A note on Riemann problems for single‐periodic polyanalytic functions

In this article, a new canonical function has been established to deal with Riemann boundary‐value problem of periodic analytic functions discussed in 16 . In comparison with the corresponding result in 16 , the expression of solution obtained here is much simpler. Then, we demonstrate the equivalence of solutions for the homogeneous Riemann problem. What's more, we obtain the precise rank of matrix of coefficients for the system of linear algebraic equations (4.35) in 16 . Those results can simplify the discussion of Riemann problem of single‐periodic polyanalytic functions in 16 .     

Spectrality of certain self‐affine measures on the generalized spatial Sierpinski gasket

The self‐affine measure corresponding to a upper or lower triangle expanding matrix M and the digit set in the space is supported on the generalized spatial Sierpinski gasket, where are the standard basis of unit column vectors in . We consider in this paper the existence of orthogonal exponentials on the Hilbert space , i.e., the spectrality of . Such a property is directly connected with the entries of M and is not completely determined. For this generalized spatial Sierpinski gasket, we present a method to deal with the spectrality or non‐spectrality of . As an application, the spectral property of a class of such self‐affine measures are clarified. The results here generalize the corresponding results in a simple manner.     

Temporal evolution of optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the short-exposure optical transfer function.     

On estimating of the number of constituents of a finite mixture of continuous distributions

Summary Suppose thatH is a mixture of distributions for a given familyF A necessary and sufficient condition is obtained under whichH is, in fact, a finite mixture. An estimator of the number of distributions constituting the mixture is proposed assuming that the mixture is finite and its asymptotic properties are investigated.     

Some generating functions of Jacobi polynomials

In this paper, Weisner’s group-theoretic method of obtaining generating functions is utilized in the study of Jacobi polynomialsP> _n ^(a,ß)(x) by giving suitable interpretations to the index (n) and the parameter (β) to find out the elements for constructing a six-dimensional Lie algebra.     

Some estimation theory on the sphere

Summary We consider distributions with densities of the formf(μ′x) andf(‖x _v ‖) where μ andx are unit vectors inR ^q and ‖x _v ‖ is the norm of the part ofx in somes dimensional subspaceV ofR ^q . For several loss functions, optimal Bayesian and Pitman estimators of μ andV are given. When uniform priors are used, these estimators are identical. Then the infinitesimal robustness characteristics of several special cases of these estimators are calculated.     

A successive quadratic programming algorithm with global and superlinear convergence properties

This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.This work was supported in part by a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan.     

The estimation of stochastic cost-quantity frontiers for discretionary cost and budgeted-expenditure systems

Two alternative approximating functions for representing the unknown composite residual density function of a cost-quantity frontier are examined. The frontier is one in which cost is regarded as preselected. This is appropriate for public sector economics and discretionary cost situations. One function requires the estimation of a single distribution parameter, whereas the other makes no a priori assumption on the shape of the density function.     

On Weighted Poincaré Inequalities

We are concerned with the problem of finding sharp summability conditions on the weights which render certain weighted inequalities of Poincaré - type true. The conditions we find consist of proper integral balances between the growths of the rearrangements of the weights.     

小康判别函数的建立与分析

近几年，国内在研究小康水平的定量指标分析中，应用较多的有综合评分法、层次分析法和模糊识别法。这几种方法比单项指标更全面、灵活，但在权数的确定上都难以克服人为因素的影响。当指标之间存在两个或两个以上的高度相关时，对问题的研究总存在一定的局限性。为了科学地研究小康问题，本文基于判别分析，建立城市小康的判别系数，来综合评价出我国城市小康水平的定量标准。