Approximation of bandlimited functions

Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions—the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae.     

Characterization of low molecular weight hydrocarbon oligomers by laser desorption/ionization time-of-flight mass spectrometry using a solvent-free sample preparation method.

A new solvent-free sample preparation method using silver trifluoroacetate (AgTFA) was developed for the analysis of low molecular weight paraffins and microcrystalline waxes by laser desorption/ionization time-of-flight mass spectrometry (LDI-TOFMS). Experiments show that spectral quality can be enhanced by dispersing AgTFA directly in liquid paraffins without the use of additional solvents. This preparation mixture is applied directly to the MALDI probe. Solid waxes could be examined by melting prior to analysis. The method also provides sufficiently reproducible spectra that peak area ratios between mono- and bicyclic alkane peaks indicated variations in the cycloalkane content of paraffin samples. Dehydrogenation of hydrocarbons observed during the desorption/ionization process was studied by analysis of alkane standards.     

Design of neutral, mono- or di-cationic water-soluble trihydrazidophosphoradamantanes

The versatile behavior of a trihydrazidophosphoradamantane allowing the synthesis of a variety of neutral, mono- or di-cationic water-soluble molecules of potential interest for biphasic catalysis is reported.     

Room temperature Ni-catalyzed reduction of aryl tosylates by borane hydrides

Mild Ni-catalyzed homogeneous reductions of aryl tosylates are described for the first time. The catalytic system Ni(PPh₃)₂Cl₂ and PCy₃ is shown to be general for hydrogenolysis of a wide range of tosylates, including hindered, deactivated, heterocyclic, and bifunctional examples.     

On the geometry of infinite cyclic subgroups

In this paper we construct an example of a word metric on an infinite cyclic subgroup. This example shows that subexponential distortion does not obstruct non-trivial growth of connected radii. This answers a question of Gromov [6]. The constructed metric has other pathological properies. Specifically, its asymptotic cone depends on the choice of ultrafilter and scaling sequence. The work has been partially supported by the Swiss National Science Foundation.     

IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.     

Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

The Problem of the Pointwise Fourier Inversion for Piecewise Smooth Functions of Several Variables

We study the pointwise convergence problem for the inverse Fourier transform of piecewise smooth functions, i.e., whether S_rD f (\bx) ? f (\bx)S_{\rho D} f (\bx) \to f (\bx) as r? ￥\rho \to \infty . r? ￥\rho \to \infty . Here for \bx,\bxi ? \Rn\bx,\bxi \in \Rn S_rDf(\bmx)=\dsf1(2p)^n/2\intli_rD [^(f)](\bxi) e^{\dst iá\bmx,\bxi?} d\bxi . S_{\rho D}f(\bm{x})=\dsf1{(2\pi)^{n/2}}\intli_{\rho D} \widehat{f}(\bxi) e^{\dst i\langle\bm{x},\bxi\rangle} d\bxi~. is the partial sum operator using a convex and open set DD containing the origin, and rD={ r\bxi:\bxi ? D }\rho D=\left\{ \rho \bxi:\bxi\in D \right\}.     

On Poisson–Malcev Structures

Malcev–Poisson structure on a manifold is analogous to a Poisson structure with the Lie identity replaced by a slightly more general Malcev identity. Examples of such structures arise naturally. In the second part of the paper we study Malcev bialgebras. A theorem of characterization is proved.