Controllable 1D Patterned Assembly of Colloidal Quantum Dots on PbSO4 Nanoribbons

Control of the 1D self‐assembly pattern of colloidal quantum dots (QDs) on PbSO₄ nanoribbon (NRb) templates is achieved. The internal structure of the NRbs is investigated by X‐ray diffraction, revealing the isotropic packing of the PbSO₄ nanoclusters in the NRbs. Colloidal QDs in a chloroform/hexane mixture are adsorbed onto the region close to the edges of the NRbs and form a 1D assembly of straight single line or double lines by controlling the amount of OAm. This is the first demonstration of a densely packed 1D self‐assembly of colloidal QDs with a straight line pattern without the use of any molecular bridge or adhesive. Atomic force microscopy measurements of the NRbs show depressions in the phase profile along the width of the NRbs, corresponding to the position of the 1D QD chain. The amount of adsorbed QDs on the NRbs in solution decreases as the addition of OAm increases, suggesting that additional OAm prevents interaction between the QDs and NRbs but facilitates the uniform adsorption of the 1D assembly. The low‐dimensional self‐assembly of colloidal QDs in this study opens up the possibility for the creation of anisotropically assembled QD superstructures.     

Linear codes associated to skew-symmetric determinantal varieties

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given.     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

Dependency distance: A new perspective on syntactic patterns in natural languages

Dependency distance, measured by the linear distance between two syntactically related words in a sentence, is generally held as an important index of memory burden and an indicator of syntactic difficulty. Since this constraint of memory is common for all human beings, there may well be a universal preference for dependency distance minimization (DDM) for the sake of reducing memory burden. This human-driven language universal is supported by big data analyses of various corpora that consistently report shorter overall dependency distance in natural languages than in artificial random languages and long-tailed distributions featuring a majority of short dependencies and a minority of long ones. Human languages, as complex systems, seem to have evolved to come up with diverse syntactic patterns under the universal pressure for dependency distance minimization. However, there always exist a small number of long-distance dependencies in natural languages, which may reflect some other biological or functional constraints. Language system may adapt itself to these sporadic long-distance dependencies. It is these universal constraints that have shaped such a rich diversity of syntactic patterns in human languages.     

Non-Poissonian statistics in an optical analog of quantum billiard with perfectly square boundaries

We study deviation from the Poissonian statistics of the frequency spacing distribution, appearing due to coupling of polarizational and transverse degrees of freedom in a perfectly square vertical cavity surface emitting laser. The deviation can be controlled by strength of the intracavity anisotropy and its alignment to the device boundaries.     

两点源诱偏ARM的效能评估模型研究

两点源诱偏是对抗反辐射导弹(ARM)的一种有效的手段。首先采用数学方法研究了两点源诱偏反辐射导弹的原理,讨论了两点源诱偏作用下被动雷达导引头的瞄准方向,给出了两点源诱骗反辐射导弹的脱靶距离模型和案例分析,为研究靶场诱偏系统的试验方法和使用原则奠定了基础。     

模拟深海采矿环境下混响的局部平稳性分析

针对深海采矿环境中强混响干扰下目标回波提取困难的问题,提出了海底强混响环境的模拟方法,在此基础上建立了采矿模拟环境中混响干扰的AR模型,并利用建立的AR模型计算了模拟环境中信号的Itakura距离.以建立的AR模型及Itakura距离为基础,建立了海底强混响仿真模型,对不同Itakura距离下的仿真信号及己知Itakura距离的大量实验数据分段预白化处理.仿真和实验数据处理结果表明模拟采矿环境下混响具有局部平稳性.