On a generalized corona problem on the unit disc

Let . We give a sufficient condition on the size of a function in order for it to be in the ideal generated by . In particular, this improves Cegrell's result on this problem.

     

IFSERF, an isotope-filtered SERF experiment for the precise measurement of proton-proton coupling constants between chemically equivalent protons

An isotope-filtered selective refocusing (IFSERF) experiment is presented for the sensitive and precise measurement of the proton-proton coupling constant between chemically equivalent protons. The 2D NMR method combines an initial doubly selective isotope filter based on heteronuclear cross-polarization followed by a selective J-resolved block. The coupling topologies obtained from several 2D variants of the IFSERF experiment are described for the simultaneous measurement of both proton-proton and proton-carbon coupling constants in the involved AA'XX' spin system. Application on the determination of the relative configuration of double bonds in symmetrical molecules is illustrated.     

Spectroscopic studies of the effect of ligand donor strength on the Fe-NO bond intradiol dioxygenases

The geometric and electronic structure of NO bound to reduced protocatechuate 3,4-dioxygenase and its substrate (3,4-dihydroxybenzoate, PCA) complex have been examined by X-ray absorption (XAS), UV-vis absorption (Abs), magnetic circular dichroism (MCD), and variable temperature variable field (VTVH) MCD spectroscopies. The results are compared to those previously published on model complexes described as [FeNO]7 systems in which an S = 5/2 ferric center is antiferromagnetically coupled to an S = 1 NO-. XAS pre-edge analysis indicates that the Fe-NO units in FeIIIPCD[NO-] and FeIIIPCD[PCA,NO-] lack the greatly increased pre-edge intensity representative of most [FeNO]7 model sites. Furthermore, from extended X-ray absorption fine structure (EXAFS) analysis, the FeIIIPCD[NO-] and FeIIIPCD[PCA,NO-] active sites are shown to have an Fe-NO distance of at least 1.91 A, approximately 0.2 A greater than those found in the model complexes. The weakened Fe-NO bond is consistent with the overall lengthening of the bond lengths and the fact that VTVH MCD data show that NO(-)-->FeIII CT transitions are no longer polarized along the z-axis of the zero-field splitting tensor. The weaker Fe-NO bond derives from the strong donor interaction of the endogenous phenolate and substrate catecholate ligands, which is observed from the increased intensity in the CT region relative to that of [FeNO]7 model complexes, and from the shift in XAS edge position to lower energy. As NO is an analogue of O2, the effect of endogenous ligand donor strength on the Fe-NO bond has important implications with respect to O2 activation by non-heme iron enzymes.     

Closures of finitely generated ideals in Hardy spaces

LetH ^∞ be the algebra of bounded analytic functions in the unit diskD. LetI=I(f ₁,...,f _N) be the ideal generated byf ₁,...,f _N∈H ^∞ andJ=J(f ₁,...,f _N) the ideal of the functionsf∈H ^∞ for which there exists a constantC=C(f) such that |f(z)|≤C(|f ₁ (z)|+...;+|f _N (z)|),z∈D. It is clear that , but an example due to J. Bourgain shows thatJ is not, in general, in the norm closure ofI. Our first result asserts thatJ is included in the norm closure ofI ifI contains a Carleson-Newman Blaschke product, or equivalently, if there existss>0 such that

Relaxed but highly compact diansa metallacyclophanes

A series of monoansa [μ-1,1'-PR-3,3'-Co(1,2-C(2)B(9)H(10))(2)](-) and diansa [8,8'-μ-(1',2'-benzene)-μ-1,1'-PR-3,3'-Co(1,2-C(2)B(9)H(9))(2)](-) (R = Ph, (t)Bu) cobaltabisdicarbollidephanes have been synthesized, characterized and studied by NMR, MALDI-TOF-MS, UV-visible spectroscopy, cyclic voltammetry, and DFT calculations. Single crystal X-ray diffraction revealed a highly relaxed structure characterized by the title angle α of 3.8° ([7](-)), this being the smallest angle α for a metallacyclophane. In such compounds, the metal-to-phosphorus distance is less than the sum of their van der Waals radii. The availability of a phosphorus lone pair causes an electron delocalization through the metal, as shown by the abnormal (31)P NMR chemical shift. Remarkably, the combination of a phosphine donor and a phenyl acceptor moieties causes a synergistic effect that is observed through the different techniques used in this study. The importance of having an available lone pair is demonstrated by the oxidation of phosphorus with hydrogen peroxide, sulfur, and elemental black selenium to produce the corresponding P(V) compounds. When the electron lone pair is used to form the bond with the corresponding chalcogen atom, the communication between the donor and acceptor moieties on the diansa metallacyclophane is shut down.     

Gravity and large black holes in Randall-Sundrum II braneworlds

We show how to construct low energy solutions to the Randall-Sundrum II (RSII) model by using an associated five-dimensional anti-de Sitter space (AdS(5)) and/or four-dimensional conformal field theory (CFT(4)) problem. The RSII solution is given as a perturbation of the AdS(5)-CFT(4) solution, with the perturbation parameter being the radius of curvature of the brane metric compared to the AdS length ?. The brane metric is then a specific perturbation of the AdS(5)-CFT(4) boundary metric. For low curvatures the RSII solution reproduces 4D general relativity on the brane. Recently, AdS(5)-CFT(4) solutions with a 4D Schwarzschild boundary metric were numerically constructed. We modify the boundary conditions to numerically construct large RSII static black holes with radius up to ~20?. For a large radius, the RSII solutions are indeed close to the associated AdS(5)-CFT(4) solution.     

Growth of the green algae Chlamydomonas reinhardtii under red and blue lasers

Red and blue lasers, holding promise as an electric light source for photosynthetic systems on account of being true monochromatic, high-power, and having high electrical-conversion efficiency, were employed in growing a green alga, Chlamydomonas reinhardtii. The laser treatments tested included: 655-nm Red; 680-nm Red; 655-nm Red+474-nm Blue and 680-nm Red+474-nm Blue. A white cold cathode lamp with spectral output similar to that of white fluorescent lamp served as control. C. reinhardtii successfully grew and divided under the 655 and 680-nm red lasers as well as under the white-light control. Supplementing either red with blue laser, however, resulted in increased algae cell count that significantly exceeded those under both red lasers and the white-light control on average by 241%.     

Carleson Measures,Riemann–Stieltjes and Multiplication Operators on a General Family of Function Spaces

Let μ be a nonnegative Borel measure on the unit disk of the complex plane. We characterize those measures μ such that the general family of spaces of analytic functions, F(p, q, s), which contain many classical function spaces, including the Bloch space, BMOA and the Q _s spaces, are embedded boundedly or compactly into the tent-type spaces ${T^{\infty}_{p, s}(\mu)}$ . The results are applied to characterize boundedness and compactness of Riemann–Stieltjes operators and multiplication operators on F(p, q, s).     

Reaction of a copper-dioxygen complex with nitrogen monoxide (*NO) leads to a copper(II)-peroxynitrite species

A discrete peroxynitrite-copper(II) complex, [(TMG3tren)CuII(-OONO)]+ (3), has been generated in solution (ESI-MS, m/z = 565.15; tetragonal EPR) by reacting *NO(g) with superoxo complex [(TMG3tren)CuII(O2*-)]+ (2). Complex 3 undergoes a thermal transformation to give CuII-nitrite complex [(TMG3tren)CuII(-ONO)]+ (4) (X-ray) along with ca. 0.5 molar equiv dioxygen. A DFT calculation derived structure with cyclic bidentate k2-O,O'-OONO bound peroxynitrite moiety and dx2-y2 ground state is proposed. Experiments using 18O2 suggest that the adjacent peroxo oxygen atoms in 3 are derived from molecular oxygen. Further, 18O2 containing 3 undergoes O-O bond cleavage to form singly 18-O-labeled 4. The results suggest the viability of biological CuI/O2/(*NO) peroxynitrite formation and chemistry, that is, not coming from free superoxide plus *NO reaction.     

An efficient protocol for the enantioselective preparation of a key polyfunctionalized cyclohexane. New access to (R)- and (S)-4-Hydroxy-2-cyclohexenone and (R)- and (S)-trans-cyclohex-2-ene-1,4-diol

Starting from very accessible raw materials such as p-methoxyphenol, ethylene glycol, and thiophenol, a protocol has been developed to prepare multigram quantities of the polyfunctionalized cyclohexane (+/-)- 7. A highly efficient resolution of (+/-)- 7 has been achieved through enantioselective acetylation catalyzed by Candida antarctica lipase B. Straightforward and enantioselective syntheses of 4-hydroxy-2-cyclohexenone, 1, trans-cyclohex-2-ene-1,4-diol, 2, and their O-protected derivatives 18 and 19 have been readily accomplished from 7.