Hypercontractivity properties of nonsymmetric ornstein-uhlenbeck semigroups in hilbert spaces

We prove hypercontractivity of nonsymmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, using direct probabilistic arguments. Our results imply exponential convergence at infinity for the semigroup. We show by examples that in our setting logarithmic Sobolev inequalities do not hold in general     

Controlling 6-endo-selectivity in oxidation/bromocyclization cascades for synthesis of aplysiapyranoids and other 2,2,6,6-substituted tetrahydropyrans

A cascade, composed of (i) oxovanadium(V)-catalyzed oxidation of bromide by tert-butyl hydroperoxide and (ii) stereoselective 6-endo-bromocyclization, affords 3-bromo-2-aryl-2,6,6-trimethyltetrahydropyrans from styrene-type tertiary alkenols in synthetically useful yields. (E)-Alkenols add the bromo- and the alkoxy substituent anti-selectively across the double bond, indicating a bromonium ion-mechanism for the ring closure. 6-endo-control of the alkenol cyclization thereby arises from the polar effect of the aryl substituent. Two methyl substituents bound to the alkene terminus are not similarly able to favor 6-endo-cyclization, because strain arising from methyl group repulsion, as the bromonium-activated π-bond and the hydroxyl oxygen approach, directs bromocyclization of tertiary prenyl-type substrates toward tetrahydrofuran formation. A hexasubstituted bromotetrahydropyran prepared from the oxidation/bromocyclization cascade served as starting material for synthesis of racemic aplysiapyranoid A, in a sequence of free radical and polar functional group interconversion.     

Numerical differentiation on scattered data through multivariate polynomial interpolation

BIT Numerical Mathematics - We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja...     

Modelling and design of a novel air-spring for a suspension seat

Air-springs used in conjunction with auxiliary volumes provide both spring stiffness and damping. The damping is introduced through the flow restriction connecting the two air volumes. This article presents a simplified model of an air-spring with an auxiliary volume derived from first principles for simulation and design of an air-spring coupled to an auxiliary volume for a suspension seat. Tests were performed on an experimental apparatus to validate the model. The simulation model of the air-spring and auxiliary volume followed the trend predicted by the literature but showed approximately 27% lower transmissibility amplitude and 21% lower system natural frequency than that obtained by tests when using large diameter flow restrictions. This inaccuracy is assumed to be introduced by the simplified mass transfer equations defining the flow restriction between air-spring and auxiliary volume. The model showed closer correlation to the experimental results when the auxiliary volume size was decreased by two-thirds of the volume actually used for the experiment. A procedure, using the developed simulation model, for the design of a prototype air-spring and auxiliary volume, is presented for application in a typical articulated or rigid frame dump truck. The goal of the study was to design a suspension seat for this application and to obtain a SEAT value below 1.1. The design was optimised by varying auxiliary volume size and flow restriction diameters for different loads. A SEAT value of less than 0.9 was achieved, clearly indicating the effectiveness of using an auxiliary volume with an air-spring as seat suspension.     

Multigrid methods for Toeplitz linear systems with different size reduction

Starting from the spectral analysis of g-circulant matrices, we study the convergence of a multigrid method for circulant and Toeplitz matrices with various size reductions. We assume that the size n of the coefficient matrix is divisible by g≥2 such that at the lower level the system is reduced to one of size n/g, by employing g-circulant based projectors. We perform a rigorous two-grid convergence analysis in the circulant case and we extend experimentally the results to the Toeplitz setting, by employing structure preserving projectors. The optimality of the two-grid method and of the multigrid method is proved, when the number θ∈ℕ of recursive calls is such that 1<θ<g. The previous analysis is used also to overcome some pathological cases, in which the generating function has zeros located at “mirror points” and the standard two-grid method with g=2 is not optimal. The numerical experiments show the correctness and applicability of the proposed ideas, both for circulant and Toeplitz matrices.     

Interval methods as a simulation tool for the dynamics of biological wastewater treatment processes with parameter uncertainties

This paper presents sophisticated interval algorithms for the simulation of discrete-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Since naive implementations of interval algorithms might lead to guaranteed enclosures of all system states which are too conservative to be practically useful, we present algorithmic extensions of classical approaches which are applicable to the simulation of non-cooperative systems with time-varying uncertain parameters. Overestimation arising in the interval evaluation of dynamical system models due to the wrapping effect is reduced by an exact pseudo-linear transformation of nonlinear state equations and by new heuristics for the subdivision of interval enclosures which especially prefer splitting of unstable intervals. To highlight the typical procedure for parameterization of interval-based simulation routines and to demonstrate their efficiency, a nonlinear model of biological wastewater treatment processes is discussed. For this application, we consider the maximum specific growth rate of substrate consuming bacteria as a time-varying uncertain parameter. Only worst-case bounds are assumed to be available for the range of this parameter while no information is provided about its actual variation rate.