The jump of the Milnor number in the X 9 singularity class

The jump of the Milnor number of an isolated singularity f ₀ is the minimal non-zero difference between the Milnor numbers of f ₀ and one of its deformations (f _s ). We prove that for the singularities in the X ₉ singularity class their jumps are equal to 2.     

Functional Central Limit Theorem for Additive Functionals of <Emphasis Type="Italic">α</Emphasis>-stable Processes

Let β be a standard Brownian motion, let X be an α-stable process, and let f=[^(m)]f=\widehat \mu be the Fourier transform of a discrete measure. It is shown that weakly in C([0, + ∞ )),

Large deviation principle for stochastic evolution equations

Summary The large deviation principle obtained by Freidlin and Wentzell for measures associated with finite-dimensional diffusions is extended to measures given by stochastic evolution equations with non-additive random perturbations. The proof of the main result is adopted from the Priouret paper concerning finite-dimensional diffusions. Exponential tail estimates for infinite-dimensional stochastic convolutions are used as main tools.     

On L2-cohomology and Property (T) for Automorphism Groups of Polyhedral Cell Complexes

We present an update of Garland's work on the cohomology of certain groups, construct a class of groups many of which satisfy Kazhdan's Property (T) and show that properly discontinuous and cocompact groups of automorphisms of (4,4) or (6,3)-complexes do not satisfy Property (T). Submitted: September 1996, final version: March 1997     

A visualization study of the interaction of a free vortex with the wake behind an airfoil

The two-dimensional interaction of a single vortex with a thin symmetrical airfoil and its vortex wake has been investigated in a low turbulence wind tunnel having velocity of about 2 m/s in the measuring section. The flow Reynolds number based on the airfoil chord length was 4.5 × 10³. The investigation was carried out using a smoke-wire visualization technique with some support of standard hot-wire measurements. The experiment has proved that under certain conditions the vortex-airfoil-wake interaction leads to the formation of new vortices from the part of the wake positioned closely to the vortex. After the formation, the vortices rotate in the direction opposite to that of the incident vortex.List of symbols c test airfoil chord - C vortex generator airfoil chord - TA test airfoil - TE test airfoil trailing edge - TE _G vortex generator airfoil trailing edge - t dimensionless time-interval measured from the vortex passage by the test airfoil trailing edge: gDt=(T-T- _TE)·U/c - T time-interval measured from the start of VGA rotation - U free stream velocity - U vortex induced velocity fluctuation - VGA vortex generator airfoil - y distance in which the vortex passes the test airfoil - Z vortex circulation coefficient: Z=/(U · c/2) - vortex generator airfoil inclination angle - vortex circulation - vortex strength: =/2     

A novel approach to the rapid determination of amoxicillin in human plasma by solid phase microextraction and liquid chromatography

A new approach to the rapid determination of amoxicillin (AMO) in human plasma followed by solid phase microextraction (SPME) fiber coatings based on conducting polymers (polypyrrole and polythiophene) and high performance liquid chromatography (HPLC) has been described. The porous structures of the electrochemically deposited polymer coatings have been characterized by scanning electron microscopy (SEM). The experimental parameters relating to the extraction efficiency of the SPME fibers such as pH, extraction time and desorption conditions (solvents, time) were studied and selected. The SPME/HPLC-UV method was linear over a working range of 1-50 μg ml(-1). The inter-day accuracy (expressed as coefficients of variations, CVs) was less than 15% and precision (expressed as the relative standard deviations, RSDs) with percentage values was less than 5.9%. Amoxicillin was found to be stable in the human plasma at room temperature (20 °C) within 8 hours. The developed method was successfully applied to the analysis of real human plasma samples. The limit of detection and limit of quantification for amoxicillin in plasma were 1.21 μg ml(-1) and 3.48 μg ml(-1), respectively.     

Experimental and Theoretical Investigation of Vibrational Spectra of Coordination Polymers Based on TCE‐TTF

The room‐temperature infrared and Raman spectra of a series of four isostructural polymeric salts of 2,3,6,7‐tetrakis(2‐cyanoethylthio)‐tetrathiafulvalene (TCE‐TTF) with paramagnetic (Co^II, Mn^II) and diamagnetic (Zn^II, Cd^II) ions, together with BF₄^? or ClO₄^? anions are reported. Infrared and Raman‐active modes are identified and assigned based on theoretical calculations for neutral and ionized TCE‐TTF using density functional theory (DFT) methods. It is confirmed that the TCE‐TTF molecules in all the materials investigated are fully ionized and interact in the crystal structure through cyanoethylthio groups. The vibrational modes related to the C?C stretching vibrations of TCE‐TTF are analyzed assuming the occurrence of electron–molecular vibration coupling (EMV). The presence of the antisymmetric C?C dimeric mode provides evidence that charge transfer takes place between TCE‐TTF molecules belonging to neighboring polymeric networks.     

Means of iterates

Aequationes mathematicae - We determine continuous bijections f, acting on a real interval into itself, whose k-fold iterate is the quasi-arithmetic mean of all its subsequent iterates from $$f^0$$...     

Unlocking a (Pseudo)-Mechanically Interlocked Molecule with a Coronene “Shoehorn”

Mechanically interlocked molecules (MIMs) have gained increasing interest during the last decades, not only because of their aesthetic appeal, but also because their unique properties have allowed them to find applications in nanotechnology, catalysis, chemosensing and biomedicine. Herein we describe how a pyrene molecule with four octynyl substituents can be easily encapsulated within the cavity of a tetragold(I) rectangle-like metallobox, by template formation of the metallo-assembly in the presence of the guest. The resulting assembly behaves as a mechanically interlocked molecule (MIM), in which the four long limbs of the guest protrude from the entrances of the metallobox, thus locking the guest inside the cavity of the metallobox. The new assembly resembles a metallo-suit[4]ane, given the number of protruding long limbs and the presence of the metal atoms in the host molecule. However, unlike normal MIMs, this molecule can release the tetra-substituted pyrene guest by the addition of coronene, which can smoothly replace the guest in the cavity of the metallobox. Combined experimental and computational studies allowed the role of the coronene molecule in facilitating the release of the tetrasubstituted pyrene guest to be explained, through a process that we named “shoehorning”, as the coronene compresses the flexible limbs of the guest so that it can reduce its size to slide in and out the metallobox.