本文主要研究具有粗糙密度场的三维非均质不可压缩非对称流体的柯西问题.通过开发一些解关于时间额外的加权估计,运用插值理论和关于时间变量的Lorentz空间的相关性质,建立了速度场的Lipschitz正则性.基于此,采用对偶方法,获得了由[Qian,Chen and Zhang,***.,2023,386:1555-1593]构造的整体弱解的唯一性.
投资组合优化问题中的输入参数大多是由历史数据估计而来,估计的不确定性可能对Markowitz投资组合模型产生巨大的影响.近期,一个联合估计与鲁棒性的优化框架(joint estimation and robustness optimization,JERO)被提出,通过结合参数估...
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投资组合优化问题中的输入参数大多是由历史数据估计而来,估计的不确定性可能对Markowitz投资组合模型产生巨大的影响.近期,一个联合估计与鲁棒性的优化框架(joint estimation and robustness optimization,JERO)被提出,通过结合参数估计和优化问题以减弱估计不确定性对优化问题的影响.JERO框架被应用到投资组合优化领域(JERO with the mean return and the risk(variance)constraints,JERO-MV),同时考量了投资组合模型中有价值的两个度量:投资组合的回报和风险.但该模型可能会导致投资组合过分集中于某几个资产,这将增加投资风险和成本.本文在JERO-MV模型的基础上增加分散化约束,并给出该模型的可行性条件.本文在真实数据集上进行了大量的数值实验,并与JERO-MV模型进行对比.在大多数情形下,我们的模型都有更好的样本外表现.
图结构学习(Graph Structure Learning, GSL)通过优化图结构,增强图的表示能力和性能。GSL能够更好地捕捉图数据中节点之间的关系,从而促进信息的有效传播。图结构优化在商品链接预测中的应用研究旨在通过改进商品间关系的图结构,提高预测精度与推荐效果。在电商平台中,商品间的复杂关系往往通过图结构表示,其中节点代表商品,边代表商品间的关联或共同特征。通过优化图的构建和学习方法,能够更准确地捕捉商品之间的潜在联系,从而提升链接预测的准确性和推荐质量。优化后的图结构可以帮助算法更好地处理大规模商品数据,增强模型的泛化能力,进而提升电商平台的个性化推荐系统,增加用户购买的可能性,并促进销售增长。本文提出了一种新的稀疏正则化与图结构学习模型搜索方法(SGSL)。通过引入边缘修剪的正则化项等技术,SGSL能够在节点不变分类任务中显著提高性能,同时减少在节点变化任务中搜索到错误边的风险。实验表明,SGSL能有效增强图神经网络模型的性能。Graph Structure Learning (GSL) enhances the representational capacity and performance of graphs by optimizing their structure. GSL better captures the relationships between nodes in graph data, which facilitates more effective information propagation. The application of graph structure optimization in product link prediction aims to improve prediction accuracy and recommendation performance by refining the graph structure that represents the relationships between products. In e-commerce platforms, the complex relationships between products are often represented through graph structures, where nodes represent products and edges represent associations or shared features. By optimizing graph construction and learning methods, the underlying relationships between products can be more accurately captured, thereby improving link prediction accuracy and recommendation quality. The optimized graph structure helps algorithms better handle large-scale product data, enhancing the model’s generalization ability, which in turn improves personalized recommendation systems, increases the likelihood of user purchases, and drives sales growth. This paper introduces a novel Sparse Regularization and Graph Structure Learning Model Search method (SGSL). By incorporating techniques such as edge pruning regularization, SGSL significantly improves performance in node-invariant classification tasks while reducing the risk of selecting incorrect edges in node-variant tasks. Experimental results show that SGSL effectively enhances the performance of graph neural network mo
本文探讨了双碳政策实施背景下,中国能源消耗结构转型与国际贸易的相互影响。随着全球对可持续发展的重视,中国正加速向可再生能源转型,逐步降低对化石燃料的依赖。这一转型不仅改善了国内能源安全,也重塑了国际能源贸易格局。文章基于线性回归模型预测了中国的碳排放量,并分析了近十年来的能源消耗模式和结构变化。同时,通过相关性分析揭示了能源消耗与国际贸易之间的内在联系,指出两者在全球绿色经济中的互动关系。中国的转型不仅有助于改善环境状况,还为国际市场带来了新的机遇与挑战。随着可再生能源比重的提升,中国在全球能源供应链中的地位也在发生变化。这一变化促使中国企业在技术创新和国际合作方面不断提升,从而推动国际贸易向更高标准和更环保的方向发展。总的来说,本文为理解中国在全球能源转型中的角色提供了重要洞见,强调了可持续发展与国际贸易之间的密切联系。This paper examines the relationship between the structural transformation of China’s energy consumption and international trade, with a particular focus on the implementation of peak carbon and carbon-neutral policy policies. In light of the global emphasis on sustainable development, China is accelerating its transition to renewable energy sources and gradually reducing its dependence on fossil fuels. This transition has the additional benefit of enhancing domestic energy security while simultaneously influencing the configuration of international energy trade patterns. The article employs a linear regression model to predict China’s carbon emissions and conducts an in-depth analysis of the shifts in energy consumption patterns and structures that have occurred over the past decade. Concurrently, correlation analyses elucidate the intrinsic interconnections between energy consumption and international trade, underscoring the interplay between the two in the global green economy. China’s transition not only has positive implications for environmental conditions, but also presents new opportunities and challenges for the international market. As the proportion of renewable energy sources increases, China’s role in the global energy supply chain is evolving. This shift has prompted Chinese companies to enhance their technological innovation and international collaboration, thereby propelling international trade towards higher standards and a more environmentally conscious approach. Overall, this paper offers valuable insights into China’s role in the global energy transition, underscoring the intrinsic link
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