52 research outputs found
On the Bohr inequality
The Bohr inequality, first introduced by Harald Bohr in 1914, deals with
finding the largest radius , , such that holds whenever in the unit disk
of the complex plane. The exact value of this largest radius,
known as the \emph{Bohr radius}, has been established to be This paper
surveys recent advances and generalizations on the Bohr inequality. It
discusses the Bohr radius for certain power series in as well as
for analytic functions from into particular domains. These domains
include the punctured unit disk, the exterior of the closed unit disk, and
concave wedge-domains. The analogous Bohr radius is also studied for harmonic
and starlike logharmonic mappings in The Bohr phenomenon which is
described in terms of the Euclidean distance is further investigated using the
spherical chordal metric and the hyperbolic metric. The exposition concludes
with a discussion on the -dimensional Bohr radius
Radical Cyclisation of α-Halo Aluminium Acetals: A Mechanistic Study
International audienceαâBromo aluminium acetals are suitable substrates for UenoâStorkâlike radical cyclisations affording Îłâlactols and acidâsensitive methyleneâÎłâlactols in high yields. The mechanistic study herein sets the scope and limitation of this reaction. The influence of the halide (or chalcogenide) atom X (X=Cl, Br, I, SPh, SePh) in the precursors αâhaloesters, as well as influence of the solvent and temperature was studied. The structure of the aluminium acetal intermediates resulting from the reduction of the corresponding αâhaloesters has been investigated by lowâtemperature 13CâINEPT diffusionâordered NMR spectroscopy (DOSY) experiments and quantum calculations, providing new insights into the structures of these thermally labile intermediates. Oxygenâbridged dimeric structures with a planar Al2O2 ring are proposed for the least hindered aluminium acetals, while monomeric structures seem to prevail for the most hindered species. A comparison against the radical cyclisation of aluminium acetals derived from allyl and propargyl alcohols with the parent UenoâStork has been made at the BHandHLYP/6â311++G(d,p) level of theory, highlighting mechanistic similarities and differences
New routes to Cu(l)/Cu nanocatalysts for the multicomponent click synthesis of 1,2,3-triazoles
An array of copper and copperâzinc based nanoparticles (NPs) have been fabricated employing a variety of polymeric capping agents. Analysis by TEM, XRPD and XPS suggests that by manipulating reagent, reductant and solvent conditions it is possible to achieve materials that are mono-/narrow disperse with mean particle sizes in the â€10 nm regime. Oxidative stability in air is achieved for monometallic NPs using poly(methyl methacrylate) (PMMA) anti-agglomerant in conjunction with a variety of reducing conditions. In contrast, those encapsulated by either poly(1-vinylpyrrolidin-2-one) (PVP) or poly(4-vinylpyridine) (PVPy) rapidly show Cu2O formation, with all data suggesting progressive oxidation from Cu to Cu@Cu2O coreâshell structure and finally Cu2O. Bimetallic copperâzinc systems, reveal metal segregation and the formation of Cu2O and ZnO. Catalysts have been screened in the synthesis of 1,2,3-triazoles through multicomponent azideâalkyne 1,3-dipolar cycloaddition. Whereas PMMA- and PVPy-coating results in reduced catalytic activity, those protected by PVP are highly active, with quantitative triazole syntheses achieved at room temperature and with catalyst loadings of 0.03 mol% metal for Cu and CuZn systems prepared using NaH2PO2, N2H4 or NaBH4 reductants.This work was generously supported by the Spanish Ministerio de Ciencia e InnovaciĂłn (MICINN; CTQ2007-65218 and Consolider Ingenio 2010-CSD2007-00006), the Generalitat Valenciana (GV; PROMETEO/2009/039), and FEDER. Y. M. and B. R. K. thank the ISO of the Universidad de Alicante, the UK EPSRC and the University of Cambridge for grants
Oxidative stress disassembles the p38/NPM/PP2A complex, which leads to modulation of nucleophosminâmediated signaling to DNA damage response
Derivatives of rational inner functions: geometry of singularities and integrability at the boundary
Synthesis and Antitumor Characterization of Pyrazolic Analogues of the Marine Pyrroloquinoline Alkaloids: Wakayin and Tsitsikammamines
Multicomponent click synthesis of 1,2,3-triazoles from epoxides in water catalyzed by Copper nanoparticles on activated carbon
Copper nanoparticles on activated carbon have been found to effectively catalyze the multicomponent synthesis of ÎČ-hydroxy-1,2,3-triazoles from a variety of epoxides and alkynes in water. The catalyst is easy to prepare, reusable at a low copper loading (0.5 mol %), and exhibits higher catalytic activity than some commercially available copper sources. The regio- and stereochemistry of the reaction has been revised and unequivocally established on the basis of X-ray crystallographic analyses. An NMR experiment has been implemented for the rapid and unmistakable determination of the regiochemistry of the process. Some mechanistic aspects of the reaction have been also undertaken which unveil the participation of copper(I) acetylides.This work was generously supported by the Spanish Ministerio de Ciencia e InnovaciĂłn (MICINN; CTQ2007-65218 and Consolider Ingenio 2010-CSD2007-00006), the Generalitat Valenciana (GV; PROMETEO/2009/039), and FEDER. Y.M. acknowledges the ISO of the Universidad de Alicante for a grant
A Non-Linear Extremal Problem on the Hardy Space
We relate some classical extremal problems on the Hardy space to norms of truncated Toeplitz operators and complex symmetric operators
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