Matrix Christoffel Functions

We introduce and study matrix Christoffel functions for a matrix weight W. We find an explicit expression of the matrix Christoffel functions in terms of any sequence of orthonormal matrix polynomials with respect to W. An extremal property related to the matrix moment problem defined by W is established for the matrix Christoffel functions. We finally find the relative asymptotic behavior of the matrix Christoffel functions associated to matrix weights in the matrix Nevai class.     

Persistent currents in a lattice correlated electron ring with a magnetic impurity

The behavior of charge and spin persistent currents in an integrable lattice ring of strongly correlated electrons with a magnetic impurity is exactly studied. Our results manifest that the oscillations of charge and spin persistent currents are similar to the ones, earlier obtained for integrable continuum models with a magnetic impurity. The difference is due to two (instead of one) Fermi velocities of low-lying excitations. The form of oscillations in the ground state is “saw-tooth”-like, generic for any multi-particle coherent one-dimensional models. The integrable magnetic impurity introduces net charge and spin chiralities in the generic integrable lattice system, which determine the initial phase shifts of charge and spin persistent currents. We show that the magnitude of the charge persistent current in the generic Kondo situation does not depend on the parameters of the magnetic impurity, unlike the (magneto)resistivity of transport currents. Received 30 January 2003 / Received in final form 12 March 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: zvyagin@fy.chalmers.se     

Detecting Mass Points of Representing Measures

We discuss a possibility of deciding whether measures representing a moment sequence or realizing orthogonality of polynomials have atoms. This is done on the real line and in several variables.     

Primitive Inner Illuminating Systems for Convex Bodies

A set X of boundary points of a (possibly unbounded) convex body KE ^d illuminating K from within is called primitive if no proper subset of X still illuminates K from within. We prove that for such a primitive set X of an unbounded, convex set KE ^d (distinct from a cone) one has X=2 if d=2, X6 if d=3, and that there is no upper bound for X if d4.     

Extended Hydrodynamics from Enskog’s Equation for a Two-Dimensional System General Formalism

Balance equations are derived from Enskog’s kinetic equation for a two-dimensional system of hard disks using Grad’s moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional fluids. The set of independent hydrodynamic fields in the present formulations are: density, velocity, temperature and also—following Grad’s original idea—the symmetric and traceless pressure tensor p _ij and the heat flux vector q ^k . An approximation scheme similar in spirit to one made by Grad in his original work is made. Once the hydrodynamics is derived it is used to discuss the nature of a simple one-dimensional heat conduction problem. It is shown that, not too far from equilibrium, the nonequilibrium pressure in this case only depends on the density, temperature and heat flux vector. PACS: 51.10.+y, 05.20.Jj, 44.10.+i, 05.70.Ln     

Line intensities in the 1.5-μm spectral region of acetylene

Line intensities are measured for 546 transitions belonging to 13 bands of the main isotopologue ¹²C₂H₂ of the acetylene molecule, in the 1.5-μm spectral domain. A multispectrum fitting procedure is used to retrieve line parameters from Fourier transform spectra. Prior to this work, line intensities were known for only 4 bands in this spectral region, from the work of El Hachtouki and Vander Auwera [Absolute line intensities in acetylene: the 1.5 μm region. J Mol Spectrosc 2002;216:355-62]. An excellent agreement is found with the results of these authors, showing that the accuracy of both results is likely better than 1% for the strong bands. However, the spectrum becomes very crowded when one wants to study weaker bands, so that the average accuracy of the intensities reported in the present work is 5%. From these data, vibrational transition dipole moments squared and Herman-Wallis coefficients have been determined for all the bands.     

S[a,b]类中边界Nevanlinna-Pick插值(Ⅱ)

继续作者最近的研究,用所谓的Hankel向量方法建立S[a,b]函数类中带边界插值数据的Nevanlinna-Pick插值问题与[a,b]上的某种带约束条件的Hausdorff矩量问题之间解集之间明确的一一对应关系.通过N[a,b]函数类与S[a,b]函数类之间的联系,从而由BNP(N[a,b])问题的可解性准则和解的参数化描述获得BNP(S[a,b)问题的可解性准则和解的参数化表示.     

Uncompensated magnetization in the layered molecular antiferromagnet {N(n-C5H11)4[MnFe(ox)3]}∞

Studies on the magnetic properties of the molecular antiferromagnetic material {N(n-C₅H₁₁)₄[Mn^IIFe^III(ox)₃]}_∞, carried out by various physical techniques (AC/DC magnetic susceptibility, magnetization, heat capacity measurements and Mössbauer spectroscopy) at low temperatures, have been presented. Different experimental observations complement each other and provide a clue for the observation of an uncompensated magnetization below the Néel temperature and short-range correlations persisting high above T_N. It is understood that the honeycomb layered structure of the compound contains non-equivalent magnetic sub-lattices, (Mn^II–ox–Fe^III_A–...) and (Mn^II–ox–Fe^III_B–...), where different responses of the Fe^III_A and Fe^III_B spin sites towards an external magnetic field might be responsible for the observation of the uncompensated magnetization in this compound at T < T_N. The present magnetic system is an S = 5/2 2-D Heisenberg antiferromagnet system with the intralayer exchange parameter J/k_B = −3.29 K. A very weak interlayer exchange interaction was anticipated from the spin wave modeling of the magnetic heat capacity for T < 0.5T_N. The positive sign of the coupling between the layers has been concluded from the Mössbauer spectrum in the applied magnetic field. Frustration in the magnetic interactions gives rise to the uncompensated magnetic moment in this compound at low temperatures.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.     

Stokes drag on axially symmetric bodies: a new approach

In this paper a new approach to evaluate the drag force in a simple way on a restricted axially symmetric body placed in a uniform stream (i) parallel to its axis, (ii) transverse to its axis, is advanced when the flow is governed by the Stokes equations. The method exploits the well-known integral for evaluating the drag on a sphere. The method not only provides the value of the drag on prolate and oblate spheroids and a deformed sphere in axial flow which already exists in literature but also new results for a cycloidal body, an egg shaped body and a deformed sphere in transverse flow. The salient results are exhibited graphically. The limitations imposed on the analysis because of the lack of fore and aft symmetry in the case of an eggshaped body is also indicated. It is also seen that the analysis can be extended to calculate the couple on a body rotating about its axis of symmetry.