A Class of Baker–Akhiezer Arrangements

We study a class of arrangements of lines with multiplicities on the plane which admit the Chalykh–Veselov Baker–Akhiezer function. These arrangements are obtained by adding multiplicity one lines in an invariant way to any dihedral arrangement with invariant multiplicities. We describe all the Baker–Akhiezer arrangements when at most one line has multiplicity higher than 1. We study associated algebras of quasi-invariants which are isomorphic to the commutative algebras of quantum integrals for the generalized Calogero–Moser operators. We compute the Hilbert series of these algebras and we conclude that the algebras are Gorenstein. We also show that there are no other arrangements with Gorenstein algebras of quasi-invariants when at most one line has multiplicity bigger than 1.     

The Generating Function for the Components of the Euler–Poinsot Tensor

Doklady Physics - Generating functions that enable us to calculate the components of the Euler–Poinsot tensor using differentiation are introduced. The role of these functions is similar to...     

A Schematic Calculation of the ββ-Decay Matrix Element Within the Green Function Approach

The time integral representation of the many-body Green function describing the two-neutrino double-beta-decay (2-decay) matrix element is used in schematic calculations within the proton-neutron Lipkin model. The two-body Hamiltonian considered includes a quadratic polynomial in bosons to describe the motion of the selected degrees of freedom. The beta-transition operators also include higher-order terms in the boson expansion. They have been shown to be of crucial importance in the determination of the 2-decay matrix element M _F. We have found that in the standard QRPA approach, which exploits the form of M _F with denominator, there is a dominant unphysical contribution to M _F arising from the non-orthogonality of the initial and final quasiparticle ground states. The physical part of M _F is negligible for small values of the particle-particle interaction strength, i.e., it exhibits a different behavior as that known from the QRPA approaches.     

The conservation of energy–momentum and the mass for the graviton

In this work we give special attention to the bimetric theory of gravitation with massive gravitons proposed by Visser in 1998. In his theory, a prior background metric is necessary to take in account the massive term. Although in the great part of the astrophysical studies the Minkowski metric is the best choice to the background metric, it is not possible to consider this metric in cosmology. In order to keep the Minkowski metric as background in this case, we suggest an interpretation of the energy–momentum conservation in Visser’s theory, which is in accordance with the equivalence principle and recovers naturally the special relativity in the absence of gravitational sources. Although we do not present a general proof of our hypothesis we show its validity in the simple case of a plane and dust-dominated universe, in which the “massive term” appears like an extra contribution for the energy density.     

The super-heat-kernel expansion and the renormalization of the pion–nucleon interaction

A recently proposed super-heat-kernel technique is applied to heavy baryon chiral perturbation theory. A previous result for the one-loop divergences of the pion–nucleon system to is confirmed, giving at the same time an impressive demonstration of the efficiency of the new method. The cumbersome and tedious calculations of the conventional approach are now reduced to a few simple algebraic manipulations. The present computational scheme is not restricted to chiral perturbation theory, but can easily be applied or extended to any (in general non-renormalizable) theory with boson–fermion interactions. Received: 21 July 1998 / Published online: 5 October 1998     

The monodromy of the Lagrange top and the Picard–Lefschetz formula

The purpose of this paper is to show that the monodromy of action variables of the Lagrange top and its generalizations can be deduced from the monodromy of cycles on a suitable hyperelliptic curve (computed by the Picard–Lefschetz formula).     

Direct Measurement of the Correlation Function of Optical–Terahertz Biphotons

JETP Letters - The second-order correlation function which characterizes the quantum correlation between the optical and terahertz photons generated under spontaneous parametric down-conversion has...     

The Toda Equations and the Gromov–Witten Theory of the Riemann Sphere

Consequences of the Toda equations arising from the conjectural matrix model for the Riemann sphere are investigated. The Toda equations determine the Gromov–Witten descendent potential (including all genera) of the Riemann sphere from the degree 0 part. Degree 0 series computations via Hodge integrals then lead to higher-degree predictions by the Toda equations. First, closed series forms for all 1-point invariants of all genera and degrees are given. Second, degree 1 invariants are investigated with new applications to Hodge integrals. Third, a differential equation for the generating function of the classical simple Hurwitz numbers (in all genera and degrees) is found – the first such equation. All these results depend upon the conjectural Toda equations. Finally, proofs of the Toda equations in genus 0 and 1 are given.     

The Carter constant and Petrov classification of the Vaidya–Einstein–Kerr spacetime

The existence of the Carter constant in the Vaidya–Einstein–Kerr (VEK) spacetime and its relation to the Petrov type is investigated. This spacetime is an example of a black hole in an asymptotically non-flat background. We construct the Carter constant and obtain the Killing tensor in the VEK spacetime. The Newman–Penrose formalism is employed to obtain the spin coefficients. We present a complete (Petrov) classification of the VEK spacetime and the special case of the non-rotating Vaidya–Einstein–Schwarzschild spacetime. We demonstrate explicitly that both spacetimes are of type-D.     

Microstructural Features and Electrophysical Characteristics of Ceramic–Crystal Matrix Composites

The electrophysical properties of ceramic–crystal matrix composites are studied. Piezoelectrically active PZT/LiNbO₃ ceramic matrix composites with LiNbO₃ concentrations of 0–20 vol % are fabricated. Complex elastic, dielectric, and piezoelectric parameters are measured, and the microstructural characteristics of the obtained samples are studied experimentally. It is found that the extreme electrophysical properties of ceramic–crystal matrix composites depend on the properties and structure of the piezoceramic matrix and crystalline filler, and on the matrix microporosity produced during sintering. The electrophysical parameters of ceramic–crystal matrix composites as functions of crystalline filler content are established through the competing microporosity growth effects of the ceramic matrix and the increase in crystalline filler content.     

Matrix of the energy operator for the nsn′g and nsn′h configurations: The fine-structure parameters of the helium atom

The matrix of the energy operator is constructed for the nsn′g and nsn′h configurations. The electrostatic, spin-own-orbit, spin-other-orbit, spin-spin, and orbit-orbit interactions are taken into account. The fine-structure parameters, the coupling coefficients, and the gyromagnetic ratios are calculated for the 1sng (n=5–9) and 1s7h configurations of a helium atom. Discrepancies between the calculated and experimental energy values are virtually zero.     

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve is calculated. The first mathematical analysis to explain the relation between the transition voltage V_t and the coercive voltage V_c is obtained. The origin of the interrelation between the transition voltage of the I–V curve and the coercive field is that the height of the boundary barrier is inversely proportional to the effective dielectric constant of the near-boundary region, which is dependent on a derivative of polarization on the electric field, ∂P/∂E. The term ξ(eV_t) plus the term (en_b²δ/dN_dP_s)(eV_c) equals a constant. V_t is the function of E_g, P_s, V_c, and E. There is a linear relation between V_c and V_t. This relationship will induce the matchable relations between the I–V curve and the E–P loop. As long as the V_c of the V–P loop exists, the correspondent V_t of I–V curve will certainly exist. It will be the foundation of a new ferroelectric memory, which operates by the I–V characteristics. These relations are the conditions that can enable nonvolatile memory and nondestructive readout.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

The Weiss model and the Landau–Khalatnikov model for the switching of ferroelectrics

It is shown that the molecular field theory by P. Weiss formally leads to the switching kinetics of ferroelectrics, which is described by the well-known Landau–Khalatnikov equation. The switching has a critical character, taking place only at E_a>E_c (E_a: external field, E_c: coercive field). The results are checked by computer simulations.