A Novel Allenic Epoxycyclohexane and Related Compounds from Eutypa lata (Pers: F.) Tul

The novel allenic epoxycyclohexanes 1 , and related compounds 2 and 3 have been isolated from the culture medium of Eutypa lata. Their structures were established by combination of spectroscopic and chemical techniques. Biogenetic origin and biological activity of these compounds are also discussed.     

Measurement of the resistivity of porous materials with an alternating air-flow method

Air-flow resistivity is a main parameter governing the acoustic behavior of porous materials for sound absorption. The international standard ISO 9053 specifies two different methods to measure the air-flow resistivity, namely a steady-state air-flow method and an alternating air-flow method. The latter is realized by the measurement of the sound pressure at 2 Hz in a small rigid volume closed partially by the test sample. This cavity is excited with a known volume-velocity sound source implemented often with a motor-driven piston oscillating with prescribed area and displacement magnitude. Measurements at 2 Hz require special instrumentation and care. The authors suggest an alternating air-flow method based on the ratio of sound pressures measured at frequencies higher than 2 Hz inside two cavities coupled through a conventional loudspeaker. The basic method showed that the imaginary part of the sound pressure ratio is useful for the evaluation of the air-flow resistance. Criteria are discussed about the choice of a frequency range suitable to perform simplified calculations with respect to the basic method. These criteria depend on the sample thickness, its nonacoustic parameters, and the measurement apparatus as well. The proposed measurement method was tested successfully with various types of acoustic materials.     

The effect of linear perturbations on the Yamabe problem

In conformal geometry, the Compactness Conjecture asserts that the set of Yamabe metrics on a smooth, compact, aspherical Riemannian manifold $\left( M,g\right) $ is compact. Established in the locally conformally flat case by Schoen (Lecture Notes in Mathematics, vol. 1365, pp. 120–154. Springer, Berlin 1989, Surveys Pure Application and Mathematics, 52 Longman Science, Technology, pp. 311–320. Harlow 1991) and for $n\le 24$ by Khuri–Marques–Schoen (J Differ Geom 81(1):143–196, 2009), it has revealed to be generally false for $n\ge 25$ as shown by Brendle (J Am Math Soc 21(4):951–979, 2008) and Brendle–Marques (J Differ Geom 81(2):225–250, 2009). A stronger version of it, the compactness under perturbations of the Yamabe equation, is addressed here with respect to the linear geometric potential $\frac{n-2}{4(n-1)} {{\mathrm{Scal}}}_g,\, {{\mathrm{Scal}}}_g$ being the Scalar curvature of $\left( M,g\right) $ . We show that a-priori $L^\infty $ –bounds fail for linear perturbations on all manifolds with $n\ge 4$ as well as a-priori gradient $L^2$ –bounds fail for non-locally conformally flat manifolds with $n\ge 6$ and for locally conformally flat manifolds with $n\ge 7$ . In several situations, the results are optimal. Our proof combines a finite dimensional reduction and the construction of a suitable ansatz for the solutions generated by a family of varying metrics in the conformal class of $g$ .     

A theory of ferromagnetism by Ettore Majorana

We present and analyze in detail an unknown theory of ferromagnetism developed by Ettore Majorana as early as the beginnings of 1930s, substantially different in the methods employed from the well-known Heisenberg theory of 1928 (and from later formulations by Bloch and others). Similarly to this, however, it describes successfully the main features of ferromagnetism, although the key equation for the spontaneous mean magnetization and the expression for the Curie temperature are different from those deduced in the Heisenberg theory (and in the original phenomenological Weiss theory). The theory presented here contains also a peculiar prediction for the number of nearest neighbors required to realize ferromagnetism, which avoids the corresponding arbitrary assumption made by Heisenberg on the basis of known (at that time) experimental observations. Some applications of the theory (linear chain, triangular chain, etc.) are, as well, considered.