A possibility of parallel and anti-parallel diffraction measurements on neutron diffractometer employing bent perfect crystal monochromator at the monochromatic focusing condition

In a conventional diffractometer having single monochromator, only one position, parallel position, is used for the diffraction experiment (i.e. detection) because the resolution property of the other one, anti-parallel position, is very poor. However, a bent perfect crystal (BPC) monochromator at monochromatic focusing condition can provide a quite flat and equal resolution property at both parallel and anti-parallel positions and thus one can have a chance to use both sides for the diffraction experiment. From the data of the FWHM and the Δd/d measured on three diffraction geometries (symmetric, asymmetric compression and asymmetric expansion), we can conclude that the simultaneous diffraction measurement in both parallel and anti-parallel positions can be achieved.     

Transverse susceptibility as the low-frequency limit of ferromagnetic resonance

A new theory of transverse susceptibility (TS) based on magnetization vector dynamics, as described by the Landau–Lifshitz equation of motion, is given. It is shown that the traditional TS experiment is, in fact, the zero-frequency limit of the ferromagnetic resonance (FMR). The importance of these results resides in the generality of the approach which allows one to find the TS for virtually any magnetic system if an expression for the magnetic free-energy density is known. Moreover, the effect of the frequency of excitatory AC field on the TS experiments and the effect of energy dissipation through the imaginary part of TS emerge coherently from the new TS model.     

Group-valued measures on coarse-grained quantum logics

In [3] it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later ([9]) this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.     

q\bar q pair creation in a flux tube with confinement

We calculate the effect of radial confinement on the Schwinger pair production rate by solving the Dirac equation in a flux-tube cylinder containing a constant chromoelectric field in the longitudinal direction. We show how the Dirac equation separates into radial and longitudinal equations for a mass term which has an arbitrary radial dependence and introduce radial confinement by having a finite mass inside the cylinder and an infinitely large mass outside. The resulting boundary conditions are equivalent to the MIT boundary condition. The equations are solved analytically for a constant quark mass inside the flux-tube, which acts like a waveguide. The discretization of the transverse wave vector which has a continuous spectrum in the non-confined case leads to a large suppression of the Schwinger pair-production rate for small radii. The minimal radius where pairs are created decreases with increasing field strength. The suppression turns out to be larger for heavier quarks than for light quarks.     

Radical Couplings as Key Steps for the Preparation of Derivatives of Nonactic Acid

Summary. Free radical couplings from furan, as cheap starting material, were studied in view of developing a rapid strategy en route to the synthesis of derivatives of nonactin. The chain containing the alcohol function was introduced in one or two steps in 86% yield. For the introduction of the second chain with the ester function two different coupling methods were tested. Starting from the advanced intermediates obtained nonactin derivatives can be prepared by catalytic hydrogenation of the furan ring.     

Engel Values in Residually Finite Groups

The following theorem is proved. Let n be a positive integer and q a power of a prime p. There exists a number m = m(n, q) depending only on n and q such that if G is any residually finite group satisfying the identity ([x _1,n y ₁] ⋯ [x _m,n y _m ])^q ≡ 1, then the verbal subgroup of G corresponding to the nth Engel word is locally finite.     

Unit squares intersecting all secants of a square

LetS be a square of side lengths>0. We construct, for any sufficiently larges, a set of less than 1.994s closed unit squares whose sides are parallel to those ofS such that any straight line intersectingS intersects at least one square ofS. It disproves L. Fejes Tóth's conjecture that, for integrals, there is no such configuration of less than 2s−1 unit squares. Supported by “Deutsche Forschungsgemeinschaft”, Grant We 1265/2-1.