Algebraic independence of the periods of abelian integrals

Abelian integrals of the first and the second kind are proved to have two algebraically independent periods. Some corollaries concerning the algebraic independence of the values of Euler's beta and gamma functions at rational points are derived.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 681–691, November, 1996.     

广义矩阵函数及其指标

本文推广了广义矩阵函数及对称张量的一些定理，给出了广义矩阵函数指标的若干关系式．     

Nonparametric tests for bounds on the derivative of a regression function

We consider two tests of the null hypothesis that the k-th derivative of a regression function is uniformly bounded by a specified constant. These tests can be used to study the shape of the regression function. For instance, we can test for convexity of the regression function by setting k=2 and the constant equal to zero. Our tests are based on k-th order divided difference of the observations. The asymptotic distribution and efficacies of these tests are computed and simulation results presented.Research supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0007969.Research supported by National Science Foundation Grant DMS-9306738.     

Jordan函数r次方Jrk（n）的均值误差项研究

设ｋ，ｒ分别是自然数和非零整数，Ｊｋ（ｎ）是Ｊｏｒｄａｎ函数．文［３］求出了和式∑ｎ≤ｘＪｒｋ（ｎ）的渐近公式．以Ｅ（ｘ；ｋ，ｒ）表示该公式中的误差项，本文研究了Ｅ（ｘ；ｋ，ｒ）的算术均值和积分均值     

Linear response and relaxation in quantum lattice systems

For spin-lattice systems, the Kubo formula, expressing the relaxation function in terms of the linear response function, is found to be exact in the thermodynamic limit. In addition, analyticity properties are obtained.     

Work function of metals: Relation between theory and experiment

Theoretical approaches to calculation of work function within jellium model and the problem of extension of this model to include the lattice corrections to the work function are briefly discussed. Lattice corrections to the work function obtained from the experiment are estimated and compared with those calculated theoretically.

It is found that the mean value of the experimental lattice correction <δψ_hkl>_hkl compared to the mean work function is negligible. It is stated that the mean work function can be treated as a material constant characterizing a given metal, such as, e.g., binding energy.An expression for the dependence of jellium work function on r_s, valid in a metallic range of r_s, is given. A comparison between then theoretical and experimental results is presented and the role of correlation energy is examined. It is shown that more accurate approximations of the correlation energy than that given by Wigner's formula lead to a better agreement with experiment. A simple model is presented for explanation of work function changes on single crystal planes. Some recent results concerning the thermal dependence of work function are given. The dependence of the work function on the degree of coverage is discussed both for alkali and non-alkali atoms adsorption. Theoretical models are briefly reviewed and comparison between theory and experiment is made. A simple model is presented for explanation of the work function variation on rough planes in metallic non-alkali atoms chemisorption.     

Partial fractions expansion: a review of computational methodology and efficiency

Nine methods for expressing a proper rational function in terms of partial fractions are presented for the case where the denominator polynomial has been reduced to linear factors. Only those methods which are amenable to computation algorithms are considered. To the extent possible, Newton's divided difference formula is used to provide a uniform derivational tool. Each method is illustrated numerically. The efficiency of the methods are compared on the basis of the number of multiplications and divisions required in the computation.     

A linear filtering problem in complete correlated actions

In the last paper, the geometry of the Sz.-Nagy-Foia model for contraction operators on Hilbert spaces was used to advantage in several problems of multivariate analysis. The lifting of intertwining operators, one of the basic results from the Sz.-Nagy-Foia theory, is now recognized as the most adequate operatorial form of the deep classical results of the extrapolation theory. The labeling of the exact intertwining dilations given by [1]Acta Sci. Math. (Szeged) 40 9–32] and the recursive methods used there open a broad perspective for using the Sz.-Nagy-Foia model in multivariate filtering theory. In this paper, using the notion of correlated action (see [5 and 6] Rev. Roumaine Math. Pures Appl. 23, No. 9 1393–1423]) as a time domain, a linear filtering problem is formulated and its solution in terms of the coefficients of the analytic function which factorizes the spectral distribution of the known data and the coefficients of an analytic function which describes the cross correlations is given. In some special cases it is shown that the filter coefficients can be determined using recursive methods from the intertwining dilation theory, of the autocorrelation function of the known data and an intertwining operator, interpreted as the initial estimator given by the prior statistics.     

A class of loss functions of catenary form

The catenary form of loss function is considered in the framework of Bayesian decision theory. The mathematical tractability of this form seems to be unrecognized; it contains quadratic loss as a limiting case. For various probability distributions expressions are given for posterior analysis, and limiting properties are investigated.