There Is No Face-to-Face Partition of R5 into Acute Simplices

We prove that a point in the Euclidean space R⁵ cannot be surrounded by a finite number of acute simplices. This fact implies that there does not exist a face-to-face partition of R⁵ into acute simplices. The existence of an acute simplicial partition of R^d for d > 5 is excluded by induction, but for d = 4 this is an open problem. Dedicated to Prof. Miroslav Fiedler on the occasion of his 80th birthday     

Dirubidium fluoro­trioxophosphate,Rb2PO3F,at 290 and 130 K,and dicaesium fluoro­trioxophosphate,Cs2PO3F,at 240 and 100 K

The structure of Rb₂PO₃F was determined at 290 and 130 K, while that of Cs₂PO₃F was determined at 240 and 100 K. Both compounds belong to the β‐K₂SO₄ family. The structure analysis did not reveal signs of a phase transition in either compound. Crystal chemical considerations do not favour the presence of a phase transition in either Rb₂PO₃F or Cs₂PO₃F. However, glass‐like phase transitions were observed by differential scanning calorimetry in slightly humid samples at 175 and 177 K for Rb₂PO₃F and Cs₂PO₃F, respectively, but were not observed in well dried samples. The bond distances are normal and Cs₂PO₃F is twinned.     

Differential invariants of generic hyperbolic Monge-Ampère equations

In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.      

The Diels-Alder reaction of ethene and 1,3-butadiene: an extended multireference ab initio investigation.

The concerted and stepwise mechanisms of the Diels-Alder reaction between 1,3-butadiene and ethene have been investigated using highly correlated multireference methods (MRAQCC) and extended basis sets. Full MRAQCC geometry optimizations have been performed in all cases. The best estimate for the energy barrier of the Diels-Alder reaction is 22 kcalmol(-1). Anti- and gauche-out minima for the biradical structures and corresponding fragmentation saddle points have been determined. The biradical anti fragmentation saddle point is located 6.5 kcalmol(-1) above the concerted saddle point. The gauche-in structure does not correspond to a local minimum, but leads on geometry optimization directly to cyclohexene.     

Isomorphic embeddings and harmonic behaviour of smooth operators

LetY be a Banach space, 1<p<∞. We give a simple criterion for embedding ℓ _p ⊂Y, namely it suffices that the positive cone ℓ _p ⁺ ⊂Y. This result is applied to the study of highly smooth operators from ℓ _p intoY (p is not an even integer). The main result is that every such operator has a harmonic behaviour unless ℓ _p/K ⊂Y for someK ∈ ℕ. Supported by grants GAUK 277/2001, GAČR 201-01-1198, A1019205.     

Weakly coupled oscillators and topological degree

By using the topological degree of Brouwer for mappings along with averaging method, we study the existence of forced periodic solutions for certain weakly coupled periodically perturbed ordinary differential equations.     

Orbitrap™ monostage MS versus hybrid linear ion trap MS: application to multi‐allergen screening in wine

Food allergen research has made giant steps in the last years thanks to the features offered by the latest technology of mass analyzers placed on the market allowing multiplex sensitive detection of proteins. Potentials and features of two mass analyzers namely a linear ion trap capable of performing a data dependent or selected reaction monitoring analysis and an Orbitrap^TM stand‐alone MS enabling a broadband fragmentation without mass selection at highest mass resolving power are herein described and applied to the multiplex screening of allergens in a type of wine chosen as a reference matrix. Quantitative and confirmative capabilities of both platforms were assessed on the specific case study, the multiple detection of egg and milk ‐related proteins, typically employed in white wines as fining agents. Commercial bioinformatic tools used for a quick allergen identification will be also discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Determination of pK a of N-alkyl-N,N-dimethylamine-N-oxides using 1H NMR and 13C NMR spectroscopy

The pK _a values of N-alkyl-N,N-dimethylamine-N-oxides were determined from the pH dependences of chemical shifts in ¹H NMR and ¹³C NMR spectra. The dependences were measured at concentrations below and above the critical micelle concentration of the amine oxides. Above the critical micelle concentration, the plots of the peak positions vs. pH were either sigmoid (the groups close to the nitrogen) or “peak type” (farther groups). The sigmoidal behaviour was a direct result of the acid-base reaction; on the other hand, the “peak type” behaviour was probably an indirect consequence of the pH variation, mediated with the change in micelle size.     

Direct Arylation of Adenine by Fluoro- and Chloronitrobenzenes: Effect of Microwaves

Direct arylation of adenine with fluoro- and chloronitrobenzenes leads to mixtures of N9 and N7 substituted adenines. After separation by column chromatography, the individual isomers can be efficiently hydrogenated on Pd to give the corresponding aminophenyladenines. A significant enhancement of the reaction rate by microwave irradiation was observed. This two-step procedure was found to be a feasible route to otherwise hardly available 7-aminophenyladenines. Correlation between calculated shielding constants and experimental values of chemical shifts in ¹³C and ¹⁵N NMR was used for assignment of the site of substitution.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]