On the Singular Direction of Entire Functions

In this paper, after defining a normal criterion with a parameter and a singular direction of an entire function corresponding to a normal criterion, we shall prove the following theorem.Theorem 1 Suppose that f(z) is a transcendental entire function. Then there exists a direction Δ: argz = θ0 (0≤0<2π) which is a singular direction of f(z) corresponding to every normal criterion with a parameter.From theorem 1 we deduce at once existence of some singular directions.     

First passage models for denumerable semi-Markov decision processes with nonnegative discounted costs

This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs.The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set.We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy.Then,we prove that the value function satisfies the optimality equation and there exists an optimal(or e-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach.Further we give some properties of optimal policies.In addition,a value iteration algorithm for computing the value function and optimal policies is developed and an example is given.Finally,it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.     

Standard tri-point transition function

It is usually difficult to express a family of tri-point transition function (TTF) by a transition matrix as Markov processes with one parameter. In this paper, we define three kinds of connection matrixes on the states of standard tri-point transition function (STTF) and study their essential character, give a constructive method on the constant-value standard tri-point transition function and a general expression of the state-symmetric standard tri-point transition function by a sequence of the transition matrixes of special and simple Markov processes with one parameter.     

Shrinkage estimation analysis of correlated binary data with a diverging number of parameters

For analyzing correlated binary data with high-dimensional covariates,we,in this paper,propose a two-stage shrinkage approach.First,we construct a weighted least-squares(WLS) type function using a special weighting scheme on the non-conservative vector field of the generalized estimating equations(GEE) model.Second,we define a penalized WLS in the spirit of the adaptive LASSO for simultaneous variable selection and parameter estimation.The proposed procedure enjoys the oracle properties in high-dimensional framework where the number of parameters grows to infinity with the number of clusters.Moreover,we prove the consistency of the sandwich formula of the covariance matrix even when the working correlation matrix is misspecified.For the selection of tuning parameter,we develop a consistent penalized quadratic form(PQF) function criterion.The performance of the proposed method is assessed through a comparison with the existing methods and through an application to a crossover trial in a pain relief study.     

Clustering for Bivariate Functional Data

In this paper,we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject.The k-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data,and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered.In addition,we also consider two other clustering ...     

Zero-sum stochastic games with average payoffs: New optimality conditions

In this paper we study zero-sum stochastic games. The optimality criterion is the long-run expected average criterion, and the payoff function may have neither upper nor lower bounds. We give a new set of conditions for the existence of a value and a pair of optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature, and some new sufficient conditions for the existence of a pair of optimal stationary strategies are imposed on the primitive data of the model. Our results are illustrated with a queueing system, for which our conditions are satisfied but some of the conditions in some previous literatures fail to hold.     

A general vectorial Ekeland’s variational principle with a P-distance

In this paper, by using p-distances on uniform spaces, we establish a general vectorial Ekeland variational principle （in short EVP）, where the objective function is defined on a uniform space and taking values in a pre-ordered real linear space and the perturbation involves a p-distance and a monotone function of the objective function. Since p-distances are very extensive, such a form of the perturbation in deed contains many different forms of perturbations appeared in the previous versions of EVP. Besides, we only require the objective function has a very weak property, as a substitute for lower semi-continuity, and only require the domain space （which is a uniform space） has a very weak type of completeness, i.e., completeness with respect to a certain p-distance. Such very weak type of completeness even includes local completeness when the uniform space is a locally convex topological vector space. From the general vectorial EVP, we deduce a general vectorial Caristi＇s fixed point theorem and a general vectorial Takahashi＇s nonconvex minimization theorem. Moreover, we show that the above three theorems are equivalent to each other. We see that the above general vectorial EVP includes many particular versions of EVP, which extend and complement the related known results.     

GENERALIZED BOCHNER''''S THEOREM FOR RADIAL FUNCTION

A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is positive definite. This requires however a n-dhnensiotial Fourier transformation and it is not very easy to calculate. Furthermore in a lot of cases we will use for spaces of various dimensions too, then for every fixed n we need do the Fourier transformation once to check if the function is positive definite in the n-di-mensional space. The completely monotone function:, which is discussed in [4] is positive definite for arbitrary space dimensions. With this technique tve can very easily characterize the positive definite, of a radial function through its generator. Unfortunately there is only a very small subset of radial function which is completely monotone. Thus this criterion excluded a lot of interesting functions such as compactly supported radial function, whcih are very useful in applic     

The generalized Bourgain-Sarnak-Ziegler criterion and its application to additively twisted sums on GLm

The Bourgain-Sarnak-Ziegler(BSZ) criterion was initially established for an arbitrary multiplicative function a(n) satisfying |a(n)| ≤1. Recently, Cafferata et al.(2020) showed that the condition |a(n)| ≤1 can be replaced by a(p) ? 1 to some extent. In this paper, we formulate and prove a further extension of the BSZ criterion, in which the restriction a(p) ? 1 is removed. As applications, we use it together with the analytic theory of automorphic L-functions to prove that there exist some cancellations in the sequence{λπ(n)e(n~kα)}n ≥1 on GL_m and the M?bius function is disjoint from this sequence.     

Some Kinds of Bargaining Equilibria of Multi-objective Games

To solve the choice of multi-objective game's equilibria,we construct general bargaining games called self-bargaining games,and define their individual welfare functions with three appropriate axioms.According to the individual welfare functions,we transform the multi–objective game into a single-objective game and define its bargaining equilibrium,which is a Nash equilibrium of the single-objective game.And then,based on certain continuity and concavity of the multi-objective game's payoff function,we proof the bargaining equilibrium still exists and is also a weakly Pareto-Nash equilibrium.Moreover,we analyze several special bargaining equilibria,and compare them in a few examples.     

A Statistical Comparison of Three Goodness-of-Fit Criteria Used in Modelling Distances

Distance predicting functions may be used in a variety of applications for estimating travel distances between points. To evaluate the accuracy of a distance pre-dicting function and to determine its parameters, a goodness-of-fit criteria is employed. AD (Absolute Deviations), SD (Squared Deviations) and NAD (Normalized Absolute Deviations) are the three criteria that are mostly employed in practice. In the literature some assumptions have been made about the properties of each criterion. In this paper, we present statistical analyses performed to compare the three criteria from different perspectives. For this purpose, we employ the l_kpθ-norm as the distance predicting function, and statistically compare the three criteria by using normalized absolute pre-diction error distributions in seventeen geographical regions. We find that there exist no significant differences between the criteria. However, since the criterion SD has desirable properties in terms of distance modelling procedures, we suggest its use in practice.     

Convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains

Summary. Three iterative domain decomposition methods are considered: simultaneous updates on all subdomains (Additive Schwarz Method), flow directed sweeps and double sweeps. By using some techniques of formal language theory we obtain a unique criterion of convergence for the three methods. The convergence rate is a function of the criterion and depends on the algorithm. Received October 24, 1994 / Revised version received November 27, 1995     

关于Orlicz空间的H性质的注记

该文给出了Orlicz函数空间具有H性质的充分必要条件．     

二维无界连通域上反常积分敛散性的判别准则

讨论了二维无界连通域上反常积分的敛散性.从柯西积分判别法出发,考察了三类特定区域上二元函数的反常积分,利用列维定理,得到了一些新的判别准则.     

正规族与复合亚纯函数

本文研究了亚纯函数族涉及复合有理函数与分担亚纯函数的正规性. 证明了一个正规定则:设 α(z) 和 F 分别是区域 D 上的亚纯函数与亚纯函数族, R(z) 是一个次数不低于 3 的有理函数.如果对族 F 中函数 f(z) 和 g(z), R○f(z) 和 R○g(z) 分担 α(z) IM,并且下述 条件之一成立:
(1) 对任何 z₀ ∈ D, R(z)-α(z₀) 有至少三个不同的零点或极点;
(2) 存在 z₀ ∈ D 使得 R(z)-α(z₀):=(z-β₀)^pH(z) 至多有两个零点(或极点) β₀,同时 k ≠ l|p|,其中 l 和 k 分别是 f(z)-β₀ 和 α(z)-α(z₀) 在 z₀ 处的零点重数, H(z) 是满足 H(β₀) ≠ 0, ∞ 的有理函数, α(z) 非常数并满足 α(z₀) ∈ C ∪{∞}.
那么 F 在 D 内正规.特别地,这个结果是著名的 Montel 正规定则的一种推广.     

Completely normal elements in some finite abelian extensions

We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.     

新产品设计前端的筛选与评价系统研究

本着重于新产品设计前端的筛选与评价系统研究。设计了若干准则，有社会环境准则、经济成本准则、技术准则、时间准则、价值准则等，对新产品构思进行筛选。运用模糊理论，确定隶属度函数，得到评价矩阵，最终得到综合评价；运用加权评分法，确定评判的各影响因素及其各自所占的权重，给每种构思进行评分，根据最后总得分的多少来评定构思的优劣。最后，阐述了评价系统在设计过程中的重要作用，评价系统贯穿于整个设计过程中。     

Bias-corrected AIC for selecting variables in multinomial logistic regression models

In this paper, we consider the bias correction of Akaike’s information criterion (AIC) for selecting variables in multinomial logistic regression models. For simplifying a formula of the bias-corrected AIC, we calculate the bias of the AIC to a risk function through the expectations of partial derivatives of the negative log-likelihood function. As a result, we can express the bias correction term of the bias-corrected AIC with only three matrices consisting of the second, third, and fourth derivatives of the negative log-likelihood function. By conducting numerical studies, we verify that the proposed bias-corrected AIC performs better than the crude AIC.     

Strongly absolute stability of Lur'e type differential-algebraic systems

In this paper, we consider Lur'e type differential-algebraic systems (LDS) and introduce the concept of strongly absolute stability. Such a notion is a generalization of absolute stability for Lur'e type standard state-space systems (LSS). By a Lur'e type Lyapunov function, we derive an LMI based stability criterion for LDS to be strongly absolutely stable. Using extended strictly positive realness (ESPR), we present the frequency-domain interpretation of the obtained criterion, by which we simplify the criterion and show that the criterion is a generalization of the well-known Popov criterion. Finally, we illustrate the effectiveness of the main results by a numerical example.     

The distributional dimension of fractals

In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.