Field cooled and zero field cooled 207Pb NMR and the local structure of relaxor PbMg1/3Nb2/3O3

An isotropic 207Pb NMR spectrum corresponding to the glassy matrix with spherical shell type Pb shifts from the cubic sites, as well as an anisotropic spectral component corresponding to polar nanoclusters with a Pb shift parallel to the [111] direction, have been observed in a PbMg(1/3)Nb(2/3)O3 (PMN) single crystal. This represents a microscopic confirmation of the model of relaxors first proposed by Burns and Dacol. A sudden increase in the intensity of the anisotropic cluster line is seen for electric fields larger than the critical field around 210 K. This demonstrates the occurrence of an orientational percolation type transition to the field-induced ferroelectric phase with about 50% of the Pb nuclei still remaining in the spherical glass matrix. A similar though smaller increase of the intensity of this line is also seen in the zero field cooled data, demonstrating that relaxor PMN is an incipient ferroelectric.     

Low temperature properties of proton and deuteron glasses

2D deuteron exchange NMR and ⁸⁷Rb spin-lattice relaxation time measurements in proton and deuteron glasses show that the O-H..O dipoles are not completely frozen out at low temperatures but show dynamic features characteristic of incoherent tunneling. RADP and DRADP are thus quantum glasses.     

On local automorphisms of group algebras of compact groups

We show that with few exceptions every local isometric automorphism of the group algebra of a compact metric group is an isometric automorphism.

     

Nutraceutical Approaches of Autophagy and Neuroinflammation in Alzheimer’s Disease: A Systematic Review

Aging and the emergence of age-associated illnesses are one of the major challenges of our present society. Alzheimer’s disease (AD) is closely associated with aging and is defined by increasing memory loss and severe dementia. Currently, there are no therapy options available that halt AD progression. This work investigates three hallmarks of the disease (autophagy, neuroinflammation, and senescence) and systematically analyzes if there is a beneficial effect from three substances derived from food sources, the so called “nutraceuticals” epigallocatechin gallate, fisetin, and spermidine, on these hallmarks. The results imply a positive outlook for the reviewed substances to qualify as a novel treatment option for AD. A combination of nutraceutical substances and other preventive measures could have significant clinical impact in a multi-layered therapy approach to counter AD.     

Non-negative Spectral Measures and Representations of C*-Algebras

Regular normalized W-valued spectral measures on a compact Hausdorff space X are in one-to-one correspondence with unital *-representations ${\rho : C(X, \mathbb{C}) \to W}$ , where W stands for a von Neumann algebra. In this paper we show that for every compact Hausdorff space X and every von Neumann algebras W ₁, W ₂ there is a one-to-one correspondence between unital *-representations ${\rho : C(X, W_1) \to W_2}$ and special B(W ₁, W ₂)-valued measures on X that we call non-negative spectral measures. Such measures are special cases of non-negative measures that we introduced in our previous paper (Cimpri? and Zalar, J Math Anal Appl 401:307–316, 2013) in connection with moment problems for operator polynomials.     

Note on coloring of double disk graphs

The coloring of disk graphs is motivated by the frequency assignment problem. In 1998, Malesińska et al. introduced double disk graphs as their generalization. They showed that the chromatic number of a double disk graph \(G\) is at most \(33\,\omega (G) - 35\) , where \(\omega (G)\) denotes the size of a maximum clique in \(G\) . Du et al. improved the upper bound to \(31\,\omega (G) - 1\) . In this paper we decrease the bound substantially; namely we show that the chromatic number of \(G\) is at most \(15\,\omega (G) - 14\) .     

Profiling the tuneable R-SMS-Phos structure in the rhodium(I)-catalyzed hydrogenation of olefins: the last stand?

A diversified family of enantiopure P-stereogenic "R-SMS-Phos" {R-SMS-Phos = 1,2-bis[(o-RO-phenyl)(phenyl)phosphino]ethane} ligands wherein R = branched or heteroatom-substituted alkyl, aralkyl, silyl, acyl, sulfonyl, etc. was screened for the Rh(I)-catalyzed hydrogenation of a representative set of olefinic substrates. This systematic and detailed investigation revealed a marked beneficial impact on enantioselectivity and catalyst activity in comparison to Knowles' ultimate DiPAMP {DiPAMP = 1,2-bis[(o-anisyl)(phenyl)phosphino]ethane} design. Mutant ligands with highly enhanced properties possessing particular features wherein the DiPAMP structure is found embedded were identified.     

Note on 3-choosability of planar graphs with maximum degree 4

Deciding whether a planar graph (even of maximum degree 4) is 3-colorable is NP-complete. Determining subclasses of planar graphs being 3-colorable has a long history, but since Grötzsch’s result that triangle-free planar graphs are such, most of the effort was focused to solving Havel’s and Steinberg’s conjectures. In this paper, we prove that every planar graph obtained as a subgraph of the medial graph of any bipartite plane graph is 3-choosable. These graphs are allowed to have close triangles (even incident), and have no short cycles forbidden, hence representing an entirely different class than the graphs inferred by the above mentioned conjectures.