Heteronuclear recoupling in solid-state magic-angle-spinning NMR via overtone irradiation

A heteronuclear dipolar recoupling scheme applicable to I-S spin pairs undergoing magic-angle-spinning (MAS) is introduced, based on the overtone irradiation of one of the coupled nuclei. It is shown that when I is a quadrupole, for instance (14)N, irradiating this spin at a multiple of its Larmor frequency prevents the formation of MAS dipolar echoes. The ensuing S-spin signal dephasing is significant and dependent on a number of parameters, including the I-S dipolar coupling, the magnitude of I's quadrupolar coupling, and the relative orientations between these two coupling tensors. When applied to a spin-1 nucleus, this overtone recoupling method differs from hitherto proposed recoupling strategies in that it involves only the +/-1> I(z) eigenstates. Its dephasing efficiency becomes independent of first-order quadrupolar effects yet shows a high sensitivity to second-order offsets. A constant-time/variable-offset recoupling sequence thus provides a simple route to acquire, in an indirect fashion, (14)N overtone spectra from rotating powders. The principles underlying this kind of S-(14)N experiments and different applications involving S = (13)C, (59)Co sites are presented.     

Heck and Sonogashira cross-coupling reactions using recyclable Pd–Fe3O4 heterodimeric nanocrystal catalysts

We have developed a convenient Pd–Fe₃O₄ heterodimeric nanocrystal catalyst system for Heck and Sonogashira reactions. This catalyst offers an environment-friendly, atom-efficient, and robust catalytic system for both reactions. Furthermore the nanocrystal catalyst could be easily separated by an external magnet and recycled six times without losing its catalytic activity.     

Effect of solution pH on the stability of mixed silica -alumina suspension in the presence of polyacrylic acid (PAA) with different molecular weights

The influence of solution pH (in the range 3–9) on mixed silica-alumina suspension in the absence and presence of polyacrylic acid (PAA) was studied. The composition of the adsorbent was SiO₂ (97%) and Al₂O₃ (3%). The turbidimetry method was applied to record changes in the stability of the investigated systems as a function of time. It was shown that the suspension without the polymer is less stable at pH 3, whereas at pH 6 and 9, the systems were stable. PAA with molecular weights 100 000 and 240 000 at pH 3 (improvement of system stability conditions) and PAA 2 000 at pH 6 (deterioration of suspension stability) have a great effect on the silica-alumina suspension stability. The stabilization-flocculation properties of polyacrylic acid are a result of a specific conformation of its chains on the solid surface where it depends on the solution pH and the polymer molecular weight.     

An elementary proof of the Loomis–Whitney theorem

Loomis and Whitney proved an inequality between volume and areas of projections of an open set in n-dimensional space related to the isoperimetric inequality. They reduced the problem to a combinatorial theorem proved by a repeated use of Hölder inequality. In this paper we prove a general inequality between real numbers which easily implies the combinatorial theorem of Loomis and Whitney.

     

The Generalized k-Resultant Modulus Set Problem in Finite Fields

Journal of Fourier Analysis and Applications - Let $${\mathbb {F}}_q^d$$ be the d-dimensional vector space over the finite field $${\mathbb {F}}_q$$ with q elements. Given k sets $$E_j\subset...     

Modification of Surface Properties of Colloidal Suspensions of NixOy-SiO2 Mixed Oxides with Different Ni Contents by the Adsorption Layers of Poly(Vinyl Alcohol)

Journal of Cluster Science - The adsorption and electrokinetic properties of hybrid silica materials composed of nickel and silicon oxides (NixOy-SiO2), characterized by different contents of...     

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