Chain partitions of ordered sets

For natural numbers s and r and a finite poset P of height h, there exists a finite poset P of height H(s, r, h) such that for an arbitrary r-colouring of the s-chains of P, a monochromatically embedded copy of P can be found in P. A best possible upper bound for H(s, r, h) in terms of the well-known Ramsey numbers is given.     

Synthesis, NMR Characterization, and a Simple Application of Lithium Borotritide

LiBH(4) is a powerful and selective reagent for regiospecific reduction reactions. A simple synthesis of LiB(3)H(4) at near theoretical specific radioactivity is reported. We have treated Li(3)H synthesized from tritium gas ((3)H(2), approximately 98%) with BBr(3) to produce LiB(3)H(4) (specific activity = 4120 GBq/mmol = 110 Ci/mmol. The maximum theoretical specific activity of LiB(3)H(4) is 4252 GBq/mmol = 115.04 Ci/mmol; 1 matom of (3)H = 1063 GBq = 28.76 Ci.) The tritium labeling performance of the reagent was tested by an exemplary reduction of 2-naphthaldehyde to 2-naphthalenemethanol. LiB(3)H(4) and the reduction products were characterized by a combination of (1)H, (3)H, and (11)B NMR techniques, as appropriate.     

Organopolysiloxanes as Chemically Sensitive Coatings for Optical Fibers

Various types of UV-curable organically modified siloxanes have been synthesized by the sol-gel method with the aim of fabricating chemically sensitive coatings for silica optical fibers. The refractive index of the coating material can be tailored in the range from 1.46 to 1.56 and sensitivity towards CO2 is achieved by incorporation of amino groups. The interaction of the cured layers with CO2 or with hydrocarbons has been studied in immersion experiments. Both the reaction of CO2 with incorporated amino groups and the penetration of hydrocarbons into the layer induce changes of the light absorption coefficient and the refractive index of the coating which are detected by measuring the output light intensity from the fiber.     

Rotational fluctuations of water inside the nanopores of SBA-type molecular sieves

The rotational molecular dynamics of water confined to nanoporous molecular sieves of a regular hexagonal (SBA-15) and of a foamlike pore structure was studied by dielectric spectroscopy in the frequency range from 10(-2) to 10(9) Hz and in a broad temperature interval. Two relaxation processes were observed: the process at lower frequencies is related to water molecules forming a layer, which is strongly adsorbed at the pore surface, whereas the relaxation process at higher frequencies is assigned to fluctuations of water molecules situated close to the center of the pore. The relaxation times of the low-frequency process for both materials and of the high-frequency process for the SBA-15 material have an unusual saddlelike temperature dependence, reported here for the first time. To describe this temperature dependence, a model developed for water confined to nanoporous glasses by Ryabov et al. [J. Phys. Chem. B 2001, 105, 1845] was applied, which considers two competing effects. The characteristic features of these two competing processes were compared with those reported for other porous systems.     

Ruthenium Cluster Chemistry with Ph2PC6H4-4-C≡CH

The new phosphines Ph₂PC₆H₄-4-CCR [R=SiMe₃ (1), H (2)] have been used to prepare Ru₃(CO)₉(Ph₂PC₆H₄-4-CCSiMe₃)₃ (4) and Ru(CCC₆H₄-4-PPh₂)(PPh₃)₂(-C₅H₅) (3), respectively, the latter with a pendent phosphine. Reaction of 4 with carbonate or fluoride affords Ru₃(CO)₉(Ph₂PC₆H₄-4-CCH)₃ (5) with pendent terminal alkynyl groups, the identity of which was confirmed by a structural study. Reaction of 5 with [Ru(NCMe)(PPh₃)₂(-C₅H₅)]PF₆ or reaction of Ru₃(CO)₁₂ with 3 gives Ru₃(CO)₉{(Ph₂PC₆H₄-4-CC)Ru(PPh₃)₂(-C₅H₅)}₃ (6). Complexes 3–6 have been studied by cyclic voltammetry. Proceeding from Ru₃(CO)₁₂ to 4 or 5 shifts the cluster-centred reduction to more negative potential and affords facile cluster-centred oxidation. Proceeding from 4/5 and 3 to 6 results in similarly-located cluster-centred reduction and peripheral ruthenium-centred oxidation, but results in a lack of observable cluster-centred oxidation. Crystal data for 5·C₆H₁₄: space group P¯1, a=12.760(1) Å, b=17.077(1) Å, c=17.924(2) Å, =108.656(5)°, =96.344(5)°, =93.523(5)°, V=3658.4(6) ų, Z=2, R=0.078, R_w=0.105 for 5008 reflections [I>2.00(I)].     

Palladium-tetraphosphine complex: an efficient catalyst for the coupling of aryl halides with alkynes

The cis,cis,cis-1,2,3,4-tetrakis(diphenylphosphinomethyl)-cyclopentane-[PdCl(eta3-C3H5)]2 system catalyses the coupling of aryl halides with alkynes with very high ratios of substrates-catalyst in good yields; a turnover number of 2600000 can be obtained for the reaction of 4-trifluoromethylbromobenzene with phenylacetylene in the presence of this catalyst.     

K-theory for the leaf space of foliations by Reeb components

The K-theory of the C¹-algebra $\text{C}{}^1\text{(V, F)}$ associated to C^∞-foliations (V, F) of a manifold V in the simplest non-trivial case, i.e., dim V = 2, is studied. Since the case of the Kronecker foliation was settled by Pimsner and Voiculescu (J. Operator Theory4 (1980), 93–118), the remaining problem deals with foliations by Reeb components. The K-theory of $\text{C}{}^1\text{(V, F)}$ for the Reeb foliation of S³ is also computed. In these cases the C¹-algebra $\text{C}{}^1\text{(V, F)}$ is obtained from simpler C¹-algebras by means of pullback diagrams and short exact sequences. The K-groups $\text{K}{}_1\text{(C}{}^1\text{(V, F))}$ are computed using the associated Mayer-Vietoris and six-term exact sequences. The results characterize the C¹-algebra of the Reeb foliation of $\text{T}$² uniquely as an extension of C(S¹) by C(S¹). For the foliations of $\text{T}$² it is found that the K-groups count the number of Reeb components separated by stable compact leaves. A C^∞-foliation of $\text{T}$² such that K₁(C¹($\text{T}$², F)) has infinite rank is also constructed. Finally it is proved, by explicit calculation using (M. Penington, “K-Theory and C¹-Algebras of Lie Groups and Foliations,” D. Phil. thesis, Oxford, 1983), that the natural map $\text{μ: K}{}_1\text{,}{}_{\mathrm{\tau }}\text{(BG) → K}{}_1\text{(C}{}^1\text{(V, F))}$ is an isomorphism for foliations by Reeb components of $\text{T}$² and S³. In particular this proves the Baum-Connes conjecture (P. Baum and A. Connes, Geometric K-theory for Lie groups, preprint, 1982; A. Connes, Proc. Symp. Pure Math.38 (1982), 521–628) when V = $\text{T}$².