Quasi-exactly solvable quartic: elementary integrals and asymptotics

We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we found an interesting identity which is used to describe the spectral locus. We also establish some asymptotic properties of the QES spectral locus.Comment: 20 pages, 1 figure. Added Introduction and several references, corrected misprint

Magnetic resonance study of the spin-reorientation transitions in the quasi-one-dimensional antiferromagnet BaCu2Si2O7

A quasi-one dimensional antiferromagnet with a strong reduction of the ordered spin component, BaCu2Si2O7, is studied by the magnetic resonance technique in a wide field and frequency range. Besides of conventional spin-flop transition at the magnetic field parallel to the easy axis of spin ordering, magnetic resonance spectra indicate additional spin-reorientation transitions in all three principal orientations of magnetic field. At these additional transitions the spins rotate in the plane perpendicular to the magnetic field keeping the mutual arrangement of ordered spin components. The observed magnetic resonance spectra and spin-reorientation phase transitions are quantitatively described by a model including the anisotropy of transverse susceptibility with respect to the order parameter orientation. The anisotropy of the transverse susceptibility and the strong reduction of the anisotropy energy due to the quantum spin fluctuations are proposed to be the reason of the spin reorientations which are observed.Comment: RevTeX, 9 pages, 7 figure

Characteristics of anomalously high multiplicity cosmic ray interactions

Six events with the number of secondaries ranging from 250 to several thousands were registered by an installation consisting of a thin graphite target, above and under which are placed photolayers followed by the usual lead X-ray film and emulsion chambers. Data concerning the number of secondaries and their angular distribution are given. The variance of the angular distribution is compared with data obtained at accelerator energies

Androgynous plot in the oeuvre of Z.N. Gippius and its reflection in the novel by V.V. Nabokov "The gift"

This article considers androgynous plot in fictional prose of Z.N. Gippius, exemplified with the short novel “The mirrors” (1896) and the novel “Roman-tzarevitch” (1913), within the frameworks of studying of creative life model of this prominent representative of Russian Silver Age. Androgynous plot as an creative life allusion by Z.N. Gippius created the base for so-called “History if Yasha Chernyshevskiy” , which from hearsay is retold by the main character of V.V. Nabokov’s novel “The Gift” F.K.Godunov-Cherdyntsev. This text vividly expresses author’s polemical attitude to Z.N. Gippius’ creativeyesBelgorod State Universit

The Effect of Random Surface Inhomogeneities on Microresonator Spectral Properties: Theory and Modeling at Millimeter Wave Range

The influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields the method of eigen-mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering which is the highly responsible for non-dissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object we use dielectric disc resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen-frequencies and the Q-factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.Comment: 17+ pages, 5 figure

Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

We prove Polya's conjecture of 1943: For a real entire function of order greater than 2, with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity with n. We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.Comment: 26 page

Transport and structural study of pressure-induced magnetic states in Nd0.55Sr0.45MnO3 and Nd0.5Sr0.5MnO3

Pressure effects on the electron transport and structure of Nd1-xSrxMnO3 (x = 0.45, 0.5) were investigated in the range from ambient to ~6 GPa. In Nd0.55Sr0.45MnO3, the low-temperature ferromagnetic metallic state is suppressed and a low temperature insulating state is induced by pressure. In Nd0.5Sr0.5MnO3, the CE-type antiferromagnetic charge-ordering state is suppressed by pressure. Under pressure, both samples have a similar electron transport behavior although their ambient ground states are much different. It is surmised that pressure induces an A-type antiferromagnetic state at low temperature in both compounds

Convergence Radii for Eigenvalues of Tri--diagonal Matrices

Consider a family of infinite tri--diagonal matrices of the form $L+ zB,$ where the matrix $L$ is diagonal with entries $L_{kk}= k^2,$ and the matrix $B$ is off--diagonal, with nonzero entries $B_{k,{k+1}}=B_{{k+1},k}= k^\alpha, 0 \leq \alpha < 2.$ The spectrum of $L+ zB$ is discrete. For small $|z|$ the $n$-th eigenvalue $E_n (z), E_n (0) = n^2,$ is a well--defined analytic function. Let $R_n$ be the convergence radius of its Taylor's series about $z= 0.$ It is proved that $$ R_n \leq C(\alpha) n^{2-\alpha} \quad \text{if} 0 \leq \alpha <11/6.$

Physical origin of the buckling in CuO2_2: Electron-phonon coupling and Raman spectra

It is shown theoretically that the buckling of the CuO$_{2}$ planes in certain cuprate systems can be explained in terms of an electric field across the planes which originates from different valences of atoms above and below the plane. This field results also in a strong coupling of the Raman-active out-of-phase vibration of the oxygen atoms ($B_{1g}$ mode) to the electronic charge transfer between the two oxygens in the CuO$_{2}$ plane. Consequently, the electric field can be deduced from the Fano-type line shape of the $B_{1g}$ phonon. Using the electric field estimated from the electron-phonon coupling the amplitude of the buckling is calculated and found to be in good agreement with the structural data. Direct experimental support for the idea proposed is obtained in studies of YBa$_{2}$Cu$_{3}$O$_{6+x}$ and Bi$_{2}$Sr$_{2}$(Ca$_{1-x}$Y$_{x}$)Cu$_{2}$O$_{8}$ with different oxygen and yttrium doping, respectively, including antiferromagnetic samples. In the latter compound, symmetry breaking by replacing Ca partially by Y leads to an enhancement of the electron-phonon coupling by an order of magnitude.Comment: 12 pages, 4 figures, and 1 tabl