广义Lagrange中值定理的逆定理

本文证明了若f(x)是[a,6]上的凸函数,则广义Lagrange中值定理逆定理成立。     

关于由广义的Fibonacci数构成的倒数和及其交错和的若干性质

本文给出了由广义的Fibonacci数构成的倒数和及其交错和之间的某种联系.     

Dirichlet分布的中立性

本文给出了随机成分向量的中立性的两个性质,并证明了Dirichlet分布具有完全中立性.     

非对称狄氏型的扰动及相应的无穷小生成元

主要研究了L^2（E;m）上的非对称狄氏型（ε,D（ε））经符号光滑测度μ扰动后得到扰动型（ε^μ,D（ε^μ））,给出了U^α＋μ（L^2（E;m））包含在D（ε^μ）中的充分条件,得到了D（L^μ）在L^2（E;m）中稠的充分条件,这里U^α＋μ、L^μ分别为扰动后得到的预解式和生成元,D（L^μ）为Lμ的定义域.同时,也得到了当μ∈S-SK0时（ε^μ,D（ε^μ））与L^μ之间的关系,并研究了当μ是光滑测度时相对核U^αptA^μf和U^^^αptA^μf与扰动型（ε^μ,D（ε^μ））的关系.     

On generalized extending modules

A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and K/N is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.     

广义Lupas-Baskakov积分算子的同时逼近

讨论了广义Lupas-Baskakov积分算子的同时逼近，推广了[3]中一些结果，得到了逼近阶的估计。     

关于广义Riccati方程的可积条件——与赵临龙先生商榷

指出《科学通报》1998年第1《Riccati微分方程一个新的可积条件》中的错误并给出正确结论，即方程y’=P（x）y^n＋Q（x）y＋R（x）的可积条件不是R=K’Pe^n∫ （Q-βD）dx（K＇β为常数），而是[Q-1-n（R＇/R-P＇/P）]^n／PR^n-1=r（r为常数）．给出了满足这一条件的方程的通积分；推广了该方程原有的可积条件R=KPe^n∫Qdx（K为常数）．     

零级Dirichlet级数

研究了平面上零级Dirichlet级数一类增长性,得到了零级Dirichlet级数系数与零级增长性关系的一些结果.     

A Simulation Study Evaluating the Generalized Additive Model for Assessing Intervention Effects with Small Samples

Single subject (SS) designs are popular in educational and psychological research. There exist several statistical techniques designed to analyze such data and to address the question of whether an intervention has the desired impact. Recently, researchers have suggested that generalized additive models (GAMs) might be useful for modeling nonlinear effects that are common with SS designs. This study sought to extend the use of GAM from SS to a research design in which individuals may be placed in separate groups and receive different interventions. Results of the simulation study found that using a mixed model form of GAM (GAMM) resulted in higher power for detecting actual effects in the population than was true for either GAM or a Bayesian GAM estimator. Thus, GAMMs are recommended for use with SS designs when interventions are expected to induce nonlinear relationships between time and the outcome variable and individuals receive different treatments.     

Shift-invariance of short-time Fourier transform in fractional Fourier domains

Fractional Fourier domains form a continuum of domains making arbitrary angles with the time or frequency domains on the time-frequency plane. Signal representations in these domains are related to the fractional Fourier transform (FrFT). In this paper, a new proof on the shift-invariance of linear time-frequency distributions on fractional Fourier domains is given. We show that short-time Fourier transform (STFT) is the unique linear distribution satisfying magnitude-wise shift-invariance in the fractional Fourier domains. The magnitude-wise shift-invariance property in arbitrary fractional Fourier domains distinguishes STFT among all linear time-frequency distributions and simplifies the interpretation of the resultant distribution as shown by numerical examples.