On continuation of inviscid vortex patches

This investigation concerns solutions of the steady-state Euler equations in two dimensions featuring finite area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape-differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov–Poincaré method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl–Batchelor solution, each of which satisfies the Kutta condition.     

Proton MRI of (13)C distribution by J and chemical shift editing.

The sensitivity of (13)C NMR imaging can be considerably favored by detecting the (1)H nuclei bound to (13)C nuclei via scalar J-interaction (X-filter). However, the J-editing approaches have difficulty in discriminating between compounds with similar J-constant as, for example, different glucose metabolites. In such cases, it is almost impossible to get J-edited images of a single-compound distribution, since the various molecules are distinguishable only via their chemical shift. In a recent application of J-editing to high-resolution spectroscopy, it has been shown that a more efficient chemical selectivity could be obtained by utilizing the larger chemical shift range of (13)C. This has been made by introducing frequency-selective (13)C pulses that allow a great capability of indirect chemical separation. Here a double-resonance imaging approach is proposed, based on both J-editing and (13)C chemical shift editing, which achieves a powerful chemical selectivity and is able to produce full maps of specific chemical compounds. Results are presented on a multicompartments sample containing solutions of glucose and lactic and glutamic acid in water.     

Raman phonon spectra and lattice dynamics of 9,10-dinitroanthracene under pressure

Abstract

Raman phonon spectra of 9, 10-dinitroanthracene have been recorded in the pressure range 0-6GPa. No phase transition is detected up to the maximum pressure studied. Quasi Harmonic Lattice Dynamics calculations, based on an atom-atom potential previously modeled on homologous 9,10-disubstituted anthracenes, have been performed. The optimized potential was used to calculate the equilibrium geometry and the lattice phonon frequencies as a function of pressure. The calculated structure at ambient conditions closely resembles the experimental one. The calculated phonon frequencies show a good agreement with the experimental values at all pressures measured.     

The magnetic hyperfine structure in the rotational spectrum of H2CNH

The hyperfine structure in the ground-state rotational spectrum of methanimine was studied in the frequency range of 64-172 GHz by means of the Lamb-dip technique. This allowed to resolve, in some hyperfine components due to the ¹⁴N nucleus, doublets separated by only some tenth of kHz. We explain the splittings as due to magnetic interactions of the three protons with their molecular environment. The analysis of the experimental spectrum has been guided by quantum-chemical calculations of the hyperfine parameters.     

Synthesis,binding and fluorescence studies of a new neutral H-bonding receptor for anions based on 3,5-bis(trifluoromethyl)phenylurea

The synthesis and anion binding studies of the new neutral receptor 1,1′-(2,2′-(4,10-dimethyl-1,4,7,10-tetraazacyclododecane-1,7-diyl)bis(2-oxoethane-2,1-diyl))bis(3-(3,5-bis(trifluoromethyl)phenyl)urea) (L1) are reported. L1 is a macrocyclic ligand containing the 3,5-trifluoromethylphenylureido-binding fragment attached as a side arm on the tetraazacyclododecane. L1 is soluble in numerous organic solvents; the binding properties of L1 towards several simple anions (G) were investigated by NMR, UV–vis and fluorescence techniques in DMSO and CH₃CN solutions. L1 is able to bind F^? , Cl^?  and AcO^?  in both solvents; in addition, it binds Br^?  in CH₃CN. Fluoride shows the highest constant values in the halide series (F^?  > Cl^?  > Br^? ) and AcO^?  is the most strongly bound among all the anions investigated. L1 is able to signal the presence of the anions in solution by fluorescence change; in the case of acetate, this occurs in the visible range.     

Principal hierarchies of infinite-dimensional Frobenius manifolds: The extended 2D Toda lattice

We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/∞$0/\infty$ respectively, which extends the dispersionless 2D Toda hierarchy of Takasaki and Takebe. Then we construct the deformed flat connection of the infinite-dimensional Frobenius manifold _M0$M_0$ introduced by Carlet, Dubrovin and Mertens (2011) [3] and, by explicitly solving the deformed flatness equations, we prove that the extended 2D Toda hierarchy coincides with principal hierarchy of _M0$M_0$.     

A unifying approach for the study of linear sampling type operators in function spaces

Sampling series play a crucial role in Signal and Image Processing. In this note, we illustrate a general method to construct Sampling series and to determine their convergence in Orlicz spaces. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)