The inherent structural instability: concentration-dependent transformation of pyrogallarene to pyrogallarene lactones

Pyrogallarene shows concentration-dependent instability in dilute solutions resulting in elimination of two ketene molecules and formation of pyrogallarene lactones. This unexpected phenomenon, which is not observed with resorcinarenes, highlights the significance of the four hydroxyl groups at 2-position for the molecular characteristics of pyrogallarenes.     

Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics

Normal mode analysis (NMA) was introduced in 1930s as a framework to understand the structure of the observed vibration-rotation spectrum of several small molecules. During the past three decades NMA has also become a popular alternative to figuring out the large-scale motion of proteins and other macromolecules. However, the “standard” NMA is based on approximations, which sometimes are unphysical. Especially problematic is the assumption that atoms move only “infinitesimally”, which, of course, is an oxymoron when large amplitude motions are concerned. The “infinitesimal” approximation has the further unfortunate side effect of masking the physical importance of the coupling between vibrational and rotational degrees of freedom. Here, we present a novel formulation of the NMA, which is applied for finite motions in non-Eckart body-frame. Contrary to standard normal mode theory, our approach starts by assuming a harmonic potential in generalized coordinates, and tries to avoid the linearization of the coordinates. It also takes explicitly into account the Coriolis terms, which couple vibrations and rotations, and the terms involving Christoffel symbols, which are ignored by default in the standard NMA. We also computationally explore the effect of various terms to the solutions of the NMA equation of motions.     

Intensely luminescent homoleptic alkynyl decanuclear gold(I) clusters and their cationic octanuclear phosphine derivatives

Treatment of Au(SC(4)H(8))Cl with a stoichiometric amount of hydroxyaliphatic alkyne in the presence of NEt(3) results in high-yield self-assembly of homoleptic clusters (AuC(2)R)(10) (R = 9-fluorenol (1), diphenylmethanol (2), 2,6-dimethyl-4-heptanol (3), 3-methyl-2-butanol (4), 4-methyl-2-pentanol (4), 1-cyclohexanol (6), 2-borneol (7)). The molecular compounds contain an unprecedented catenane metal core with two interlocked 5-membered rings. Reactions of the decanuclear clusters 1-7 with gold-diphosphine complex [Au(2)(1,4-PPh(2)-C(6)H(4)-PPh(2))(2)](2+) lead to octanuclear cationic derivatives [Au(8)(C(2)R)(6)(PPh(2)-C(6)H(4)-PPh(2))(2)](2+) (8-14), which consist of planar tetranuclear units {Au(4)(C(2)R)(4)} coupled with two fragments [AuPPh(2)-C(6)H(4)-PPh(2)(AuC(2)R)](+). The titled complexes were characterized by NMR and ESI-MS spectroscopy, and the structures of 1, 13, and 14 were determined by single-crystal X-ray diffraction analysis. The luminescence behavior of both Au(I)(10) and Au(I)(8) families has been studied, revealing efficient room-temperature phosphorescence in solution and in the solid state, with the maximum quantum yield approaching 100% (2 in solution). DFT computational studies showed that in both Au(I)(10) and Au(I)(8) clusters metal-centered Au → Au charge transfer transitions mixed with some π-alkynyl MLCT character play a dominant role in the observed phosphorescence.     

Weak and strong type estimates for maximal truncations of Calderón-Zygmund operators on A p weighted spaces

We show that for 1 < p < ??, weight w ?? A _p , and any L ²-bounded Calderón-Zygmund operator T, there is a constant C _T,p such that the weak- and strong-type inequalities $${\left\| {{T_\natural}f} \right\|_{{L^{p,\infty }}(w)}} \le {C_{T,p}}{\left\| w \right\|_{{A_p}}}{\left\| f \right\|_{{L^p}(w )}}$$ $${\left\| {{T_\natural}f} \right\|_{{L^p}(w)}} \le {C_{T,p}}\left\| w \right\|_{{A_p}}^{\max \{ 1,{{(p - 1)}^{ - 1}}}{\left\| f \right\|_{{L^p}(w)}}$$ hold, where T _? denotes the maximal truncations of T and ${\left\| w \right\|_{{A_p}}}$ denotes the Muckenhoupt A _p characteristic of w. These estimates are not improvable in the power of ${\left\| w \right\|_{{A_p}}}$ . Our argument follows the outlines of those of Lacey-Petermichl-Reguera (Math. Ann. 2010) and Hyt?nen-Pérez-Treil-Volberg (arXiv, 2010) and contains new ingredients, including a weak-type estimate for certain duals of T _? and sufficient conditions for two-weight inequalities in L ^p for T _?. Our proof does not rely upon extrapolation.     

Functional Columnar Liquid Crystalline Phases From Ionic Complexes of Dendronized Polymers and Sulfate Alkyl Tails

We describe how cationic dendronized polymers of generations 1, and 2 and anionic monoalkyl tails can be combined by supramolecular ionic complexation into comb-like liquid crystalline polymers. The final structures in bulk of these supramolecular complexes were studied by differential scanning calorimetry (DSC), cross-polarized optical microscopy (CPOM), small angle x-rays scattering (SAXS) and transmission electron microscopy (TEM). The combination of these techniques allowed elucidating (i) that these complexes exhibit thermotropic behaviour, (ii) that various liquid crystalline structures in the 3–5 nm length scale can be obtained such as columnar rectangular, columnar tetragonal, columnar hexagonal and lamellar, depending both on alkyl tail length and polymer generation, (iii) that although the alkyl tails represent the majority phase in the columnar phases, they form the cylindric domains, and the dendronized polymers occupy the continuous domains. Therefore, upon selective cleavage of the alkyl tails in the columnar phases, the present self-assembly approach may constitute an efficient strategy towards the formation of porous organic matrices with ultra-dense pore size in the range of 2 to 4 nm.     

Inner functions in weak Besov spaces

It is shown that inner functions in weak Besov spaces are precisely the exponential Blaschke products.     

On the Borel-Cantelli lemma

Necessary and sufficient conditions for P(A_n infinitely often) = , [0, 1], are obtained, where {A_n} is a sequence of events such that P(A _n ) = .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 200–207, 1990.     

Surface characterization of unbleached kraft pulps by means of ESCA

The effect of digestion conditions (amount of effective alkali, digestion time) on the surface compositions of unbleached softwood (Pinus sylvestris) kraft pulp has been investigated by electron spectroscopy for chemical analysis (ESCA). The quantities monitored were the angular dependence of the total O/C ratio, the relative amounts of carbons in different states of oxidation and the adsorption of Al and Ca ions to the carboxyl groups in the surface. Examination of the angular dependence of ESCA intensities shows that the concentration of alkyl carbon is high in a very thin surface layer and that it decreases linearly with decreasing kappa number. The concentration of alkyl carbon is decreased by extraction of the fibres with dichloromethane, but the amount remaining in the surface after extraction still decreases linearly with decreasing kappa number (i.e. it decreases with increasing digestion time). It is suggested that the observed enrichment of alkyl carbon in the outermost surface layers most probably is due to reprecipitation of lignin. In pulp that has not been extracted, there is also strong enrichment of extractives in the surface. This amount increases with increasing effective alkali but is relatively independent of digestion time. ESCA analysis of the Al and Ca bound to the carboxyl groups shows that the amount depends on digestion time; the results are consistent with the notion that the reprecipitated lignin contains carboxyl groups.