Several logarithmic Caffarelli–Kohn–Nirenberg inequalities and applications

In this paper, based on the Caffarelli–Kohn–Nirenberg inequalities on the Euclidean space and the weighted Hölder inequality, we establish the logarithmic Caffarelli–Kohn–Nirenberg inequalities and parameter type logarithmic Caffarelli–Kohn–Nirenberg inequalities, and give applications for the weighted ultracontractivity of positive strong solutions to a kind of evolution equations. We also prove corresponding logarithmic Caffarelli–Kohn–Nirenberg inequalities and parameter type logarithmic Caffarelli–Kohn–Nirenberg inequalities on the Heisenberg group and related to generalized Baouendi–Grushin vector fields. Some applications are provided.     

Fractional diffusion-type equations with exponential and logarithmic differential operators

We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi et al. (2001)): the first equation considered here is obtained by adding an exponential differential (or shift) operator expressed in terms of the Riesz–Feller derivative. We prove that this produces a random component in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involving the Riesz-derivative, we obtain, as a solution, the transition semigroup of a stable process subordinated by an independent gamma subordinator with drift. Finally, we show that an extension of the space-fractional diffusion equation, containing both the fractional shift operator and the Feller integral, is satisfied by the transition density of the process obtained by time-changing the stable process with an independent linear birth process with drift.     

含结构零2×2表中风险比齐性检验的样本量研究

本文研究了在临床和流行病学中出现的K个独立含结构零的2×2列联表.利用风险比推导出基于Wald型,基于对数变换型以及基于Score型的三个检验统计量,以检验层间齐性假设,获得了分别基于这三个检验统计量的控制功效的样本量公式和数值实验结果.模拟研究表明基于Score检验和基于对数变换检验的样本量公式比基于Wald检验的样本量公式更精确,更能有效保证预先给定的功效.推广了基于列联表问题的假设检验方法.     

多层螺旋CT诊断甲状腺癌中的辐射和对比剂剂量选择

本文对多层螺旋CT（MSCT）诊断甲状腺癌中的辐射和对比剂剂量选择进行了分析。选取2016年12月～2018年12月本院行MSCT检查的甲状腺癌、甲状腺良性结节患者各200例,依据随机数字表分为A组、B组、C组、D组,每组50例,A组参数为对比剂1.2 mL/kg、120 kV、180 mA,B组为对比剂1.0 mL/kg、120 kV、180 mA,C组为对比剂1.2 mL/kg、100 kV、100 mA,D组为对比剂1.0 mL/kg、100 kV、100 mA。结果显示,A组和B组CT容积剂量指数（CTDIvol）、剂量长度乘积（DLP）、有效辐射剂量（ED）明显低于C组和D组,A组和B组甲状腺CT值、背景信号、背景噪声明显高于C组和D组,差异有统计学意义（P<0.05）,A组、B组、C组、D组信噪比（SNR）、对比信噪比（CNR）、图像质量评分比较,差异无统计学意义（P>0.05）;A组、B组、C组、D组诊断甲状腺癌的敏感度、特异度、准确度比较,差异无统计学意义（P>0.05）。本文证实,对于MSCT诊断甲状腺癌中的辐射和对比剂剂量,选择1.0 mL/kg、100 kV、100 mA可在不严重影响图像质量及检查结果下有效减少患者的CT辐射,值得临床推广。     

QK乘子代数上的Corona定理和Wolff定理

本文给出对数K-Carleson测度的一个新特征,并以此为工具研究Q_K空间的乘子代数M(Q_K),给出乘子代数M(Q_K)的某些特征描述.利用对数K-Carleson测度及Q_K空间的一个新特征,建立乘子代数M(Q_K)上的Corona定理和Wolff定理.     

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.