On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities

In order to construct fixed-width (2d) confidence intervals for the mean of an unknown distribution function F, a new purely sequential sampling strategy is proposed first. The approach is quite different from the more traditional methodology of Chow and Robbins (1965, Ann. Math. Statist., 36, 457–462). However, for this new procedure, the coverage probability is shown (Theorem 2.1) to be at least (1-)+Ad ²+o(d²) as d0 where (1-) is the preassigned level of confidence and A is an appropriate functional of F, under some regularity conditions on F. The rates of convergence of the coverage probability to (1-) obtained by Csenki (1980, Scand. Actuar. J., 107–111) and Mukhopadhyay (1981, Comm. Statist. Theory Methods, 10, 2231–2244) were merely O(d^1/2-q), with 0<q<1/2, under the Chow-Robbins stopping time ^*. It is to be noted that such considerable sharpening of the rate of convergence of the coverage probability is achieved even though the new stopping variable is O_p(^*). An accelerated version of the stopping rule is also provided together with the analogous second-order characteristics. In the end, an example is given for the mean estimation problem of an exponential distribution.     

An adaptive stochastic global optimization algorithm for one-dimensional functions

In this paper a new algorithm is proposed, based upon the idea of modeling the objective function of a global optimization problem as a sample path from a Wiener process. Unlike previous work in this field, in the proposed model the parameter of the Wiener process is considered as a random variable whose conditional (posterior) distribution function is updated on-line. Stopping criteria for Bayesian algorithms are discussed and detailed proofs on finite-time stopping are provided.This research has been partially supported by Progetto MURST 40% Metodi di Ottimizzazione per le Decisioni.     

On countable choice and sequential spaces

Under the axiom of choice, every first countable space is a Fréchet‐Urysohn space. Although, in its absence even ? may fail to be a sequential space. Our goal in this paper is to discuss under which set‐theoretic conditions some topological classes, such as the first countable spaces, the metric spaces, or the subspaces of ?, are classes of Fréchet‐Urysohn or sequential spaces. In this context, it is seen that there are metric spaces which are not sequential spaces. This fact raises the question of knowing if the completion of a metric space exists and it is unique. The answer depends on the definition of completion. Among other results it is shown that: every first countable space is a sequential space if and only if the axiom of countable choice holds, the sequential closure is idempotent in ? if and only if the axiom of countable choice holds for families of subsets of ?, and every metric space has a unique ‐completion. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sequential Fourier-Feynman transform, convolution and first variation

Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or continuous. Also we study the relationships involving this transform and the first variation.

     

近代化学巨匠:尤斯图斯?冯?李比希

尤斯图斯?冯?李比希是近代化学史上最杰出的化学家之一。李比希的人生经历中蕴含着许多教学元素,如教育报国,创新改革化学教育模式;不畏艰难,开拓学科新领域;开放创新,创建基于大学的自然科学学派;辩证唯物,坚持真理的科学态度;学以致用,联系实际的实践精神等值得我们深入分析,并将其精华在新时代的教学育人和学科建设中实践应用。     

三价铁离子和二价铁离子的鉴别与转化的绘画实验*

以Fe³⁺、Fe²⁺的鉴别和转化为例,详细介绍了绘画实验的纸笔与试剂浓度选择、绘画图案设计、微课应用及效果分析,还进行了“铁及其化合物”的一些化学反应。绘画实验突出了化学实验现象的色彩美,一定程度上激发了学生的学习热情,是一种值得尝试的创新实验方式。     

Sustainable extraction of ligustilide and ferulic acid from Angelicae Sinensis Radix,for antioxidant and anti-inflammatory activities

The 2030 Agenda for Sustainable Development envisions a rational use of energy and resources in all technological processes. However, in the extraction methods of compounds from medicinal plants and herbs, there is an urgent to reduce the use of organic solvents and increase the energy efficiency of these methods. Therefore, a sustainable extraction method (enzyme and ultrasonic co-assisted aqueous two-phase extraction, EUA-ATPE) of simultaneous extraction and separation of ferulic acid and ligustilide from Angelicae Sinensis Radix (ASR) was developed by integrating enzyme-assisted extraction (EAE) with ultrasonic-assisted aqueous two-phase extraction (UAE- ATPE). The effects of different enzymes, extraction temperature, pH, ultrasonic time, liquid-to-materials ratio, etc., were optimized by single-factor experiments and central composite design (CCD). Under the optimum conditions, the highest comprehensive evaluation value (CEV) and extraction yield were obtained by EUA-ATPE. Furthermore, recovery (R), partition coefficient (K), and scanning electron microscopy (SEM) analysis revealed that enzyme and ultrasonic treatment improved mass transfer diffusion and increased the degree of cell disruption. Besides, the EUA-ATPE extracts have shown great antioxidant and anti-inflammatory activity in vitro. Finally, compared to different extraction methods, EUA-ATPE achieved higher extraction efficiency and higher energy efficiency due to the synergistic effect between EAE and UAE-ATPE. Therefore, the EUA-ATPE provides a sustainable method for extracting bioactive compounds from medicinal plants and herbs, contributing to Sustainable Development Goals (SDG), including SDG-6, SDG-7, SDG-9, SDG-12, and SDG-15.     

武器结构－机构耦合系统的最优化设计

本文提出了具有结构，机构耦合形式的自动武器系统的最优化设计问题，建立了这种武器系统在射击载荷作用下的ＮＬＰ模型。针对武器系统的非线性耦合特性，提出了状态和设计敏度分析的混合预测校正方法。建立的ＮＬＰ问题用改进的ＳＬＰ方法求解。通过对－简单的后退式武器后座力的最小化设计说明本文方法是有效的。     

弹塑性结构优化的并行算法

本文给出了弹塑性结构优化设计的序列二次规划算法，分别考虑了弹塑性结构分析，灵敏度分析和二次规划的Ｌｅｍｋｅ算法的并行计算。针对弹塑性结构灵敏度的不连续性，比较了连续模型和间断模型的计算结果，结果是接近的。算例表明此算法有很好的并行性。     

基于可拓物元模型的技术协同创新风险评价研究——基于企业主体的视角

基于可拓物元理论,对基于企业主体视角的技术协同创新风险进行评价分析.在技术协同创新关键风险指标体系的基础上,构建了企业技术协同创新风险测评的可拓物元模型.以各项关键风险因素的专家打分原始数据为依据,对各项风险因素指标的专家打分的平均值进行归一化处理,并将归一化结果作为企业技术协同创新关键风险因素的权重系数,提高了企业技术协同创新风险度量的精确度和时效性.最后,以某企业与北京科技大学的协同创新项目进行了实证分析.