Boundaries of Coxeter Matroids

The purpose of this paper is to introduce, for a finite Coxeter groupW, the mod 2 boundary operator on the space of all Coxeter matroids (also known asWP-matroids) forWandP, wherePvaries through all the proper standard parabolic subgroups ofW(Theorem 3 of the paper). A remarkably simple interpretation of Coxeter matroids as certain sets of faces of the generalized permutahedron associated with the Coxeter groupW(Theorem 1) yields a natural definition of the boundary of a Coxeter matroid. The latter happens to be a union of Coxeter matroids for maximal standard parabolic subgroupsQ_iofP(Theorem 2). These results have very natural interpretations in the case of ordinary matroids and flag-matroids (Section 3).     

Transverse Frames for Petrov Type I Spacetimes: A General Algebraic Procedure

We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars ₁ and ₃ equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov type I spacetime, setting ₁ and ₃ to zero makes apparent the superposition of a Coulomb-type effect ₂ with transverse degrees of freedom ₀ and ₄.     

Continuous wave mirrorless lasing in cholesteric liquid crystals with a pitch gradient across the cell gap

Despite numerous efforts, continuous wave (CW) lasing in dye doped, one-dimensional (1D) photonic bandgap cholesteric liquid crystal (CLC) structures has not been previously reported, to our knowledge. Here we report on the observation of lasing in such structures under both coherent (laser) and incoherent (LED) CW light excitation. To achieve this effect, we used a 1D-photonic bandgap structure made of a polymer stabilized CLC with a pitch gradient across the cell thickness. A spectral reflectivity profile of such a CLC structure reveals local minima in the area within a photonic stopband and close to it. The realization of lasing pumped by low power CW light sources opens the possibility of all-organic, compact, tunable CW lasers for display and medical applications.     

Mechanistic control of product selectivity. Reactions between cis-/trans cis-/trans-[OsVI(tpy)(Cl)2(N)]+ and triphenylphosphine sulfide

Reactions between the Os(VI)-nitrido complexes cis- and trans-[Os(VI)(tpy)(Cl)2(N)]+ (tpy is 2,2':6',2"-terpyridine) and triphenylphosphine sulfide, SPPh3, give the corresponding Os(IV)-phosphoraniminato, [Os(IV)(tpy)(Cl)2(NPPh3)]+, and Os(II)-thionitrosyl, [Os(II)(tpy)(Cl)2(NS)]+, complexes as products. The Os-N bond length and Os-N-P angle in cis-[Os(IV)(tpy)(Cl)2(NPPh3)](PF6) are 2.077(6) A and 138.4(4) degrees. The rate law for formation of cis- and trans-[Os(IV)(tpy)(Cl)2(NPPh3)]+ is first order in both [Os(VI)(tpy)(Cl)2(N)]+ and SPPh3 with ktrans(25 degrees C, CH3CN) = 24.6 +/- 0.6 M(-1) s(-1) and kcis(25 degrees C, CH3CN) = 0.84 +/- 0.09 M(-1) s(-1). As found earlier for [Os(II)(tpm)(Cl)2(NS)]+, both cis- and trans-[Os(II)(tpy)(Cl)2(NS)]+ react with PPh3 to give [Os(IV)(tpy)(Cl)2(NPPh3)]+ and SPPh3. For both complexes, the reaction is first order in each reagent with ktrans(25 degrees C, CH3CN) = (6.79 +/- 0.08) x 10(2) M(-1) s(-1) and kcis(25 degrees C, CH3CN) = (2.30 +/- 0.07) x 10(2) M(-1) s(-1). The fact that both reactions occur rules out mechanisms involving S atom transfer. These results can be explained by invoking a common intermediate, [Os(IV)(tpy)(Cl)2(NSPPh3)]+, which undergoes further reaction with PPh3 to give [Os(IV)(tpy)(Cl)2(NPPh3)]+ and SPPh3 or with [Os(VI)(tpy)(Cl)2(N)]+ to give [Os(IV)(tpy)(Cl)2(NPPh3)]+ and [Os(II)(tpy)(Cl)2(NS)]+.     

The design and synthesis of novel IBiox N-heterocyclic carbene ligands derived from substituted amino-indanols

A synthetic route towards a number of novel IBiox N-heterocyclic carbene (NHC) ligands has been developed. The resulting ligands have restricted flexibility and high steric demand. Preliminary studies have shown these ligands to give high levels of asymmetric induction in the copper-free allylic alkylation of cinnamyl bromide.     

Synthetic versatility in C-H oxidation: a rapid approach to differentiated diols and pyrans from simple olefins

Conventionally, C-H oxidation reactions are used to install functional groups. The use of C-H oxidation to transform simple starting materials into highly versatile intermediates, which enable rapid access to a range of complex target structures, is a new area with tremendous potential in synthesis. Herein we report a Pd(II)/sulfoxide-catalyzed allylic C-H oxidation to form anti-1,4-dioxan-2-ones from homoallylic oxygenates. These versatile building blocks are rapidly elaborated to differentiated syn-1,2-diols, stereodefined amino-polyols, and syn-pyrans, structures ubiquitous in medicinally important complex molecules found in Nature. We also demonstrate that a C-H oxidation approach to the synthesis of these motifs is orthogonal and complementary to other state-of-the-art methods.     

Application of isotopic labeling,and gas chromatography mass spectrometry,to understanding degradation products and pathways in the thermal-oxidative aging of Nylon 6.6

Nylon 6.6 containing ¹³C isotopic labels at specific positions along the macromolecular backbone has been subjected to extensive thermal-oxidative aging at 138 °C for time periods up to 243 days. In complementary experiments, unlabeled Nylon 6.6 was subjected to the same aging conditions under an atmosphere of ¹⁸O₂. Volatile organic degradation products were analyzed by cryofocusing gas chromatography mass spectrometry (cryo-GC/MS) to identify the isotopic labeling. The labeling results, combined with basic considerations of free radical reaction chemistry, provided insights to the origin of degradation species, with respect to the macromolecular structure. A number of inferences on chemical mechanisms were drawn, based on 1) the presence (or absence) of the isotopic labels in the various products, 2) the location of the isotope within the product molecule, and 3) the relative abundance of products as indicated by large differences in peak intensities in the gas chromatogram. The overall degradation results can be understood in terms of free radical pathways originating from initial attacks on three different positions along the nylon chain which include hydrogen abstraction from: the (CH₂) group adjacent to the nitrogen atom, at the (CH₂) adjacent the carbonyl group, and direct radical attack on the carbonyl. Understanding the pathways which lead to Nylon 6.6 degradation ultimately provides new insight into changes that can be leveraged to detect and reduce early aging and minimize problems associated with material degradation.