Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Quantitative and Qualitative Analysis of the Anti-Proliferative Potential of the Pyrazole Scaffold in the Design of Anticancer Agents

The current work presents an objective overview of the impact of one important heterocyclic structure, the pyrazole ring, in the development of anti-proliferative drugs. A set of 1551 pyrazole derivatives were extracted from the National Cancer Institute (NCI) database, together with their growth inhibition effects (GI%) on the NCI’s panel of 60 cancer cell lines. The structures of these derivatives were analyzed based on the compounds’ averages of GI% values across NCI-60 cell lines and the averages of the values for the outlier cells. The distribution and the architecture of the Bemis–Murcko skeletons were analyzed, highlighting the impact of certain scaffold structures on the anti-proliferative effect’s potency and selectivity. The drug-likeness, chemical reactivity and promiscuity risks of the compounds were predicted using AMDETlab. The pyrazole ring proved to be a versatile scaffold for the design of anticancer drugs if properly substituted and if connected with other cyclic structures. The 1,3-diphenyl-pyrazole emerged as a useful scaffold for potent and targeted anticancer candidates.     

Azides in the Synthesis of Various Heterocycles

In this review, we focus on some interesting and recent examples of various applications of organic azides such as their intermolecular or intramolecular, under thermal, catalyzed, or noncatalyzed reaction conditions. The aforementioned reactions in the aim to prepare basic five-, six-, organometallic heterocyclic-membered systems and/or their fused analogs. This review article also provides a report on the developed methods describing the synthesis of various heterocycles from organic azides, especially those reported in recent papers (till 2020). At the outset, this review groups the synthetic methods of organic azides into different categories. Secondly, the review deals with the functionality of the azido group in chemical reactions. This is followed by a major section on the following: (1) the synthetic tools of various heterocycles from the corresponding organic azides by one-pot domino reaction; (2) the utility of the chosen catalysts in the chemoselectivity favoring C−H and C-N bonds; (3) one-pot procedures (i.e., Ugi four-component reaction); (4) nucleophilic addition, such as Aza-Michael addition; (5) cycloaddition reactions, such as [3+2] cycloaddition; (6) mixed addition/cyclization/oxygen; and (7) insertion reaction of C-H amination. The review also includes the synthetic procedures of fused heterocycles, such as quinazoline derivatives and organometal heterocycles (i.e., phosphorus-, boron- and aluminum-containing heterocycles). Due to many references that have dealt with the reactions of azides in heterocyclic synthesis (currently more than 32,000), we selected according to generality and timeliness. This is considered a recent review that focuses on selected interesting examples of various heterocycles from the mechanistic aspects of organic azides.     

L波段高功率线极化径向线阵列天线理论分析与数值模拟

 探索了L波段的高功率线极化径向线阵列天线。基于三角形栅格形式实现了径向线圆形平面阵列天线,分析并给出了径向线并联馈电网络,并以同轴馈电的水平单圆环线极化天线为基础,利用径向线并联馈电网络设计出了间距小于一个波长下L波段高功率线极化径向线阵列天线。研究结果表明：这种结构实现径向线阵列天线的线极化辐射是可行的,该天线在中心频率1.57 GHz下,增益为19.97 dBi,轴比为-52.06 dB,反射系数为0.105 2;在1.37～1.77 GHz的频率范围内增益大于18.64 dBi,轴向轴比值小于-46.45 dB。     

The Conformation of Sterically Congested Seven-Membered Rings Containing Tetracoordinate Germanium(IV): A First X-Ray Crystallographic Structure Determination

The X-ray crystallographic analysis of 6,6-dimethyl-2,4,8,10-tetra-tert-octyl-dibenzo[d,f][1,3,2]dioxagermepin, 1 is reported. In the solid-state conformation of 1, the dihedral angle about the C─C sp²-sp ² σ bond connecting the two aryl rings is 50.1°. The observed C₂ symmetry in the solid-state conformation of 1 is consistent with the previously suggested solution conformation.     

Magnetoexciton in semiconductor concentric double rings

We investigate theoretically the magnetoexciton states in semiconductor concentric quantum double rings using the multi-band effective mass theory. We find that a perpendicular magnetic field can lead to oscillations in the exciton energy which appear as kinks in the magneto-photoluminescence (PL) spectra as the magnetic field increases. The spatial distribution of the exciton over the rings depends sensitively on the thicknesses of the inner and outer rings. The tunneling coupling between the inner and outer rings and the heavy-hole and light-hole mixing results in different anticrossing behaviors. Exciton can be converted into a spatially separated type-II exciton by tuning the thickness, the inner and/or outer ring radius and the magnetic field. We show that this type I–type II transition is reflected in the oscillator strength of the PL spectrum which will be the experimental signature that will provide us with information about the spatial distribution of the exciton.     

近红外光谱分析中建模校正集的选择

将极大线性无关组的概念及方法引入近红外光谱分析,探讨了在建立定量分析模型时代表性样品,即校正集样品的选择问题。以2 652个烟末样品为实验材料,随机选取1 001个样品构成预测集,其余1 651个样品为代表性样品备选集。用Matlab软件求出代表性样品备选集光谱矩阵的极大线性无关组,以此作为代表性样品,构成建模的校正集。用PLS回归法建立了烟末样品总糖含量定量分析的预测模型,并将模型用于预测集中1 001个烟末样品总糖含量的预测分析。实验结果表明,当选择的校正集包含的样品数量大于32时,所建各模型对预测集样品预测的平均相对误差均小于4%,平均相关系数大于0.96。其中选择32个代表性样品和146个代表性样品所建模型定量分析预测集中各样品的总糖含量,两个结果经统计检验没有显著性差异(α=0.05),说明求极大线性无关组的方法用于校正集样品的选择,可实现“少而精”选择样品的目的。此外,我们用求极大线性无关组选择校正集样品和随机方法选择校正集样品两种方法,选择了同样数目28,32,41,76,146,163个样品建模进行预测效果的对比实验,结果显示,求极大线性无关组法选择校正集建模的预测效果优于随机选择校正集建模的预测效果。     

Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators

A nonlinear (piecewise linear) optical transfer function for optical applications generally and isolator especially is introduced and a realization method for the introduced block based on array of two-port nonlinear ring resonators is proposed. The effect of system parameters on the transfer function is studied. The characteristics of the introduced nonlinear device such as the threshold value and the slope of linear part can be controlled using the coupling coefficients and ring lengths. We show that using our proposed idea, easily more than 30-dB isolation well over 3 THz can be obtained only with similar two rings. Also, insertion loss less than 1 dB can be obtained using optical amplifier between rings. The proposed circuit is compact (0.2 mm²) and easily can be integrated with semiconductor lasers as well as other integrated devices and systems. Finally, the analytical result for approximation of the threshold and slope of linear part is presented.     

A planar chiral nanostructure with asymmetric transmission of linearly polarized wave and huge optical activity in near-infrared band

Just like an electronic diode that allows the electrical current to flow in one direction only, a kind of chiral metamaterial structure with a similar functionality for the electromagnetic wave is proposed. The designed nanostructure that consists of twisted metallic split-ring resonators on both sides of a dielectric substrate achieves asymmetric transmission for a forward and backward propagating linearly polarized wave by numerical simulation in near-infrared band. Difference in transmission efficiency of the optimized structure between the same polarized waves incident from opposite directions can reach a maximum at the communication wavelength （1.55 μm）. Moreover, the simulation results of this structure also exhibit strong optical activity and circular dichroism.