Spin Factors as Generalized Hermitian Algebras

We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two. S. Pulmannová was supported by Research and Development Support Agency under the contract No. APVV-0071-06, grant VEGA 2/0032/09 and Center of Excellence SAS, CEPI I/2/2005.     

Generalized Hermitian Algebras

We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. In this paper we define and launch a study of a class of generalized Hermitian (GH) algebras. Among the examples of GH-algebras are ordered special Jordan algebras, JW-algebras, and AJW-algebras, but unlike these more restricted cases, a GH-algebra is not necessarily a Banach space and its lattice of projections is not necessarily complete. In this paper we develop the basic theory of GH-algebras, identify their unit intervals as effect algebras, and observe that their projection lattices are sigma-complete orthomodular lattices. We show that GH-algebras are spectral order-unit spaces and that they admit a substantial spectral theory. The second author was supported by Research and Development Support Agency under the contract No. APVV-0071-06, grant VEGA 2/0032/09 and Center of Excellence SAS, CEPI I/2/2005.     

Stereoselective Palladium‐Catalyzed Carboaminoxylations of Indoles with Arylboronic Acids and TEMPO

Indoles are not indolent : Various indoles react with arylboronic acids chemodivergently. C? H arylation of free indole and N‐methylindole gives the corresponding C(2)‐arylated indoles A whereas N‐acylated, N‐benzoylated, and N‐Boc‐protected indoles provide the corresponding arylcarboaminoxylated products B with excellent diastereoselectivity in good to excellent yields.

     

Structurally characterized hetero-oligopolyphenylenes: synthetic advances toward next-generation heterosuperbenzenes

The successful Diels-Alder [2+4] cycloaddition of dipyrimidyl acetylene and suitably substituted 2,3,4,5-tetraarylcyclopenta-2,4-dien-1-ones (3-7) generates a series of selectively functionalized hexaarylbenzenes. Each has two pairs of peripheral functional groups (R' and R=tert-butyl 8 and R=methyl 9, methoxy 10, bromo 11, triisopropylsilylethynyl 12) and four ortho-imine nitrogen atoms. The dibromo derivative 11 is a useful precursor for the formation of a mono ethynyl 13 and diethynyl 14 substituted polyphenylene. Changing the dienophile to di(2-thienyl)acetylene gives an S-heteroatom polyphenylene 15. The compounds were fully characterized by using (1)H, (13)C and a range of 2 D NMR spectroscopic techniques, elemental analysis, and mass spectrometry. Oxidative cyclodehydrogenation of dimethoxy hexaphenylbenzene 10 by using iron(III) chloride results in the formation of a spirocyclic dienone 16, which in a separate reaction undergoes dienone/phenol rearrangement to give the first 4-fused-ring, N-heterosuperbenzene (HSB) 17. Six single crystal molecular structures reveal the commonality of unidirectional twisting of the external aromatic rings in these heteroatom polyphenylenes. The twist angles and any H-bonding or interdigitation in these structures are discussed.     

Solution 1H NMR characterization of the axial bonding of the two His in oxidized human cytoglobin

Solution 1H NMR spectroscopy has been used to determine the relative strengths (covalency) of the two axial His-Fe bonds in paramagnetic, S = 1/2, human met-cytoglobin. The sequence specific assignments of crucial portions of the proximal and distal helices, together with the magnitude of hyperfine shifts and paramagnetic relaxation, establish that His81 and His113, at the canonical positions E7 and F8 in the myoglobin fold, respectively, are ligated to the iron. The characterized complex (approximately 90%) in solution has protohemin oriented as in crystals, with the remaining approximately 10% exhibiting the hemin orientation rotated 180 degrees about the alpha-, gamma-meso axis. No evidence could be obtained for any five-coordinate complex (<1%) in equilibrium with the six-coordinate complexes. Extensive sequence-specific assignments on other dipolar shifted helical fragments and loops, together with available alternate crystal coordinates for the complex, allowed the robust determination of the orientation and anisotropies of the paramagnetic susceptibility tensor. The tilt of the major axis is controlled by the His-Fe-His vector, and the rhombic axes are controlled by the mean of the imidazole orientations for the two His. The anisotropy of the paramagnetic susceptibility tensor allowed the quantitative factoring of the hyperfine shifts for the two axial His to reveal an indistinguishable pattern and magnitudes of the contact shifts or pi spin densities, and hence, indistinguishable Fe-imidazole covalency for both Fe-His bonds.