Bergeʼs maximum theorem for noncompact image sets

This note generalizes Berge?s maximum theorem to noncompact image sets. It also clarifies the results from Feinberg, Kasyanov and Zadoianchuk (2013) [7] on the extension to noncompact image sets of another Berge?s theorem, that states semi-continuity of value functions. Here we explain that the notion of a K$\mathbb{K}$-inf-compact function introduced there is applicable to metrizable topological spaces and to more general compactly generated topological spaces. For Hausdorff topological spaces we introduce the notion of a KN$\mathbb{K}\mathbb{N}$-inf-compact function (N$\mathbb{N}$ stands for “nets” in K$\mathbb{K}$-inf-compactness), which coincides with K$\mathbb{K}$-inf-compactness for compactly generated and, in particular, for metrizable topological spaces.     

Nickel‐Catalyzed Chain‐Walking Cross‐Electrophile Coupling of Alkyl and Aryl Halides and Olefin Hydroarylation Enabled by Electrochemical Reduction

The first electrochemical approach for nickel‐catalyzed cross‐electrophile coupling was developed. This method provides a novel route to 1,1‐diarylalkane derivatives from simple and readily available alkyl and aryl halides in good yields and excellent regioselectivity under mild conditions. The procedure shows good tolerance for a broad variety of functional groups and both primary and secondary alkyl halides can be used. Furthermore, the reaction was successfully scaled up to the multigram scale, thus indicating potential for industrial application. Mechanistic investigation suggested the formation of a nickel hydride in the electroreductive chain‐walking arylation, which led to the development of a new nickel‐catalyzed hydroarylation of styrenes to provide a series of 1,1‐diaryl alkanes in good yields under mild reaction conditions.     

Lattice Boltzmann representation of neutral turbulence in the cold gas blanket divertor regime

In the divertor plasma detachment regime one expects to encounter turbulent collisional neutral gas dynamics. These conditions are ideally simulated by lattice Boltzmann methods — methods ideal for application on multi-parallel processors. As illustrative of this method, we specifically show the effect of conductivity in the Rayleigh-Benard convection cells, using an octagonal velocity lattice. This work was supported by DoE and a joint U.S-Czech grant. These results were presented at the 6th International Workshop on Plasma Edge Theory in Fusion Devices, 15–17 September 1997.     

Interpretation of measured data and the resolution analysis of the RTP 4-channel pulsed radar

In the present work, the resolution of a 4-channel pulsed radar being built at Rijnhuisen for RTP tokamak is analyzed. The achievable resolution depends mainly on the accuracy of the time-of-flight measurements and the number of sampling frequencies; since the technological solution and the configuration have already been set, the emphasis is laid on the interpretation of the measured data (inversion problem) and minimization of the overall error. For this purpose, a specific neural network — Multi Layer Perceptron (MLP) — has been successfully applied.The central density in the range 0.2–0.6×10²⁰ m^–3 was considered, i.e., above the critical density for all four frequencies but not too high to restrict the measurements just to the edge of plasma. For a wide class of density profiles, by balancing the inversion error and the time measurement error, the overall error in estimating the reflection point position between 0.72cm (for the lowest frequency) and 0.52cm (for the highest frequency) root mean square was obtained, assuming an RMS error of 70 ps in the time of flight measurements. It is probably much better than what could have been obtained by Abel transform. Moreover, the mapping by MLP is incomparably faster and should be considered for routine multichannel pulsed radar data processing.The author thanks Dr. J. B. Lister for his drawing his attention to the MLP technique.     

Toric Networks,Geometric R-Matrices and Generalized Discrete Toda Lattices

We use the combinatorics of toric networks and the double affine geometric R-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the R-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.     

The R<Subscript>2</Subscript>Pd<Subscript>3</Subscript>Ge<Subscript>5</Subscript> (R = La–Nd,Sm) germanides: synthesis,crystal structure and symmetry reduction

Direct synthesis and structural characterization of a series of polar rare earth palladium germanides of R₂Pd₃Ge₅ composition (R = La–Nd, Sm) is reported. The crystal structure of the Nd representative was determined by single-crystal X-ray diffraction analysis (U₂Co₃Si₅-type, SG: Ibam, oI40, Z = 4, a = 10.1410(6), b = 12.0542(8), c = 6.1318(4) Å, wR ₂ = 0.0306, 669 F ² values, 31 variables). The crystal structures of the other homologues were ensured by powder X-ray diffraction pattern analysis. A smooth variation of the cell dimensions is observed through the rare earth series. The structure of the studied compounds can be interpreted as consisting of a complex three-dimensional [Pd₃Ge₅]^δ? network spaced by the rare earth cations. Within the concept of symmetry reduction, a Bärnighausen tree is used to rationalize the related crystal structures of the RPd₂Ge₂, RPdGe₃ and R₂Pd₃Ge₅ ternary compounds, enriching the large family of the BaAl₄ derivatives. Moreover, syntheses with metal fluxes were performed, some of which were successful to obtain large crystals of La₂Pd₃Ge₅ (using Bi as solvent) and Nd₂Pd₃Ge₅ (using Pb as solvent) stoichiometry.     

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.     

From Biomass‐Derived Furans to Aromatics with Ethanol over Zeolite

We report a novel catalytic conversion of biomass‐derived furans and alcohols to aromatics over zeolite catalysts. Aromatics are formed via Diels–Alder cycloaddition with ethylene, which is produced in situ from ethanol dehydration. The use of liquid ethanol instead of gaseous ethylene, as the source of dienophile in this one‐pot synthesis, makes the aromatics production much simpler and renewable, circumventing the use of ethylene at high pressure. More importantly, both our experiments and theoretical studies demonstrate that the use of ethanol instead of ethylene, results in significantly higher rates and higher selectivity to aromatics, due to lower activation barriers over the solid acid sites. Synchrotron‐diffraction experiments and proton‐affinity calculations clearly suggest that a preferred protonation of ethanol over the furan is a key step facilitating the Diels–Alder and dehydration reactions in the acid sites of the zeolite.     

A parameter choice strategy for the inversion of multiple observations

In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate strategies are required to choose a set of ‘good’ parameters. In this study, we present a fairly general method for choosing such a set of parameters, provided that discrete direct, but maybe noisy, measurements of the underlying quantity are included in the observation data, and the inner product of the reconstruction space can be accurately estimated by the inner product of the discretization space. Then the proposed parameter choice method gives an accuracy that only by an absolute constant multiplier differs from the noise level and the accuracy of the best approximant in the reconstruction and in the discretization spaces.