A Chebotarev Theorem for finite homogeneous extensions of shifts

We derive a Chebotarev Theorem for finite homogeneous extensions of shifts of finite type. These extensions are of the form :X×G/H→X×G/H where (x,gH)=(σx, α(x)gH), for some finite groupG and subgroupH. Given a σ-closed orbit τ, the periods of the -closed orbits covering τ define a partition of the integer |G/H|. The theorem then gives us an asymptotic formula for the number of closed orbits with respect to the various partitions of the integer |G/H|. We apply our theorem to the case of a finite extension and of an automorphism extension of shifts of finite type. We also give a further application to ‘automorphism extensions’ of hyperbolic toral automorphisms. Financially supported by Universiti Kebangsaan Malaysia     

Multi-electron reduction from alkyl/hydride ligand combinations in U4+ complexes

The U4+ mixed alkyl hydride complex (C5Me5)U[mu-C5Me3(CH2)2](mu-H)2U(C5Me5)2, 1, which contains a cyclopentadienyl ligand with two metalated methylene substituents, can effect four, six, and eight-electron reductions in which the combination of the two H1- ligands and the [C5Me3(CH2)2]3- moiety delivers four electrons and forms (C5Me5)1-. The reaction is formally equivalent to an alkyl hydride reductive elimination, a transformation common with transition metals not previously observed with f element compounds. This type of alkyl hydride reduction reactivity is also observed with a combination of U4+ alkyl and hydride complexes, (C5Me5)2UMe2/[(C5Me5)2UH2]2, which reduces benzene to make [(C5Me5)2U]2(C6H6), a U3+ complex formally containing a (C6H6)2- ligand.     

Stabilization of platinum(II) hydrides by tri-t-butylarsine; facile syntheses of stable trans-PtH2[As(t-Bu)3]2 and trans-PtHX[As(t-Bu)3]2 complexes

trans-PtH₂[As(t-Bu)₃]₂ was prepared in very good yield by afacile reaction of K₂PtC1₄ with As(t-Bu)₃ in alkaline ethanol. Treatment of trans-PtH₂[As(t-Bu)₃]₂ with CF₃CO₂H or HCI afforded trans-PtH(O₂CCF₃)[As(t-Bu)₃]₂ or trans-PtHCl[As(t-Bu)₃]₂. respectively, in almost quantitative yield.     

Reactions of Lewis bases with tetrakisdiphenylamide uranium(IV)

The coordinatively unsaturated uranium(IV) complex U[N(C₆H₅)₂]₄ has been prepared via the stoichiometric reaction of diphenylamine with [(Me₃Si)₂N]₂ H₂. U[N(C₆H₅)₂]₄ coordinates Lewis bases such as Et₂O, THF, pyridine or (EtO)₃PO, based on electronic absorption spectroscopy and ¹H NMR studies. Exchange between U[N(C₆H₅)₂]₄ and U[N(C₆H₅)₂]₄(L), where L is THF or pyridine, is rapid on the NMR time-scale between 307 and 323 K. Measurement of equilibrium constants for L = THF provides ΔH and ΔS values of −60 kJ mol⁻¹ and −1.8 × 10² J K⁻¹ mol⁻¹, respectively. U[N(C₆H₅)₂]₄ coordinates and binds (EtO)₃PO much more tightly (K_eq = & > 10⁴ M⁻¹) than THF or pyridine with the exchange rate between U[N(C₆H₅)₂]₄ and U[N(C₆H₅)₂]₄[OP(OEt)₃] being close to the NMR time-scale.     

Origins of the high 14-helix propensity of cyclohexyl-rigidified residues in beta-peptides

[structure: see text] beta-Peptides containing residues derived from trans-2-aminocyclohexanecarboxylic acid (ACHC) display high population of 14-helical secondary structure in aqueous solution. We show that hydrophobic interactions between cyclohexyl rings are not responsible for this conformation-promoting effect, and that polar groups may be attached to the cyclohexyl ring without diminishing the effect.     

(Terpyridine)manganese(II) Coordination Polymers with Thio‐ and Selenidoarsenate(III) Ligands: Coligand Influence on the Chalcogenidoarsenate(III) Species and Coordination Mode

Hydrothermal reaction of [MnCl₂(terpy)] with elemental As and Se at 150 °C in 1:2:4 and 1:4:8 molar ratios in the presence of Cs₂CO₃ affords the complexes [{Mn(terpy)}₂ (As₂Se₅)]₂ ( 1 ) and [{Mn(terpy)}₂ (As₄Se₈)] ( 2 ), respectively. 1 contains dipyramidal [As₂Se₅]^4? ligands that bridge three Mn^II atoms in a tetradentate μ₃‐1κ²Se¹,Se²:2κSe⁴:3κSe⁵ manner. The tetranuclear complex is centrosymmetric and exhibits a central 8‐membered (MnSeAsSe)₂ ring. Cyclic [As₄Se₈]^4? ligands are present in the centrosymmetric dinuclear complex 2 and chelate the Mn(II) atoms through adjacent terminal Se atoms. Both 1 and 2 are linked into infinite chains through weak Mn···Se interactions. [{Mn(terpy)}₂(As₄S₈)] ( 3 ) and ( 4 ) can be obtained by hydrothermal reaction of [MnCl₂(terpy)] with As₂S₃ at respectively 150 °C and 190 °C. Whereas 3 exhibits an identical connectivity pattern to that of 2 , the coordination polymer 4 contains vierer chains that coordinate {(terpy)Mn}²⁺ fragments in a bidentate manner through terminal S atoms. The complex ( 5 ) contains double chains and results from the analogous hydrothermal reaction of [MnCl₂(tren)] with As₂S₃ at 150 °C.     

Carbon-13 nuclear magnetic resonance studies of coumarin and related compounds

Fourier-transform ¹³C NMR spectra of nine coumarinoid compounds of medicinal interest are reported. All of the carbon resonances are assigned with the aid of various spectral techniques and stable isotopic labeling. The substituent effects on the chemical shifts in several systems are also discussed.     

High-resolution 17O NMR spectroscopy of wadsleyite (beta-Mg2SiO4)

The sensitivity of high-resolution 17O (I = 5/2) NMR spectroscopy of solids has advanced significantly in recent years. Here, we show that excellent results are now obtainable from milligram quantities of 17O-enriched materials, thereby allowing the technique to be applied to silicate phases synthesized under very high pressures in a multiple-anvil apparatus. We report the first 17O NMR study of beta-Mg2SiO4 (9.6 mg of 35% 17O-enriched material, synthesized at p = 16 GPa and T = 1873 K), a dense phase believed to have a significant role in the Earth's mantle. Using STMAS at magnetic fields of B0 = 9.4 and 11.7 T and MQMAS at B0 = 18.8 T, we have resolved and assigned all four crystallographically distinct O sites and determined their chemical shift and quadrupolar parameters.