Canonical partition theorems for parameter sets

A canonical (i.e., unrestricted) version of the partition theorem for k-parameter sets of Graham and Rothschild (Trans. Amer. Math. Soc.159 (1971), 257–291) is proven. Some applications, e.g., canonical versions, of the Rado-Folkman-Sanders theorem and of the partition theorem for finite Boolean algebras are given. Also the Erdös-Rado canonization theorem (J. London Math. Soc.25 (1950), 249–255) turns out to be an immediate corollary.     

From workplace air measurement results toward estimates of exposure? Development of a strategy to assess exposure to manufactured nano-objects

In the past few years, an increasing number of studies on workplace air measurements on manufactured nano-materials and -objects have been published. Most of the studies had a more explorative character, so a direct interpretation to workers” exposure for a given exposure situation, activity, or process is not a straight-forward process. In general, the studies use a quite similar package of devices for near real-time monitoring of particle number- and mass concentration in size ranges <100 nm up to 10 μm, and the collection of samples for off-line characterization of air samples. Various approaches for addressing background concentrations and its use to indicate the potential for exposure to nano-objects could be observed. Within the EU-sponsored NANOSH project, a harmonized approach for measurement strategy, data analysis and reporting was developed. In addition to time/activity–concentration profiles as reported by most studies, this approach enables a first step to estimate the potential for exposure to manufactured nano-objects, more quantitatively. The NANOSH data will be collated into a base, which may form the starting point for a harmonized database facilitating overall analysis in near future, to derive estimates for exposure for several exposure situations.     

Current partition in multiprobe conductors in the presence of slowly oscillating external potentials

In the presence of a static potential drop a carrier stream incident at a contact of the sample is partitioned into the other contacts according to the transmission probabilities of the sample. The bare response to oscillating potentials, on the other hand, violates current conservation due to the piling up of unscreened charges in the sample, and has to be modified by taking the induced screening potential into account. We present a novel derivation of the conductance response to oscillating external chemical potentials, find the response to an arbitrary internal potential in terms of functional derivatives with respect to the local potential of the scattering matrix of the conductor, and determine the screening potential for slowly oscillating potentials from the condition of local charge neutrality. We find that the current partitioning depends on ratios of local densities of states which reflect the injection and emission properties of the contacts of the sample.     

A canonical partition theorem for equivalence relations on Zt

A canonical version of the multidimensional version of van der Waerden's theorem on arithmetic progressions is proved.     

Ein Distributivitätskriterium für Verbände

Those one-place functions on a latticeL with values inL which can be obtained from the identityx and the constant functions by means of the fundamental operations ofL in a finite number of steps are called one-place polynomial functions. —It is shown that a latticeL is distributive iff all its one-place polynomial functions can be represented by words such that in every word the indeterminatex occurs at most once.     

Tetrahedral onsager crosses for solubility improvement and crystallization bypass

Pure organic molecules exhibiting a suitable concave rigid shape are expected to give porous glasses in the solid state. Such a feature opens new opportunities to avoid crystallization and to improve molecular solubility in relation to the high internal energy of these solid phases. To quantitatively explore the latter strategy, a series of rigid tetrahedral conjugated molecules nC and the corresponding models nR have been synthesized. Related to the present purpose, several properties have been investigated using UV absorption, steady-state fluorescence emission, differential scanning calorimetry, (1)H NMR translational self-diffusion, magic angle spinning (13)C NMR, and multiple-beam interferometry experiments. The present tetrahedral crosses are up to 8 orders of magnitude more soluble than the corresponding model compounds after normalization to the same molecular length. In addition, they give concentrated monomeric solutions that can be used to cover surfaces with homogeneous films whose thickness goes down to the nanometer range. Such attractive features make cross-like molecular architectures promising for many applications.     

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

The Aitken's ²-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's ²-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of ²-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.     

An ylide-like phosphasilene and striking formation of a 4π-electron, resonance-stabilized 2,4-disila-1,3-diphosphacyclobutadiene

The first N-donor-stabilized phosphasilene LSi(SiMe(3))═PSiMe(3) (L = PhC(NtBu)(2)) has been synthesized in 87% yield through 1,2-silyl migration of the (Me(3)Si)(2)P-substituted, N-heterocyclic silylene [LSi-P(SiMe(3))(2)]. Remarkably, the latter reacts with dichlorotriphenylphosphorane Ph(3)PCl(2) to give the unprecedented 4π-electron Si(2)P(2)-cycloheterobutadiene [(LSi)(2)P(2)] with two-coordinate phosphorus atoms. The striking molecular structures as well as the (29)Si and (31)P NMR spectroscopic features of both products indicate the presence of zwitterionic Si═P bonds which is also in accordance with results by DFT calculations.     

Synthesis of 2,3-anti-3,4-anti and 2,3-anti-3,4-syn propionate motifs: a diastereoselective tandem sequence of Mukaiyama and free-radical-based hydrogen transfer reactions

[reaction: see text] Reported herein is a strategy employing a Mukaiyama reaction in tandem with a hydrogen transfer reaction for the elaboration of 2,3-anti-3,4-anti and 2,3-anti-3,4-syn propionate motifs. The mode of complexation is controlled through monodentate or chelate pathways for the Mukaiyama reaction to give access to either syn or anti aldol products, precursors of the free-radical reduction reaction. Boron Lewis acid is used to control the free-radical reaction through the exocyclic pathway.