Preparation of partially functionalised resorcinarene derivatives

The conditions for synthesis of mono-, di- and trifunctionalised resorcinarenes by catalysed Mannich reaction are described. A series of these compounds are functionalised with different functional groups.     

Comment on “Extending Hirshfeld‐I to bulk and periodic materials”

In recent years, several methods have been developed that partition the electron density among atoms using spherically symmetric atomic weights. D. E. P. Vanpoucke, P. Bultinck, and I. Van Driessche (J. Comput. Chem. 2012, doi: 10.1002/jcc.23088) recently reported a periodic implementation of the Hirshfeld‐I method that uses a combination of Becke‐style and uniform integration grids and modified atomic reference densities to compute net atomic charges in periodic materials. Herein, this method is discussed in the context of earlier periodic implementations of the Hirshfeld‐I method, the Iterated Stockholder Atoms method, and the density derived electrostatic and chemical method.     

股本稀释效应下的认股权证定价模型与数值方法

本文研究了在股本稀释效应下认股权证的定价问题.假设随机利率服从Vasicek模型,利用Δ-对冲方法建立了权证价格所满足的偏微分方程.然后,通过计价单位变换,将偏微分方程降维,求得了权证价格的显式解,并给出了一种较好的数值计算方法,可运用市场的可观测变量来计算权证价值.     

Scalable and Transferable Reinforcement Learning for Multi-Agent Mixed Cooperative–Competitive Environments Based on Hierarchical Graph Attention

Most previous studies on multi-agent systems aim to coordinate agents to achieve a common goal, but the lack of scalability and transferability prevents them from being applied to large-scale multi-agent tasks. To deal with these limitations, we propose a deep reinforcement learning (DRL) based multi-agent coordination control method for mixed cooperative–competitive environments. To improve scalability and transferability when applying in large-scale multi-agent systems, we construct inter-agent communication and use hierarchical graph attention networks (HGAT) to process the local observations of agents and received messages from neighbors. We also adopt the gated recurrent units (GRU) to address the partial observability issue by recording historical information. The simulation results based on a cooperative task and a competitive task not only show the superiority of our method, but also indicate the scalability and transferability of our method in various scale tasks.     

A Characterization of Maximally Entangled Two-Qubit States

As already known by Rana’s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval [−12,1]. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are −12. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is −12 if and only if such a two-qubit state is maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.     

高阶拟线性中立型偏泛函微分方程组解的振动性

1 引言 由于在人口动力学、生物遗传工程和化学反应过程等自然的和人为的过程中都存在滞后现象,因而偏泛函微分方程(组)的研究能更精确地揭示事物本质,同时能丰富微分方程(组)理论的研究。近十几年来,很多学者在泛函偏微分方程解的振动理论的研究方面作了大量工作,取得了许多成果。然而,关于泛函偏微分方程组解的振动性的研     

不完全边值问题的极小二乘解及其稳定性

定义了一类在部分边界上函数值为0函数的Sobolev空间，并用以讨论部分边界缺乏边值的二阶散度型椭圆型微分方程与其最小范数极小二乘解的稳定性．     

A Novel Approach to the Partial Information Decomposition

We consider the “partial information decomposition” (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique components. In the first part of this paper, we propose a general framework for constructing a multivariate PID. Our framework is defined in terms of a formal analogy with intersection and union from set theory, along with an ordering relation which specifies when one information source is more informative than another. Our definitions are algebraically and axiomatically motivated, and can be generalized to domains beyond Shannon information theory (such as algorithmic information theory and quantum information theory). In the second part of this paper, we use our general framework to define a PID in terms of the well-known Blackwell order, which has a fundamental operational interpretation. We demonstrate our approach on numerous examples and show that it overcomes many drawbacks associated with previous proposals.     

局部偏最小二乘回归建模参数对近红外检测结果的影响研究

报道了在局部加权(LWR)回归方法基础上,自主改进的更简单、实用的局部偏最小二乘回归(LPLS)的原理和方法。并以云南优质烤烟为实验材料,在国产光栅漫反射型近红外仪器上,研究了主成分数以及局部建模样品数对检测结果的影响。结果表明：应用交叉验证方法推荐的尼古丁组分模型主成分数并不是最优,通过适当降低主成分数可提高检测效果;局部建模样品数为30～50个时总糖、总氮、尼古丁预测准确度的提高幅度可分别达7%,14%,10%以上。该方法能有效提高近红外数学模型的预测准确度,是建立具有高度适应性近红外数学模型的有效方法。     

Limit Gaussian Behavior of the Solutions of the Multidimensional Burger'; Equation with Weak-Dependent Initial Conditions

Asymptotic normality of the solutions of the initial-value problems for multidimensional Burgers' equation with weakly dependent possible non-Gaussian initial condition is proved.