Study of Features of the Diffraction of X Rays in a Quartz Crystal Modulated by Longitudinal and Transverse Ultrasonic Vibrations

JETP Letters - Features of the simultaneous action of longitudinal and transverse ultrasonic vibrations in the quartz crystal on the parameters of reflected X-rays are studied. It is shown that...     

Aminolysis of 6-[1-(2,6-difluorophenyl)cyclopropyl]-5-methyl-2-(nitroamino)pyrimidin-4(3<Emphasis Type="Italic">H</Emphasis>)-one

The aminolysis of 6-[1-(2,6-difluorophenyl)cyclopropyl]-5-methyl-2-(nitroamino)pyrimidin-4(3H)-one with various amines in butan-1-ol and under solvent-free conditions is successful when the amino group in the reagent is sterically unshielded and the reaction medium is characterized by a high dielectric permittivity. Reactions of the title compound with sterically shielded amines are accompanied by alcoholysis where the amine acts as a base catalyst.     

Influence of acoustic oscillations on coherent bremsstrahlung of electrons

The results of experiments on investigation of the influence of acoustic oscillations on the coherent bremsstrahlung of electrons with the energy 20 MeV are presented. The experiments were carried out on the extracted beam of the YerPhI linear accelerator LEU-50.     

A generating function for the cubic interactions of higher spin fields

We present an off-shell generating function for all cubic interactions of higher spin gauge fields constructed in Manvelyan et al. (2010) [1]. It is a generalization of the on-shell generating function proposed by Sagnotti and Taronna [2], is written in a very compact way, and turns out to have a remarkable structure.     

Universal volume of groups and anomaly of Vogel’s symmetry

We show that integral representation of universal volume function of compact simple Lie groups gives rise to six analytic functions on \({ CP }^2\), which transform as two triplets under group of permutations of Vogel’s projective parameters. This substitutes expected invariance under permutations of universal parameters by more complicated covariance. We provide an analytic continuation of these functions and calculate their change (anomaly) under permutations of parameters (Vogel’s symmetry). This last relation is universal generalization, for an arbitrary simple Lie group and, moreover, to an arbitrary point in Vogel’s plane, of the Kinkelin’s reflection relation on Barnes’ \(G(1+N)\) function. Kinkelin’s relation gives asymmetry of the \(G(1+N)\) function (which is essentially reciprocal of the volume function for \({ SU }(N)\) groups) under \(N\leftrightarrow -N\) transformation (which is equivalent of the permutation of Vogel’s parameters for \({ SU }(N)\) groups), and coincides with above-mentioned anomaly of permutations at the \({ SU }(N)\) line on Vogel’s plane. Our results also give an anomaly of Vogel’s symmetry of the universal partition function of Chern–Simons theory on three-dimensional sphere. This effect is analogous to modular covariance, instead of invariance, of partition functions of appropriate gauge theories under modular transformation of couplings.