The aza Arndt–Eistert reaction based on N-trifluoromethylsulfonylarenecarboximidoyl chlorides

The aza analogues of carboxylic acids chlorides containing the NSO₂CF₃ and NSO₂CH₃ groups instead of oxygen atom were used in the Arndt–Eistert reaction. It was found that N-trifluoromethylsulfonyl-(4-fluorophenyl)-carboximidoyl chloride 1 reacts with diazomethane vigorously even at ?70 °C with formation of 1-trifluoromethylsulfonylamino-2-(4-fluorophenyl)-2,3-dimorpholine-4-yl-propane 3, 2-trifluoromethylsulfonylamino-2-(4-fluorobenzyl)-7-oxa-4-azonia-spiro[3.5]nonane 4, 2-trifluoromethylsulfonylamino-2-(4-fluorobenzyl)-1,3-dimorpholine-4-yl-propane 5 and 1-trifluoromethylsulfonylamino-2-(4-fluorobenzyl)-2,3-dimorpholine-4-yl-propane 6. Reaction of N-methylsulfonylbenzcarboximidoyl chloride 8 with diazomethane proceeds at ?15 °C yielding 4-chloro-4-methylsulfonylaminomethyl-3-phenyl-4,5-dihydro-1H-pyrazoline 9.     

Multi-tiling and Riesz bases

Let S   be a bounded, Riemann measurable set in R^d${\mathbb{R}}^d$, and Λ be a lattice. By a theorem of Fuglede, if S   tiles R^d${\mathbb{R}}^d$ with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles  R^d${\mathbb{R}}^d$ with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer?s quasicrystals.     

Generalized Stationary Processes: Applications and Examples

We introduce and investigate special classes of generalized stationary processes: white-noise-type processes and power-low processes. Operators which generate white-noise-type processes are interesting, in particular, because of their importance to random matrix theory, triangular factorization of operators and spectral theory.     

The former "C60F16" is actually a double-caged adduct: (C60F16)(C60)

X-ray diffraction study of the substance originally believed to be C(60)F(16) reveals a double-caged structure, (C(60)F(16))(C(60)); MALDI mass spectra, 19F NMR spectral data and reasons for stability are discussed.     

Behaviour of π mesons and synchrotron radiation in a strong magnetic field

The analogue of coherent states for scalar charged particles in a strong magnetic field is developed. The trajectory of such a wave packet in a strong magnetic field is shown to differ considerably from the classical one. This results in a low frequency modulation of synchrotron radiation intensity. The possible experimental observation is discussed.     

Nuclear effects at large transverse momentum in a QCD parton model

Production of single mesons and opposite side pairs of mesons in hadron-nucleus and nucleusnucleus collisions are calculated in the framework of the QCD parton model, with the assumption that quarks and gluons undergo multiple scattering in the nucleus. A comparison with all available data is made. It is also shown that the anomalous nuclear enhancement, especially its dependence on the flavour, can be quantitatively described within the model. Furthermore, we predict no enhancement for symmetric pairs as it seems to be indicated by the data. Predictions for largep _T production in α?α scattering at ISR are made.     

The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper, we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the “near-flip” instability, we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.      

Restricted set addition in groups,III. Integer sumsets with generic restrictions

Let Abe a finite set of integers. Assuming that R⊆A×Ais “not too large”, we give a lower-bound estimate for the cardinality of the restricted sumset A+ ^R A:= {a1 + a2 : a1; a2 ∈A;(a1; a2) ∉R}in terms of the cardinality and the length of A.