Besicovitch triangles cover unit arcs

A long standing conjecture is that the Besicovitch triangle, i.e., an equilateral triangle with side is a worm-cover. We will show that indeed there exists a class of isosceles triangles, that includes the above equilateral triangle, where each triangle from the class is a worm-cover. These triangles are defined so that the shortest symmetric z-arc stretched from side to side and touching the base would have length one.      

Synthesis and study of the structure of o-hydroxyaryl-1,2,4-oxadiazoles

The reaction of 4-oxo-1,3-benz- and -naphthoxazinium perchlorates with hydroxylamine leads to 5-(o-hydroxyaryl)-1,2,4-oxadiazoles rather than to 3-(o-hydroxyaryl)-1,2,4-oxadiazoles, as was previously assumed. The structure of the compounds obtained was proved by alternative synthesis, as well as by mass spectrometry and comparison of the experimentally found and calculated dipole moments and Kerr constants of the possible structures of the o-hydroxyaryl-1,2,4-oxadiazoles.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 540–549, April, 1992.     

Ni2X2 (X = pnictide,chalcogenide, or B) based superconductors

We review the properties of Ni-based superconductors which contain Ni₂X₂ (X = As, P, Bi, Si, Ge, B) planes, a common structural element found also in the recently discovered FeAs superconductors. Strong evidence for the fully gapped nature of the superconducting state has come from field dependent thermal conductivity results on BaNi₂As₂. Coupled with the lack of magnetism, the majority of evidence suggests that the Ni-based compounds are conventional electron–phonon mediated superconductors. However, the increase in T_c in LaNiAsO with doping is anomalous, and mimics the behavior in LaFeAsO. Furthermore, comparisons of the properties of Ni- and Fe-based systems show many similarities, particularly with regards to structure–property relationships. This suggests a deeper connection between the physics of the FeAs superconductors and the related Ni-based systems which deserves further investigation.     

Low temperature spin dynamics of the geometrically frustrated antiferromagnetic garnet Gd3Ga5O12

The low temperature spin dynamics of the geometrically frustrated antiferromagnet Gd 3Ga 5O (12) (GGG) have been investigated using muon spin relaxation. No evidence for static order is seen down to a temperature of 25 mK or a few percent of the Curie-Weiss temperature. Instead there is a linear decrease in the Gd spin fluctuation rate below 1 K which extrapolates to a small but finite value of 2 GHz at zero temperature. In terms of the spin fluctuations the system appears essentially to remain dynamic at low temperatures (T>0.02 K) and magnetic fields up to 1.8 T.     

Local ferromagnetic resonance imaging with magnetic resonance force microscopy

We report nanoscale scanned probe ferromagnetic resonance force microscopy (FMRFM) imaging of individual ferromagnetic microstructures. This reveals the mechanism for high spatial resolution in FMRFM imaging: the strongly inhomogeneous local magnetic field of the cantilever mounted micromagnetic probe magnet used in FMRFM enables selective, local excitation of ferromagnetic resonance (FMR). This approach, demonstrated here in individual permalloy disks, is straightforwardly extended to excitation of localized FMR modes, and hence imaging in extended films.