Low-acceleration instability of a Bose-Einstein condensate in an optical lattice

We study a Bose-Einstein condensate in a one-dimensional accelerated optical lattice using the mean-field version of the Bose-Hubbard model. Reminiscent of recent experiments [M. Cristiani et al., Opt. Express 12, 4 (2004)], we find a new type of an instability in this system that occurs in the limit when the acceleration is small.     

Investigation of solid phase upon γ-irradiation of ferrihydrite-ethanol suspension

Ferrihydrite (FH) nanoparticles were synthesised and subjected to γ-irradiation in the form of FH-ethanol suspension. The dose rate of γ-radiation was ～16 kGy/h and the samples were irradiated to doses of up to 2590 kGy. γ-irradiation of FH-ethanol suspensions did not cause the transformation of FH to any of the other iron oxide phases. Likewise, neither the Mössbauer and FT-IR spectroscopy nor the quantitative analysis using Energy Dispersive X-ray Spectroscopy gave any evidence of structural changes of FH upon γ-irradiation. C, H analysis showed that the C concentration in FH gradually increased with dose and was higher in γ-irradiated FH samples than in non-irradiated FH sample. This finding suggested that carbon in FH originated from ethanol degradation. The H concentration in FH gradually increased to the dose of up to 340 kGy and then slightly decreased. Magnetic measurements showed a progressive decrease in magnetisation with an increase in γ-irradiation. The results of magnetic measurements and C, H analysis suggested the carbonisation of FH surface. It was supposed that γ-irradiation of FH-ethanol suspension reductively decomposed ethanol thus generating unsaturated hydrocarbons and acetylides, which in turn formed a conjugate iron complex, thus carbonating the FH surface. The carbonisation of the FH surface prevented FH transformation to other iron oxide phases.     

Microwave-Assisted Synthesis of Organophosphorus Compounds

Abstract

Kabachnik-Fields reactions of a variety of amines, phospha-Michael additions to maleimide derivatives and alcoholysis of dialkyl phosphites were studied under microwave conditions.     

Lipschitz constants for the real part and modulus of analytic mappings on a negatively curved surface

Archiv der Mathematik - We prove that if f, $$|\mathfrak {R}f|<1$$ , is an analytic mapping on a surface $$\Sigma $$ with curvature bounded from below by a constant $$k<0$$ , and if...     

Ring-opening reactions of 1,4-diazabicyclo[2.2.2]octane (DABCO) derived quaternary ammonium salts with phenols and related nucleophiles

1,4-Diazabicyclo[2.2.2]octane (DABCO) has been evaluated as a starting material for the synthesis of 1-alkyl-4-(2-phenoxyethyl)piperazines and related derivatives. We found that 1-alkyl-1,4-diazabicyclo[2.2.2]octan-1-ium salts, resulting from the alkylation of DABCO, efficiently react with a variety of nucleophiles in polyethyleneglycol (PEG) or diglyme at high temperatures to give piperazine products resulting from the nucleophilic ring-opening reaction. The benzylation side reaction was found to be relevant with softer nucleophiles when using 1-benzyl-1,4-diazabicyclo[2.2.2]octan-1-ium salts, while other types of alkylations were not observed. One-pot methodologies allow for the synthesis of piperazines directly from primary alcohols, alkyl halides or sulfonates, using phenols, or other nucleophile sources, and DABCO.     

A way to avoid using precious metals: the application of high-surface activated carbon for the synthesis of isoindoles via the Diels-Alder reaction of 2H-pyran-2-ones

The application of activated carbon (Darco KB) for the acceleration and direction of the transformation of various 2H-pyran-2-ones with N-substituted maleimides toward isoindole derivatives through the reaction sequence cycloaddition/elimination/dehydrogenation is described. In this reaction, the catalyst mainly influences the dehydrogenation step, which is essential to avoid the formation of bicyclo[2.2.2]octenes as the other possible products. We found that the combination of Darco KB, as the metal-free catalyst, and decalin, as the solvent in a closed vessel, represents the most successful conditions. A comparison of the effect of various dehydrogenation catalysts and reaction conditions is also presented. In addition, we have proven that the aromatization occurs via a hydrogen transfer from the cyclohexadiene intermediate to the maleimide derivative (therefore producing succinimides). This transfer is facilitated by the active surface of the heterogeneous carbon-based catalyst.     

α‐Aminophosphonates and α‐Aminophosphine Oxides by the Microwave‐Assisted Kabachnik–Fields Reactions of 3‐Amino‐6‐methyl‐2 H‐pyran‐2‐ones

The microwave‐assisted Kabachnik–Fields reaction of a series of 3‐amino‐6‐methyl‐2H‐pyran‐2‐ones, paraformaldehyde, and dialkyl phosphites or diphenylphosphine oxide led to α‐aminophosphonates or α‐aminophosphine oxides, respectively. The α‑aminophosphonates were obtained under solvent‐free conditions, whereas the α‑aminophosphine oxides in acetonitrile. The novel products were characterized by NMR and mass spectral data. © 2013 Wiley Periodicals, Inc. Heteroatom Chem 24:221–225, 2013; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.21086     

Optimal Estimates for the Gradient of Harmonic Functions in the Unit Disk

Let U be the unit disk, p ≥ 1 and let h ^p (U) be the Hardy space of complex harmonic functions. We find the sharp constants C _p and the sharp functions C _p = C _p (z) in the inequality $$|Dw (z)|\leq {C_p}(1-|z|^2)^{-1-1/p} \|w\|_{h^p(\mathbf U)}, w\in h^p(\mathbf U), z\in \mathbf U,$$ in terms of Gaussian hypergeometric and Euler functions. This generalizes some results of Colonna related to the Bloch constant of harmonic mappings of the unit disk into itself and improves some classical inequalities by Macintyre and Rogosinski.