Pressure beneath a Stokes wave

We investigate the pressure within an irrotational fluid in a periodic, steady, two‐dimensional gravity wave above a flat bed. We prove that the pressure in the fluid strictly decreases horizontally away from the crest line. Furthermore, the pressure strictly increases with depth. We also investigate the effect of an underlying current on the paths of the particles. © 2009 Wiley Periodicals, Inc.     

A new Technique for Measurement of Myocardial O2-Utilization

The coronary reserve of mammalian hearts is significantly heterogeneous. From this phenomenon we conclude on a heterogeneous energy-demand, i.e., ATP-demand and therefore on a nonuniform ischemic tolerance of cardiomyocytes.

Our aim was to establish a method for direct quantification of cardiomyocyte energy production. According to Langendorff, 10 isolated rabbit hearts were perfused with oxygen enriched Krebs-Henseleit solution. Using the stable oxygen isotope ¹⁸O₂, respiratory water of 7 hearts was labelled, and samples were taken from the coronary venous effluent. Defined cardiac tissue areas were lyophylized. Using the guanidine-hydrochloride technique, μl-water samples from the tissue and the coronary venous effluent were quantitatively converted to CO₂. With the help of mass-spectrometry the δ¹⁸O/¹⁶O-isotope ratios were determined and related to the SMOW-scale.

Compared to control hearts, a significant shift to higher SMOW-values within respiratory water from ¹⁸O-labelled hearts was detected (mean = 14.61%). Control hearts (maximal scatter = 1.42%) as well as ¹⁸O-labelled hearts (4.06%) showed high reproducibilit, of the method. With the employed experimental setup, significant regional differences were not detected. The kinetics of the coronary venous effluent showed a tendency toward saturation with H₂ ¹⁸O within 2 min after starting the ¹⁸O₂-perfusion. After 50 s perfusion increase in SMOW-values reached statistical significance.     

A molecular dynamics method for simulations in the canonical ensemble

A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed. The physical system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added. This device allows the total energy of the physical system to fluctuate. The equilibrium distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space. The method is tested for an atomic fluid (Ar) and works well.     

Incremental Tuning Up of Fluorous Phenazine Acceptors

In a simple, one‐step direct trifluoromethylation of phenazine with CF₃I we prepared and characterized nine (poly)trifluoromethyl derivatives with up to six CF₃ groups. The electrochemical reduction potentials and gas‐phase electron affinities show a direct, strict linear relation to the number of CF₃ groups, with phenazine(CF₃)₆ reaching a record‐high electron affinity of 3.24 eV among perfluoroalkylated polyaromatics.     

Spectralizable Operators

We introduce the notion of spectralizable operators. A closed operator A in a Hilbert space is called spectralizable if there exists a non-constant polynomial p such that the operator p(A) is a scalar spectral operator in the sense of Dunford. We show that such operators belongs to the class of generalized spectral operators and give some examples where spectralizable operators occur naturally. Vladimir Strauss gratefully acknowledges support by DFG, Grant No. TR 903/3-1.     

ESR‐Vis/NIR Spectroelectrochemical Study of C70(CF3)2−. and C70(C2F5)2−. Radical Anions

A spectroelectrochemical study of the two isostructural asymmetric perfluoroalkyl derivatives C₁‐7,24‐C₇₀(CF₃)₂ and C₁‐7,24‐C₇₀(C₂F₅)₂ is presented. Reversible formation of their stable monoanion radicals is monitored by cyclic voltammetry and by in situ ESR‐Vis‐NIR spectroelectrochemistry. The ESR spectrum of the C₇₀(CF₃)₂^?. radical is a 1:3:3:1 quartet with a ¹⁹F hyperfine coupling constant (a(F)) of 0.323(4) G, demonstrating that the unpaired spin is coupled to only one of the two CF₃ groups. The ¹³C satellites are assigned to specific carbon atoms. The ESR spectrum of the C₇₀(C₂F₅)₂^?. radical is an apparent octet with an apparent a(F) value of 0.83(2) G. DFT calculations suggest that this pattern is due to the superposition of spectra for four nearly isoenergetic C₇₀(C₂F₅)₂^?. conformers. Time‐dependent DFT calculations suggest that the NIR band at 1090 nm exhibited by both C₇₀(R_f)₂^?. radical anions is assigned to the SOMO→LUMO+3 transition. The analogous NIR band exhibited by the closed‐shell C₇₀(CF₃)₂^2? dianion was blue‐shifted to 1000 nm.     

Some new results in multiplicative and additive Ramsey theory

There are several notions of largeness that make sense in any semigroup, and others such as the various kinds of density that make sense in sufficiently well-behaved semigroups including and . It was recently shown that sets in which are multiplicatively large must contain arbitrarily large geoarithmetic progressions, that is, sets of the form , as well as sets of the form . Consequently, given a finite partition of , one cell must contain such configurations. In the partition case we show that we can get substantially stronger conclusions. We establish some combined additive and multiplicative Ramsey theoretic consequences of known algebraic results in the semigroups and , derive some new algebraic results, and derive consequences of them involving geoarithmetic progressions. For example, we show that given any finite partition of there must be, for each , sets of the form together with , the arithmetic progression , and the geometric progression in one cell of the partition. More generally, we show that, if is a commutative semigroup and a partition regular family of finite subsets of , then for any finite partition of and any , there exist and such that is contained in a cell of the partition. Also, we show that for certain partition regular families and of subsets of , given any finite partition of some cell contains structures of the form for some .

     

Analysis of size-classified fine and ultrafine particulate matter on substrates with laser-induced breakdown spectroscopy

Airborne particulate matter in the fine (0.1 µm–2.5 µm) and ultrafine (≤ 0.1 µm) size range is supposed to affect human health significantly. Smaller particles intrude more deeply into the lungs, so that an organism directly absorbs toxic compounds. Therefore, knowledge of the size-dependent composition of airborne particles is required to determine their health hazard. In this paper, we demonstrate the application of laser-induced breakdown spectroscopy to directly analyze size-classified particulate matter samples without any sample preparation. Samples analyzed are collected on filter substrates using a cascade impactor. Greased aluminum foils are used as filter substrate. To reduce ablation of the substrate material, low pulse energies of 0.6 mJ are used for plasma excitation. The plasma light is observed using an Echelle spectrometer. The effect of ambient gas and pressure on the line intensities is studied. Calibration samples for 14 elements relevant for human health were produced, and the system was calibrated for concentration ranges up to four orders of magnitude. Finally, the collected samples of particulate originating from steel-making processes were analyzed. The measurements show that the composition of these particles depends strongly on their size. For example, the elements lead, cadmium and copper are enriched within particles of about 200 nm diameter.