Statistical and Geometrical Way of Model Selection for a Family of Subdivision Schemes

The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes.     

一类新的(2n-1)点二重动态逼近细分

利用正弦函数构造了一类新的带有形状参数ω的(2n-1)点二重动态逼近细分格式.从理论上分析了随n值变化时这类细分格式的C~k连续性和支集长度;算法的一个特色是随着细分格式中参数ω的取值不同,相应生成的极限曲线的表现张力也有所不同,而且这一类算法所对应的静态算法涵盖了Chaikin,Hormann,Dyn,Daniel和Hassan的算法.文末附出大量数值实例,在给定相同的初始控制顶点,且极限曲线达到同一连续性的前提下和现有几种算法做了比较,数值实例表明这类算法生成的极限曲线更加饱满,表现力更强.     

Efficient Near-Infrared Electroluminescence from Lanthanide-Doped Perovskite Quantum Cutters

Perovskite nanocrystals (PeNCs) deliver size- and composition-tunable luminescence of high efficiency and color purity in the visible range. However, attaining efficient electroluminescence (EL) in the near-infrared (NIR) region from PeNCs is challenging, limiting their potential applications. Here we demonstrate a highly efficient NIR light-emitting diode (LED) by doping ytterbium ions into a PeNCs host (Yb³⁺ : PeNCs), extending the EL wavelengths toward 1000 nm, which is achieved through a direct sensitization of Yb³⁺ ions by the PeNC host. Efficient quantum-cutting processes enable high photoluminescence quantum yields (PLQYs) of up to 126 % from the Yb³⁺ : PeNCs. Through halide-composition engineering and surface passivation to improve both PLQY and charge-transport balance, we demonstrate an efficient NIR LED with a peak external quantum efficiency of 7.7 % at a central wavelength of 990 nm, representing the most efficient perovskite-based LEDs with emission wavelengths beyond 850 nm.     

Perfectly Encoding π-Conjugated Anions in the RE5(C3N3O3)(OH)12 (RE=Y,Yb, Lu) Family with Strong Second Harmonic Generation Response and Balanced Birefringence

Nonlinear optical (NLO) crystal, which simultaneously exhibits strong second-harmonic-generation (SHG) response and desired optical anisotropy, is a core optical material accessible to the modern optoelectronics. Accompanied by strong SHG effect in a NLO crystal, a contradictory problem of overlarge birefringence is ignored, leading to low frequency doubling efficiency and poor beam quality. Herein, a series of rare earth cyanurates RE₅(C₃N₃O₃)(OH)₁₂ (RE=Y, Yb, Lu) were successfully characterized by 3D electron diffraction technique. Based on a “three birds with one stone” strategy, they enable the simultaneous fulfillment of strong SHG responses (2.5–4.2× KH₂PO₄), short UV cutoff (ca. 220 nm) and applicable birefringence (ca. 0.15 at 800 nm) by the introduction of rare earth coordination control of π-conjugated (C₃N₃O₃)³⁻ anions. These findings provide high-performance short-wavelength NLO materials and highlight the exploration of cyanurates as a new research area.     

A Factorization Theorem for Topological Abelian Groups

Using the nice properties of the w-divisible weight and the w-divisible groups, we prove a factorization theorem for compact abelian groups K; namely, K = K _tor  × K _d , where K _tor is a bounded torsion compact abelian group and K _d is a w-divisible compact abelian group. By Pontryagin duality this result is equivalent to the same factorization for discrete abelian groups proved in [9 Galindo , J. , Macario , S. ( 2011 ). Pseudocompact group topologies with no infinite compact subsets . J. Pure and Appl. Algebra 215 : 655 – 663 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Strichartz Estimates for Non-Elliptic Schrödinger Equations on Compact Manifolds

In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, the same Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for Riemannian metrics proved by Burq-Gérard-Tzvetkov to the non-elliptic case and improves the result by Salort for the degenerate case. We also investigate the optimality of the result for the case on 𝕊³ × 𝕊³.     

广义sine-Gordon方程高精度隐式紧致差分方法

本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.