The space of selections of smooth fans

In this paper we show that the space of selections of a smooth fan is a complete separable absolute retract. Then, we show that it is homeomorphic to the Hilbert space l₂.     

Portfolio selection with divisible and indivisible assets: Mathematical algorithm and economic analysis

We extend the classic mean-variance framework to a broad class of investment decisions under risk where investors select optimal portfolios of risky assets that include perfectly divisible as well as perfectly indivisible assets. We develop an algorithm for solving the associated mixed-integer nonlinear program and report on the results of a computational study. We then study the mean-variance structure of the investment frontier facing an individual investor in the presence of investment opportunities in both risky divisible and indivisible assets. Finally, we analyze the economic implications of the presence of investment opportunities in risky indivisible assets on the investor’s investment strategy and on his risk evaluation.     

基于均值-VaR的投资组合最优化

利用均值-VaR方法,提出了有交易费用存在时的最优投资组合模型。通过求解均值-方差模型来研究均值-VaR模型的有效前沿,并指出在收益率的分布为正态分布的假设下,均值-VaR模型的有效集是均值-方差有效前沿的子集。有关全局最小VaR的存在性的分析显示在选择VaR的置信水平时必须非常小心。最后给出了应用均值-VaR模型的实例分析。     

带有模糊系数的投资组合模型研究

在证券市场,由于各种不确定因素的存在,证券的预期收益率是难以精确估算的。本文采用模糊数来处理不确定性,提出了一种基于模糊收益率的投资组合模型。为度量投资组合的风险,将绝对偏差扩展到模糊情形。通过引入模糊数绝对值的概念和不等关系的两种占优准则,将该模型转化为相应的确定性线性规划问题,投资者可根据自己的主观态度选择参数和投资策略。最后用一个具体例子验证了模型的合理性和有效性。     

塞曼调制磁旋转分子光谱特征的研究

以Ｎ２第一正带（Ｂ３Πｇ－Ａ３Σ＋ｕ）为对象，研究塞曼调制磁旋转光谱技术的主要特征，对谱线的线型和位相做了详细的分析，同时，还提出并解释了谱线强度分布中的塞曼选态效应，结果均与实验相符合。     

A Note on the Mean-Variance Criteria for Discrete Time Financial Markets

It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.     

Bandwidth selection for the local polynomial estimator under dependence: A simulation study

Summary  Seven of the most popular methods for bandwidth selection in regression estimation are compared by means of a thorough simulation study, when the local polynomial estimator is used and the observations are dependent. The study is completed with two plug-in bandwidths for the generalized local polynomial estimator proposed by Vilar-Fernandez & Francisco-Fernández (2002).     

Existence Theorems of Random Nash Equilibrium Points for Random Set-valued Maps

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内容分发协议ShareStorm的Neighbor Selection机制

针对BitTorrent行为及其Neighbor Selection机制存在的缺陷,提出一种有效度量P2P内容分发协议的实验方法,并设计一种新的内容分发协议ShareStorm,该协议的Neighbor Selection机制充分考虑互联网拓扑和通讯成本,更倾向于与本地的peers建立邻居关系.经初步验证,在下载完成时间这个最主要的性能指标上,ShareStorm比BitTorrent至少减少50%.     

On the determination of particle impact breakage in selection function

This paper presents a thorough study of particle impact breakage in selection function with a unified breakage criterion. The impact mode and breakage pattern for particulate materials are classified based on a significant review of well-established impact testers. It was found that the lack of a unified breakage criterion to determine the breakage probability disables a direct comparison of particle breakage propensity from different impact loading testers. The literature breakage models to describe the breakage probability are reviewed where the advantage and drawback of these models are scrutinized. The sourced literature breakage models are compared with the zeolite breakage datasets in a unified breakage criterion to evaluate the model performance. A novel computational modelling workflow for a milling process is proposed to provide a guidance in implementing the digital twin in milling process prediction. The breakage probability models, i.e. the selection functions are comprehensively assessed in population balance model to examine the model serviceability. The model simplicity and fidelity in the model assessment are specifically discussed and the value of digital twin in substantially reducing the experimental trials is highlighted.