obtaining a new correctness criterion and of course a new polynomial algorithm for testing correctness. This homology also bears information on sequentialization. An unexpected geometrical interpretation of the linear connectives is given in the last section. This paper exclusively focuses onabstract proof-structures, i.e. paired-graphs. The relation with actual proofs is investigated in [Gir1], [Gir2], [Dan], [Ret] and [Tro].     

Acousto-optic mode coupling of partially coherent light in two-mode optical fibers

An acoustic pulse propagating on a two-mode fiber can act as a beam splitter in a scanning interferometer. When this device is employed in white-light interferometry, the effects of distributed coupling and dispersive interferometer arms need to be considered. A theory suitable for treating acousto-optic interaction of partially coherent light in a moving interaction region was developed. It was found that differential optical dispersion should be negligible and the acoustic pulse length short. Also the coherence time should be short but long compared to the intermodal group delay difference over a pulse length. Experiments with long acoustic pulses were performed, and fairly good agreement with theory was obtained.     

On uniformly Gâteaux smooth norms and normal structure

It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure.

     

Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces

We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.     

Phase diagram of a two-frequency chiral nematic mixture in an electric field

The behaviour of a chiral nematic mixture with low frequency dielectric relaxtion was studied between two electrodes, with homeotropic anchoring, in the presence of an AC electric field E. The phase diagram in the parameter plane (d/p, E) was determined for this mixture which could be dielectrically negative or positive in different frequency ranges. The determination was carried out by changing the sample thickness d and both the amplitude and frequency of the electric field at a constant cholesteric pitch p.     

The complexification and degree of a semi-algebraic set

The complexification of a semi-algebraic set is the smallest complex algebraic set containing S. Let S be defined by s polynomials of degrees less than d. We prove that the geometric degree of the complexification is less than . Received: 9 January 1997; in final form: 11 August 2000 / Published online: 17 May 2001     

Matrix-Untersuchungen zu monomerem Kupfer(I)-chlorid und seinen Komplexen mit N2 und PN IR-spektroskopische Nachweise und ab-initio Rechnungen

Matrix-Investigations on Monomeric Copper(I) Chloride and its Complexes with N₂ and PN Ligands. IR Spectroscopic Results and ab-initio Calculation In solid argon the reaction of monomeric CuCl with N₂ yields ClCuN₂. On the basis of two absorptions in the ir-spectrum and their corresponding isotopic shifts (_14/15N) and with the help of a normal coordinate analysis, linearity of the molecule has been deduced. These results are confirmed by large scale ab-initio Calculations (CPF, MP2). Reaction of monomeric CuCl with molecular PN under matrix condition is shown to give rise to new absorptions in the IR spectrum which arev assigned to a linear molecule ClCuNP.