Exact Solutions of Covariant Wave Equations with a Multipole Source Term on Curved Spacetimes

A formalism is presented for calculating exactsolutions of covariant inhomogeneous scalar and tensorwave equations whose source terms are arbitrary ordermultipoles on a curved background spacetime. The developed formalism is based on the theory ofthe higher-order fundamental solutions for wave equationwhich are the distributions that satisfy theinhomogeneous wave equation with the corresponding order covariant derivatives of the Dirac deltafunction on the right-hand side. Like the classicalGreen's function for a scalar wave equation, thehigher-order fundamental solutions contain a direct termwhich has support on the light cone as well as a tailterm which has support inside the light cone. Knowinghow to compute the fundamental solutions of arbitraryorder, one can find exact multipole solutions of wave equations on curved spacetimes. Wepresent complete recurrent algorithms for calculatingthe arbitrary-order fundamental solutions and the exactmultipole solutions in a form convenient for practical computations. As an example we apply thealgorithm to a massless scalar wave field on aparticular Robertson-Walker spacetime.     

The reactions of tellurium tetrahalides with triphenylphosphine under ambient conditions

The reactions of tellurium tetrahalides and triphenylphosphine in tetrahydrofuran have been carried out under ambient conditions and afford [(Ph(3)PO)(2)H](2)[Te(2)X(10)] [X = Cl (1), Br (2)] and [(Ph(3)PO)(3)(OH(3)])(2)[TeI(6)] (4). The X-ray structures of 1 and 2 show that they are isostructural and contain discrete [Te(2)X(10)](2-) anions exhibiting octahedral coordination around both tellurium atoms with one shared edge and [Ph(3)POH...OPPh(3)](+) cations that show strong hydrogen bonds (the O...O distances are 2.399 and 2.404 A for 1 and 2, respectively). The compound 4 is built up with discrete octahedral hexaiodotellurate anions and [(Ph(3)PO)(3)(OH(3))](+) cations. The reaction of TeBr(4) and PPh(3) also results in the formation of formally zwitterionic Ph(3)PO(CH(2))(4)TeBr(4) (3). This reaction involves an unprecedented THF ring opening in which the oxygen atom becomes bonded to the phosphorus atom of triphenylphosphine and the carbon atom at the other end of the five-atomic chain becomes bonded to the tellurium atom of TeBr(4). The ring opening of the solvent THF is also taking place in the reaction involving tellurium tetraiodide, as indicated by the formation of C(4)H(8)TeI(2) (5). The reaction may initially lead to Ph(3)PI(2) that reacts with THF yielding Ph(3)PO and ICH(2)(CH(2))(2)CH(2)I. The latter species reacts with elemental tellurium producing 5. Depending on the conditions upon crystallization, two polymorphs of C(4)H(8)TeI(2) (5a and 5b) are observed. While the molecular structures of the two forms are virtually identical, their packing and intermolecular contacts are different. Two further minor products (6a and 6b) were isolated in the reaction of TeI(4) and PPh(3): Both are formally 1:1 adducts of 5 and TeI(4), but they differ considerably in their structures. 6a can be formulated as [C(4)H(8)TeI(+)](2)[Te(2)I(10)(2-)] and 6b as [C(4)H(8)TeI(+)](2)(TeI(3)(+))(2)(I(-))(4). The latter compound exhibits framework similar to that of the tetramers in gamma- and delta-TeI(4).     

Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces

We extend the Besicovitch-Federer projection theorem to transversal families of mappings. As an application we show that on a certain class of Riemann surfaces with constant negative curvature and with boundary, there exist natural 2D measures invariant under the geodesic flow having 2D supports such that their projections to the base manifold are 2D but the supports of the projections are Lebesgue negligible. In particular, the union of complete geodesics has Hausdorff dimension 2 and is Lebesgue negligible.     

Feasibility of a liquid-phase microextraction sample clean-up and liquid chromatographic/mass spectrometric screening method for selected anabolic steroid glucuronides in biological samples

Anabolic androgenic steroids (AAS) are metabolized extensively in the human body, resulting mainly in the formation of glucuronide conjugates. Current detection methods for AAS are based on gas chromatographic/mass spectrometric (GC/MS) analysis of the hydrolyzed steroid aglycones. These analyses require laborious sample preparation steps and are therefore time consuming. Our interest was to develop a rapid and straightforward method for intact steroid glucuronides in biological samples, using liquid-phase microextraction (LPME) sample clean-up and concentration method combined with liquid chromatographic/tandem mass spectrometric (LC/MS/MS) analysis. The applicability of LPME was optimized for 13 steroid glucuronides, and compared with conventional liquid-liquid extraction (LLE) and solid-phase extraction (SPE) procedures. An LC/MS/MS method was developed for the quantitative detection of AAS glucuronides, using a deuterium-labeled steroid glucuronide as the internal standard. LPME, owing to its high specificity, was shown to be better suited than conventional LLE and SPE for the clean-up of urinary AAS glucuronides. The LPME/LC/MS/MS method was fast and reliable, offering acceptable reproducibility and linearity with detection limits in the range 2-20 ng ml(-1) for most of the selected AAS glucuronides. The method was successfully applied to in vitro metabolic studies, and also tested with an authentic forensic urine sample. For a urine matrix the method still has some unsolved problems with specificity, which should be overcome before the method can be reliably used for doping analysis, but still offering additional and complementary data for current GC/MS analyses.     

The Reception of Frege''sBegriffsschrift

The topic of the paper is the public reception of Gottlob Frege's (1848–1925)Begriffsschriftright after its publication in 1879. According to a widespread conception, the reception of the book was “unfavorable” and even “tragic.” The aim of the paper is to correct this exaggerated and even false view. The arguments are based, above all, on the six journal reviews of Frege's book in 1879 and 1880, and on Leonhard Rabus's critical comment on it in his bookDie neuesten Bestrebungen auf dem Gebiete der Logik bei den Deutschen und die logische Frage(1880). The conclusion is that it is misleading to regard the reception of Frege's first work as unfair and hostile even though it is apparent thatsomereviewers of the book were rather poorly motivated to comment on theBegriffsschrift.Copyright 1998 Academic Press.Der Gegenstand dieses Beitrags ist die öffentliche Rezeption von Gottlob Freges (1848–1925)Begriffsschriftnach ihrer Publikation 1879. Nach einer weitverbreiteten Auffassung war die Rezeption “ungünstig,” sogar “tragisch.” Ziel des Beitrags ist es zu zeigen, dass solche Interpretationen überspannt, teilweise sogar falsch sind. Der Verfasser gründet seine Behauptung vor allem auf die Rezensionen, die in verschiedenen Zeitschriften in den Jahren 1879 und 1880 erschienen sind. Er benutzt auch den Kommentar von Leonhard RabusDie neuesten Bestrebungen auf dem Gebiete der Logik bei den Deutschen und Die logische Frage(1880). Die Untersuchung kommt zu dem Schluss, dass, obwohl offensichtlicheinigeRezensenten dem Buch eher ablehnend gegenüberstanden, es irreführend ist, von einer ungerechtfertigten oder abweisenden Rezeption der Fregeschen Begriffsschrift zu sprechenCopyright 1998 Academic Press.AMS subject classification: 00A30, 01A55, 03A05     

A computational and experimental study of the structures and Raman and 77Se NMR spectra of SeX3+ and SeX2 (X = Cl, Br, I): FT-Raman spectrum of (SeI3)[AsF6

The ability of MP2, B3PW91 and PBE0 methods to produce reliable predictions in structural and spectroscopic properties of small selenium-halogen molecules and cations has been demonstrated by using 6-311G(d) and cc-pVTZ basis sets. Optimized structures and vibrational frequencies agree closely with the experimental information, where available. Raman intensities are also well reproduced at all levels of theory. Calculated GIAO isotropic shielding tensors yield a reasonable linear correlation with the experimental chemical shift data at each level of theory. The largest deviations between calculated and experimental chemical shifts are found for selenium-iodine species. The agreement between observed and calculated chemical shifts for selenium-iodine species can be improved by inclusion of relativistic effects using the ZORA method. The best results are achieved by adding spin-orbit correction terms from ZORA calculations to nonrelativistic GIAO isotropic shielding tensors. The calculated isotropic shielding tensors can be utilized in the spectroscopic assignment of the 77Se chemical shifts of novel selenium-halogen molecules and cations. The experimental FT-Raman spectra of (SeI3)[AsF6] in the solid state and in SO2(l) solution are also reported.