Bilinear Sobolev–Poincaré Inequalities and Leibniz-Type Rules

The dual purpose of this article is to establish bilinear Poincaré-type estimates associated with an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato–Morrey spaces under Sobolev scaling.     

The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators

We investigate the weighted bounds for multilinear maximal functions and Calderón–Zygmund operators from \(L^{p_1}(w_1)\times \cdots \times L^{p_m}(w_m)\) to \(L^{p}(v_{\vec {w}})\), where \(1<p_1,\cdots ,p_m<\infty \) with \(1/{p_1}+\cdots +1/{p_m}=1/p\) and \(\vec {w}\) is a multiple \(A_{\vec {P}}\) weight. We prove the sharp bound for the multilinear maximal function for all such \(p_1,\ldots , p_m\) and prove the sharp bound for \(m\)-linear Calderón–Zymund operators when \(p\ge 1\).     

Higher-Order Multilinear Poincaré and Sobolev Inequalities in Carnot Groups

The notions of higher-order weighted multilinear Poincaré and Sobolev inequalities in Carnot groups are introduced. As an application, weighted Leibniz-type rules in Campanato-Morrey spaces are established.     

Model study of CO inhibition of [NiFe]hydrogenase

We propose a modified mechanism for the inhibition of [NiFe]hydrogenase ([NiFe]H(2)ase) by CO. We present a model study, using a NiRu H(2)ase mimic, that demonstrates that (i) CO completely inhibits the catalytic cycle of the model compound, (ii) CO prefers to coordinate to the Ru(II) center rather than taking an axial position on the Ni(II) center, and (iii) CO is unable to displace a hydrido ligand from the NiRu center. We combine these studies with a reevaluation of previous studies to propose that, under normal circumstances, CO inhibits [NiFe]H(2)ase by complexing to the Fe(II) center.     

Photochemical reaction of silyl-substituted 1,4-disila(dewar-benzene) with isocyanide and phenylacetylene

The irradiation of silyl-substituted 1,4-disila(Dewar-benzene) 1 with light of wavelength λ > 320 nm in the presence of 2,6-dimethylphenyl-isocyanide or phenylacetylene produced 1,4-bis(di-tert-butylmethylsilyl)-2,3,5,6-tetraethyl-7-(2,6-dime-thylphenylimino)-1,4-disilabicyclo[2.2.1]hepta-2,5-diene 5 or 1,4-bis(di-tert-butylmethylsilyl)-2,3,5,6-tetraethyl-1-(2-phenylethynyl)-1,4-disilacyclohexa-2,5-diene 6 , respectively. The molecular structures of 5 and 6 were determined by spectroscopic data and X-ray crystallography. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:87–92, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20411     

Organic superbase-induced chemiluminescent decomposition of a hydroxyaryl-substituted dioxetane: Unique effect of a bifunctional guanidine base on the chemiluminescence profile of a bicyclic dioxetane bearing a 4-(benzoxazol-2-yl)-3,5-dihydroxyphenyl moiety

Organic superbases represented by TBD (1,5,7-triazabicyclo[4.4.0]dec-5-ene) effectively induced the decomposition of hydroxyaryl-substituted dioxetanes in acetonitrile to give bright light. The color of the chemiluminescence from a dioxetane bearing a 4-(benzoxazol-2-yl)-3,5-dihydroxyphenyl moiety varied depending on the base used. In addition to this change in the color of emission, TBD increased the chemiluminescence efficiency 2- to 5-fold compared to the results with other base systems and accelerated decomposition of the dioxetane. These unique effects of TBD may be due to its “bifunctional” character, which is different from those of other organic superbases. Chemiluminescent decomposition of the dioxetane was effectively induced by superbases even in apolar p-xylene.     

Formation and characterization of Co(III)-semiquinonate phenoxyl radical species

Co(III) complexes of N(3)O-donor tripodal ligands, 2,4-di(tert-butyl)-6-{[bis(2-pyridyl)methyl]aminomethyl}phenolate (tbuL), 2,4-di(tert-butyl)-6-{[bis(6-methyl-2-pyridyl)methyl]aminomethyl}phenolate (tbuL(Mepy)(2)), were prepared, and precursor Co(II) complexes, [Co(tbuL)Cl] (1) and [Co(tbuL(Mepy)(2))Cl] (2), and ternary Co(III) complexes, [Co(tbuL)(acac)]ClO(4) (3), [Co(tbuL)(tbu-cat)] (4), and [Co(tbuL(Mepy)(2))(tbu-SQ)]ClO(4) (5), where acac, tbu-cat, and tbu-SQ refer to pentane-2,4-dionate, 3,5-di(tert-butyl)catecholate, and 3,5-di(tert-butyl)semiquinonate, respectively, were structurally characterized by the X-ray diffraction method. Complexes 3 and 5 have a mononuclear structure with a fac-N(3)O(3) donor set, while 4 has a mer-N(3)O(3) structure. The cyclic voltammogram (CV) of complex 3 exhibited one reversible redox wave centered at 0.93 V (vs Ag/AgCl) in CH(3)CN. Complex 5 was converted to a phenoxyl radical species upon oxidation with Ce(IV), showing a characteristic pi-pi* transition band at 412 nm. The ESR spectrum at low temperature and the resonance Raman spectrum of 3 established that the radical species has a Co(III)-phenoxyl radical bond. On the other hand, the CVs showed two oxidation processes at E(1/2) = 0.01 and E(pa) = 0.92 V for 4 and E(1/2a) = 0.05 and E(1/2b) = 0.69 V for 5. The rest potential of 4 (-0.11 V) was lower than the E(1/2) value, whereas that of 5 (0.18 V) was higher, indicating that the first redox wave of 4 and 5 is assigned to the tbu-cat and the tbu-SQ redox process, respectively. One-electron oxidized 4 showed absorption, resonance Raman, and ESR spectra which are similar to those of 5, suggesting formation of a stable Co(III)-semiquinonate species, which has the same oxidation level of 5. The resonance Raman spectrum of two-electron oxidized 4 showed the nu(8a) bands of the semiquinonate and phenoxyl radical, which were absent in the spectrum of one-electron oxidized 5. Since both oxidized species were ESR inactive at 5 K, the former was concluded to be a biradical species containing semiquinonate and phenoxyl radicals coupled antiferromagnetically and the latter to a species with a coordinated quinone.     

Diastereoselective syntheses and oxygenation of silyl fulleroids

The addition of silyl diazomethane (1a-d) to fullerene C₆₀ at room temperature provided the mono-adducts, the bis- and tris-adducts of silyl fulleroid (3a-d) in moderate yields. The structures of the silyl fulleroids were characterized by mass spectroscopy, as well as ¹H and ¹³C NMR. The gated ¹H NMR and ¹³C-¹H COLOC analyses of 3a-d showed a correlation between the methine proton resonances and three fullerene carbons. These observations, as well as the ¹H NMR chemical shifts of the methine protons, suggest a remarkable diastereoselectivity, with the silyl groups located above a five-membered ring. Two transition states of the thermal nitrogen-extrusion of pyrazoline intermediate (2a) were theoretically obtained, the structures of which disclosed that the diastereoselectivity is a consequence of minimization of the repulsive interaction between the silyl groups and the N₂ moiety. The bridgehead CC double bond of the silyl fulleroid is thought to be reactive by POAV analyses. The silyl fulleroids (3a,b) were found to react with singlet oxygen to afford the silyl enol ether (9a,b) via 1,3-silyl migration of a diketone (8a,b). This is the first example of ¹O₂ oxygenation of fulleroids.     

ON TESTING THE EQUALITY OF K MULTIPLE AND PARTIAL CORRELATION COEFFICIENTS

1 IntroductionWe are given k independent Wishart densities of the p x p random symmetric positivedefinite matrices G1, G2,' t Gkwhere Ri denotes the population correlation matrir, and K as a generic letter denotes thenormalizing constants of density functions in this paper. The squared multiple correlationcoefficient of the i-th population is pf = r:Riz1.)ri, whereand a likelihood ratio test for testing the hypothesisis desired.Now Wilks (l932, l946) provides certain procedures and guidel…