Hydroxyl-directed cyclizations of 1,6-enynes

The palladium-catalyzed, hydroxyl-directed cyclization reactions of 1,6-enynes provide a highly diastereoselective process for the syntheses of stereochemically defined cyclopentanes. Consistently high levels of cis-selectivity are possible using homopropargyl alcohols in contrast to the corresponding propargyl alcohols. Hydroborylative enyne cyclizations coupled with this directing group effect provide a useful method for the syntheses of multifaceted compounds bearing all carbon quaternary centers.     

A cubic, 12-connected, microporous metal-organometallic phosphate framework sustained by truncated tetrahedral nodes

A rare example of a microporous metal-organic phosphate, [Co(12)(L)(6)(μ(3)-PO(4))(4)(μ(3)-F)(4)(μ-H(2)O)(6)][NO(3)](2) (1), is synthesized by the reaction of a [(η(5)-C(5)H(5))Fe(II)](+)-functionalized terephthalate ligand with Co(NO(3))(2)·6H(2)O and phosphate and fluoride ions generated from the in situ hydrolysis of hexafluorophosphate. 1 is a cubic, 12-connected, face-centered cubic framework sustained by the linear connection of unprecedented, dodecanuclear truncated tetrahedral coordination clusters.     

Chlorotrimethylsilane activation of acylcyanamides for the synthesis of mono-N-acylguanidines

A simple and efficient one-pot method for the synthesis of monoprotected guanidines is presented. Treatment of an acylcyanamide with chlorotrimethylsilane generates a reactive N-silylcarbodiimide capable of guanylating a variety of amines. Typically the reaction is complete in 15 min for primary and secondary aliphatic amines at rt. Hindered amines and anilines are also competent nucleophiles but require extended reaction times.     

Electron paramagnetic resonance study of the reactions of tetrathiomolybdate with roussin salts and esters, and with some related iron nitrosyls

The tetrathiomolybdate ion [MoS₄]²⁻ reacts in DMF solution with Roussin esters Fe₂(SR)₂(NO)₄ (R = Me, Et, n-Pr, i-Pr, n-Bu,t-Bu, n-C₅H₁₁) to yield the paramagnetic iron nitrosyls [Fe(NO)₂(SR)₂]⁻ (1), [Fe(NO)₂(S₂MoS₂]⁻ (2) and [Fe(NO)(S₂MOS₂)₂]⁻ (3). The new complexes (2) and (3) have been characterized by EPR spectroscopy and the assignment to them of constitutions based respectively upon tetrahedral and square pyramidal iron is supported by EHMO calculations. Fe₂(SPh)₂(NO)₄ with [MoS₄]²⁻ yields only [Fe(NO)₂(SPh)₂]⁻, and preformed (3) reacts with PhS⁻ to give firstly EPR-silent species, and then [Fe(NO)₂(SPh)₂]⁻. The mononitrosyl (3) can also be formed by reaction of [MoS₄]²⁻ with [Fe₄S₃(NO)₇]⁻, Fe₄S₄(NO)₄, or Fe₂I₂(NO)₄.     

Differentiable rigidity for hyperbolic toral actions

Our aim is to extend existing results about differentiable rigidity of higher rank abelian actions by automorphisms of a torus. Previous proofs have required an assumption of semisimplicity, that is, that the action is by commuting diagonalizable matrices. Here we introduce a technique that utilizes the unipotent part of a non-semisimple action, which allows us to discard the semisimplicity assumption. In its place we will make a technical assumption that the spectrum of the action restricted to leaves of the coarse Lyapunov decomposition is sufficiently narrow.     

Partial differential equations with deviating arguments in the time variable

Some classes of partial differential equations with deviating arguments in the time variable are investigated. The equations are written as abstract ordinary functional differential equations of the form $\text{d}\text{dt}\text{u(t) = ?Au(t) + F(u}{}_{\mathrm{t}}\text{), u}{}_0\text{= φ}$, where ?A is the infinitesimal generator of a linear semigroup and F is not necessarily continuous. Existence, uniqueness, and stability properties are developed by studying the equations in appropriately chosen spaces of initial functions φ.     

The numerical solution of the matrix equationXA+AY=F

An iterative method for solving the matrix equationXA+AY=F is discussed Algorithms and techniques for accelerating convergence are outlined. The method compares favourably with existing techniques.