Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

^** Email: todor{at}math.ethz.ch^*** Corresponding author. Email: schwab{at}math.ethz.ch A scalar, elliptic boundary-value problem in divergence formwith stochastic diffusion coefficient a(x, ) in a bounded domainD ^d is reformulated as a deterministic, infinite-dimensional,parametric problem by separation of deterministic (x D) andstochastic ( ) variables in a(x, ) via Karhúnen–Loèveor Legendre expansions of the diffusion coefficient. Deterministic,approximate solvers are obtained by projection of this probleminto a product probability space of finite dimension M and sparsediscretizations of the resulting M-dimensional parametric problem.Both Galerkin and collocation approximations are considered.Under regularity assumptions on the fluctuation of a(x, ) inthe deterministic variable x, the convergence rate of the deterministicsolution algorithm is analysed in terms of the number N of deterministicproblems to be solved as both the chaos dimension M and themultiresolution level of the sparse discretization resp. thepolynomial degree of the chaos expansion increase simultaneously.     

Production of charged pions, kaons and antikaons in relativistic C + C and C + Au collisions

Production cross-sections of charged pions, kaons and antikaons have been measured in C+C and C+Au collisions at beam energies of 1.0 and 1.8 AGeV for different polar emission angles. The kaon and antikaon energy spectra can be described by Boltzmann distributions whereas the pion spectra exhibit an additional enhancement at low energies. The pion multiplicity per participating nucleon M(π⁺)/<A _part> is a factor of about 3 smaller in C+Au than in C+C collisions at 1.0 AGeV whereas it differs only little for the C and the Au target at a beam energy of 1.8 AGeV. The K⁺ multiplicities per participating nucleon M(K⁺)/ <A _part> are independent of the target size at 1 AGeV and at 1.8 AGeV. The K^- multiplicity per participating nucleon M(K^-)/ <A _part> is reduced by a factor of about 2 in C+Au as compared to C+C collisions at 1.8 AGeV. This effect might be caused by the absorption of antikaons in the heavy target nucleus. Transport model calculations underestimate the K^-/K⁺ ratio for C+C collisions at 1.8 AGeV by a factor of about 4 if in-medium modifications of K-mesons are neglected. Received: 10 December 1999 / Accepted: 14 November 2000     

Ring opening of unprotected aziridines by zinc selenolates in a biphasic system

A set of chiral β-seleno amines were prepared by the ring-opening reaction of unprotected aziridines. Under acid conditions diaryl or dialkyl diselenides were reduced by zinc and treated with unprotected aziridines to produce the desired products in good yields. Chiral β-telluro amine was also obtained using this method.     

Sparse p-version BEM for first kind boundary integral equations with random loading

We consider the weakly singular boundary integral equation on a deterministic smooth closed curve with random loading g(ω). Given the kth order statistical moment of g, the aim is the efficient deterministic computation of the kth order statistical moment of u. We derive a deterministic formulation for the kth statistical moment. It is posed in the tensor product Sobolev space and involves the k-fold tensor product operator . The standard full tensor product Galerkin BEM requires unknowns for the kth moment problem, where N is the number of unknowns needed to discretize Γ. Extending ideas of [V.N. Temlyakov, Approximation of functions with bounded mixed derivative, Proc. Steklov Inst. Math. (1989) vi+121. A translation of Trudy Mat. Inst. Steklov 178 (1986)], we develop the p-Sparse Grid Galerkin BEM to reduce the number of unknowns from to .     

Approximation by Shepard type pseudo-linear operators and applications to Image Processing

Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the practical point of view in Image Processing. We study max–min, max–product Shepard type approximation operators together with Shepard operators based on pseudo-operations generated by an increasing continuous generator. It is shown that in several cases these outperform classical approximation operators based on sum and product operations.     

Self-assembly of peptide porphyrin complexes: toward the development of smart biomaterials

The anionic porphyrin, meso-tetrakis(4-sulfonatophenyl)porphine, is found to tightly bind to an engineered 14-residue peptide, resulting in induced alpha-helix formation when mixed in aqueous solutions. The small porphyrin-peptide dissociation constant (2 muM) observed is related to the energetics of peptide helix formation coupled with electrostatic interactions between the anionic porphyrin and cationic residues in the coiled peptide. Analytical ultracentrifugation measurements indicate the porphyrin-peptide complexes dimerize, probably into a coiled coil, and weakly associate to form even higher order structures.     

Easy dual-mode ambient mass spectrometry with Venturi self-pumping, canned air, disposable parts and voltage-free sonic-spray ionization

An exceptionally easy to assemble source for ambient mass spectrometry is described. Based on Venturi easy ambient sonic-spray ionization (V-EASI), the source was further simplified by the use of a can of compressed air which simultaneously provides solution or solvent Venturi self-pumping and continuous, stable and abundant low-noise ion signal via voltage-free sonic-spraying. Further simplification was also attained by the use of inexpensive and readily commercially available parts: a surgical 2-way catheter, an aerosol can of compressed air, a 30 cm long fused-silica capillary and a hypodermic needle. This "Spartan" V-EASI source seems to offer one of the easiest and cheapest ways to make ions for ambient desorption/ionization mass spectrometry analysis of both liquid and solid samples.     

One-nucleon removal cross-sections for 17, 19C and 8, 10B

One-neutron removal cross-sections ( ) of ^{17, 19}C in various targets at about 900 MeV/nucleon, and one-proton removal cross-sections ( ) of ^{8, 10}B at about 1400 MeV/nucleon were measured using the fragment separator FRS at GSI. A significant increase of for ¹⁹C compared to its neighbors was observed. The same behavior was found for for the neutron-deficient nucleus ⁸B compared to the stable isotope ¹⁰B. These results support a one-neutron halo structure in ¹⁹C and a one-proton halo in ⁸B. Received: 26 July 2000 / Accepted: 11 January 2001