On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

Nerve growth factor selectively regulates expression of transcripts encoding ribosomal proteins

Background  

NGF exerts a variety of actions including promotion of neuronal differentiation and survival. The PC12 rat pheochromocytoma cell line has proved valuable for studying how NGF works and has revealed that the NGF mechanism includes regulation of gene expression. Accordingly, we used SAGE (Serial Analysis of Gene Expression) to compare levels of specific transcripts in PC12 cells before and after long-term NGF exposure. Of the approximately 22,000 transcripts detected and quantified, 4% are NGF-regulated by 6-fold or more. Here, we used database information to identify transcripts in our SAGE libraries that encode ribosomal proteins and have compared the effect of NGF on their relative levels of expression.     

Well-posed absorbing layer for hyperbolic problems

Summary. The perfectly matched layer (PML) is an efficient tool to simulate propagation phenomena in free space on unbounded domain. In this paper we consider a new type of absorbing layer for Maxwell's equations and the linearized Euler equations which is also valid for several classes of first order hyperbolic systems. The definition of this layer appears as a slight modification of the PML technique. We show that the associated Cauchy problem is well-posed in suitable spaces. This theory is finally illustrated by some numerical results. It must be underlined that the discretization of this layer leads to a new discretization of the classical PML formulation. Received May 5, 2000 / Published online November 15, 2001     

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     

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.

     

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.     

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.     

Spectroscopic study on the complex formation of chromogenic bridged calixarenes with aliphatic amines

The complex formation between chromogenic capped calix 4 arene derivatives comprising indophenol indicator group(s), and aliphatic amines has been studied by UV/Vis spectroscopy. The equilibrium constants have been determined in ethanol, and—for one ligand—also in dimethylsulfoxide. The results have been interpreted in terms of various types of host–guest interactions and of steric effects.