Low-temperature specific heat of real crystals: Possibility of leading contribution of optical and short-wavelength acoustical vibrations

We point out that the repeatedly reported glass-like properties of crystalline materials are not necessarily associated with localized (or quasilocalized) excitations. In real crystals, optical and short-wavelength acoustical vibrations remain damped due to defects down to zero temperature. If such a damping is frequency-independent, e.g. due to planar defects or charged defects, these optical and short-wavelength acoustical vibrations yield a linear-in-$T$ contribution to the low-temperature specific heat of the crystal lattices. At low enough temperatures such a contribution will prevail over that of the long-wavelength acoustical vibrations (Debye contribution). The crossover between the linear and the Debye regime takes place at $T^* \propto \sqrt N$, where $N$ is the concentration of the defects responsible for the damping. Estimates show that this crossover could be observable.Comment: 5 pages. v4: Error in Appendix corrected, which does not change the main results of the pape

MENINGOCOCCUS GROWTH STIMULATORS FOR MENINGITIS DIAGNOSTICS BASED ON 2-HYDROXYLALKYLAMINE SALTS

The methods for the synthesis of 4-(4 '-nitrophenyl)-L-(+)-treo- and 2,8-dimethyl-4-(4 '-nitro-phenyl)-L-(+)-treo- 1-aza-3,7-dioxabicyclo-[3,3,0]octanes as well as iodomethylates of L-(+)-treo-, D-(-)-treo- and. D-(-)-, L-(+)-treo -4-(4 '-nitrophenyl)-1-aza-3,7-dioxabicyclo-[3,3,0]-octanes have been developed. It has been shown for the first time that optically isomeric iodo-methylates of 4-(4 '-nitrophenyl)-1-aza-3,7-dioxabicyclo[3,3,0]octanes possess high growth-stimulating activity with respect to meningococcus strains isolated from cerebrospinal fluid of patients thus indicating the possibility of these compounds application for qualitative diagnostics of meningitis. A method for the preparation of elective «Dry medium nutritium. ad. meningococcos siccum» for isolation and. cultivation of meningococci has been elaborated. Methods for the synthesis of novel potential stimulators of microorganisms growth have been worked out on the basis of biologically active aryloxy(arylsulfanyl)acetic acids and. waste of Levomecytin (Chloramphenicol) production, «L-treoamine»

The graded Jacobi algebras and (co)homology

Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Ge

Heating of gas inside radio sources to mildly relativistic temperatures via induced Compton scattering

Measured values of the brightness temperature of low-frequency synchrotron radiation emitted by powerful extragalactic sources reach 10^11--10^12 K. If some amount of nonrelativistic ionized gas is present within such sources, it should be heated as a result of induced Compton scattering of the radiation. If this heating is counteracted by cooling due to inverse Compton scattering of the same radio radiation, then the plasma can be heated up to mildly relativistic temperatures kT~10--100 keV. The stationary electron velocity distribution can be either relativistic Maxwellian or quasi-Maxwellian (with the high-velocity tail suppressed), depending on the efficiency of Coulomb collisions and other relaxation processes. We derive several easy-to-use approximate expressions for the induced Compton heating rate of mildly relativistic electrons in an isotropic radiation field, as well as for the stationary distribution function and temperature of electrons. We also give analytic expressions for the kernel of the integral kinetic equation (one as a function of the scattering angle and another for the case of an isotropic radiation field), which describes the redistribution of photons in frequency caused by induced Compton scattering in thermal plasma. These expressions can be used in the parameter range hnu<< kT<~ 0.1mc^2 (the formulae earlier published in Sazonov, Sunyaev, 2000 are less accurate).Comment: 22 pages, 7 figures, submitted to Astronomy Letter

On the error term in Weyl's law for the Heisenberg manifolds (II)

In this paper we study the mean square of the error term in the Weyl's law of an irrational $(2l+1)$-dimensional Heisenberg manifold . An asymptotic formula is established

Hamiltonian structure of real Monge-Amp\`ere equations

The real homogeneous Monge-Amp\`{e}re equation in one space and one time dimensions admits infinitely many Hamiltonian operators and is completely integrable by Magri's theorem. This remarkable property holds in arbitrary number of dimensions as well, so that among all integrable nonlinear evolution equations the real homogeneous Monge-Amp\`{e}re equation is distinguished as one that retains its character as an integrable system in multi-dimensions. This property can be traced back to the appearance of arbitrary functions in the Lagrangian formulation of the real homogeneous Monge-Amp\`ere equation which is degenerate and requires use of Dirac's theory of constraints for its Hamiltonian formulation. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. The simplest Hamiltonian operator results in the Kac-Moody algebra of vector fields and functions on the unit circle.Comment: published in J. Phys. A 29 (1996) 325

Semi-contact AFM for surface characterisation in case of holographic PDADMAC films and functionalised paper

The research was carried out using equipment of the Ural Center for Shared Use "Modern Nanotechnologies" Ural Federal University. A. Vinogradov acknowledges the scholarship of the President of the Russian Federation (SP-1158.2019.1): S. Vasilev acknowledges the mobility programs of the Institute of Natural Sciences and Mathematics for the Young scientists in the 2018 year