Hilbert’s Nullstellensatz for analytic trigonometric polynomials

This paper proves such a new Hilbert’s Nullstellensatz for analytic trigonometric polynomials that if ${\left\{f_j\right\}}_{j=1}^{n\ge 2}$ are analytic trigonometric polynomials without common zero in the finite complex plane $?$ then there are analytic trigonometric polynomials ${\left\{g_j\right\}}_{j=1}^{n\ge 2}$ obeying ${\sum }_{j=1}^{n\ge 2}{f}_j{g}_j=1$ in $?$, thereby not only strengthening Helmer’s Principal Ideal Theorem for entire functions, but also finding an intrinsic path from Hilbert’s Nullstellensatz for analytic polynomials to Pythagoras’ Identity on $?$.     

基于混合空穴注入层的湿法制备高效蓝光热激活延迟有机发光二极管

在溶液法制备有机电致发光器件(OLEDs)的研究中, PEDOT∶PSS由于具有较好的成膜性与高透光性而常被用作器件的空穴注入层。但相关研究表明, PEDOT∶PSS本身稳定性较差以及功函数较低,这使得溶液法制备OLEDs的性能差且不稳定。蓝色作为全彩色的三基色之一,制备高效的蓝光器件对于实现高质量显示器件和固态照明装置必不可少。而目前溶液法制备蓝光OLEDs的器件效率普遍较差,针对此问题,本文利用传统的蓝光热激活延迟荧光发光(TADF)材料DMAC-DPS作为发光层,用溶液法制备了蓝光TADF OLEDs,通过在PEDOT∶PSS中掺杂PSS-Na制备混合空穴注入层(mix-HIL)来提高空穴注入层的功函数,研究其对于蓝光TADF OLEDs器件性能的影响。首先在PEDOT∶PSS水溶液中掺入不同体积的PSS-Na溶液,在相同条件下旋涂制膜,进行器件制备。通过观测各个实验组器件的电致发光(EL)光谱,发现掺入PSS-Na后器件EL谱存在光谱蓝移的现象,这是由于掺入PSS-Na水溶液后, mix-HIL层的厚度有所降低,使得在微腔效应作用下, EL光谱发生蓝移。通过对比各组器件的电流密度-电压-亮度(J-V-L)曲线及其计算所得器件的电流效率,结果显示随着PSS-Na的掺入,器件的亮度和电流都有所增大,器件的电流效率也得到了提升,当掺杂比例为0.5∶0.5(PEDOT∶PSS/PSS-Na)时提升幅度最大(亮度提升86.7%,电流效率提升34.3%)。通过在瞬态电致发光测试过程中施加或撤去驱动电压观测了器件EL强度的变化,分析了在混合空穴注入层/发光层(mix-HIL/EML)界面处的电荷积累情况。实验证明,通过在PEDOT∶PSS中掺杂PSS-Na制备mix-HIL获得了蓝光TADF OLEDs器件性能的提升,这是一个获得高效率溶液法制备OLEDs的可行方法。     

Vertex-disjoint cycles in local tournaments

Let $r$ be a positive integer. The Bermond–Thomassen conjecture states that, a digraph of minimum out-degree at least $2r-1$ contains $r$ vertex-disjoint directed cycles. A digraph $D$ is called a local tournament if for every vertex $x$ of $D$, both the out-neighbours and the in-neighbours of $x$ induce tournaments. Note that tournaments form the subclass of local tournaments. In this paper, we verify that the Bermond–Thomassen conjecture holds for local tournaments. In particular, we prove that every local tournament $D$ with ${\delta }^{+}\left(D\right)\ge 2r-1$ contains $r$ disjoint cycles $C_1,C_2,\dots ,C_r$, satisfying that either $C_i$ has the length at most 4 or is a shortest cycle of the original digraph of $D-C_1-\dots -C_{i-1}$ for $1\le i\le r$.     

A hybrid numerical approach to predict the vibrational responses of panels excited by a turbulent boundary layer

In this work, a hybrid numerical approach to predict the vibrational responses of planar structures excited by a turbulent boundary layer is presented. The approach combines an uncorrelated wall plane wave technique with the finite element method. The wall pressure field induced by a turbulent boundary layer is obtained as a set of uncorrelated wall pressure plane waves. The amplitude of these plane waves are determined from the cross spectrum density function of the wall pressure field given either by empirical models from literature or from experimental data. The response of the planar structure subject to a turbulent boundary layer excitation is then obtained from an ensemble average of the different realizations. The numerical technique is computationally efficient as it rapidly converges using a small number of realizations. To demonstrate the method, the vibrational responses of two panels with simply supported or clamped boundary conditions and excited by a turbulent flow are considered. In the case study comprising a plate with simply supported boundary conditions, an analytical solution is employed for verification of the method. For both cases studies, numerical results from the hybrid approach are compared with experimental data measured in two different anechoic wind tunnels.