Representation of quasi‐monotone functionals by families of separating hyperplanes

We characterize when the level sets of a continuous quasi‐monotone functional defined on a suitable convex subset of a normed space can be uniquely represented by a family of bounded continuous functionals. Furthermore, we investigate how regularly these functionals depend on the parameterizing level. Finally, we show how this question relates to the recent problem of property elicitation that simultaneously attracted interest in machine learning, statistical evaluation of forecasts, and finance.     

碳纳米管的拉曼散射

本文报道了经电弧放电产生的阴极沉积物外壳与内芯，以及石墨电极的喇曼光谱。     

广义投影梯度型约束变尺度法

本文将广义投影梯度方向移植到约束变尺度算法之中，得到了一类新型算法：广义投影梯度型约束变尺度算法，并成功的使用了Ａｒｍｉｊｏ规则．该算法将广义投影类可行方向法和约束变尺度算法的优点溶为一体．并且由于使用了拟下降的概念，算法变得更为灵活．     

随机积分的拟必然逼近

该文证明了随机积分的拟必然逼近. 基于此,作者用更简化的方法得到并拓展了文献[8]的主要结果. 并且, 该方法可以应用到光滑两参数鞅情形.     

余代数和Morita-Takeuchi关系

本文证明了若余代数Ｃ和Ｄ是Ｍｏｒｉｔａ Ｔａｋｅｕｃｈｉ等价的，则Ｃ的子余代数格和Ｄ的子余代数格同构．设ＭΓ，ＮΓ是拟有限右Γ 余模，则（ｈ－Γ（Ｍ，Ｍ），ｈ－Γ（Ｎ，Ｎ）；ｈ－Γ（Ｎ，Ｍ），ｈ－Γ（Ｍ，Ｎ）；ｆ，ｇ）有Ｍｏｒｉｔａ Ｔａｋｅｕｃｈｉ关系．并给出了此Ｍ Ｔ关系是Ｍ Ｔ等价条件的及由已知的Ｍ Ｔ关系构造新的Ｍ Ｔ关系的方法．     

半相依非线性回归方程组中的近似得分函数和拟近似得分函数

本文定义了半相依非线性回归方程组中的近似得分函数和拟近似得分函数．这些函数利用了样本信息和附加信息，在均方误差准则下改进了独立得分函数和拟独立得分函数．     

On steepest descent curves for quasi convex families in Rn

A connected, linearly ordered subset $\gamma ?{\mathbb{R}}^n$ satisfying $$x_1,x_2,x_3\in \gamma ,\text{and}{x}_1?x_2?x_3\to |x_2?x_1|\le |x_3?x_1|$$ is shown to be a rectifiable curve; a priori bounds for its length are given; moreover, these curves are generalized steepest descent curves of suitable quasi convex functions. Properties of quasi convex families are considered; special curves related to quasi convex families are defined and studied; they are generalizations of steepest descent curves for quasi convex functions and satisfy the previous property. Existence, uniqueness, stability results and length bounds are proved for them.     

Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square

We prove lower bounds for the error of optimal cubature formulae for d‐variate functions from Besov spaces of mixed smoothness in the case , and , where is either the d‐dimensional torus or the d‐dimensional unit cube . In addition, we prove upper bounds for QMC integration on the Fibonacci‐lattice for bivariate periodic functions from in the case , and . A non‐periodic modification of this classical formula yields upper bounds for if . In combination these results yield the correct asymptotic error of optimal cubature formulae for functions from and indicate that a corresponding result is most likely also true in case . This is compared to the correct asymptotic of optimal cubature formulae on Smolyak grids which results in the observation that any cubature formula on Smolyak grids can never achieve the optimal worst‐case error.     

Weak and quasi approximation properties in Banach spaces

In this paper, we introduce weak versions (the weak approximation property, the bounded weak approximation property, and the quasi approximation property) of the approximation property and derive various characterizations of these properties. And we show that if the dual of a Banach space X has the weak approximation property (respectively the bounded weak approximation property), then X itself has the weak approximation property (respectively the bounded weak approximation property). Also we observe that the bounded weak approximation property is closely related to the quasi approximation property.