A Lie theoretic categorification of the coloured Jones polynomial

We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labelled by an arbitrary finite-dimensional representation. As a special case, we obtain a categorification of the coloured Jones polynomial of links.     

Termination of a pinned spiral wave by the wave train with a free defect

Nonlinear Dynamics - Spiral waves in the cardiac tissue may cause life-threatening arrhythmia. Such waves can be anchored to a local heterogeneity and form stable pinned waves, which are difficult...     

水热法制备二氧化锡/钨酸铋复合光催化材料及其催化活性研究

本文用水热法制备了正交晶系的纳米球状结构的二氧化锡和正交晶系的由片状聚集成球状结构的钨酸铋,并且对二者进行了复合,制备出了二氧化锡/钨酸铋复合光催化材料。采用X射线衍射(XRD)、扫描电子显微镜(SEM)、比表面积测试仪(BET)、紫外可见分光光度计等技术对复合样品的结构、形貌、比表面积、孔容孔径和光学性质进行了表征。用碘钨灯模拟太阳光,分别以二氧化锡、钨酸铋和二氧化锡/钨酸铋复合材料为催化剂降解罗丹明B(RhB),研究所制备的二氧化锡/钨酸铋复合材料的光催化活性。光催化90 min时二氧化锡、钨酸铋和二氧化锡/钨酸铋对罗丹明B的降解率分别是9%、22%和30%。实验结果表明,在可见光下,二氧化锡/钨酸铋复合材料的光催化活性要高于单一的二氧化锡和钨酸铋。     

Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m

In this paper, we study the explicit expansion of the first order Melnikov function near a double homoclinic loop passing through a nilpotent saddle of order m in a near-Hamiltonian system. For any positive integer $m(m\ge 1)$, we derive the formulas of the coefficients in the expansion, which can be used to study the limit cycle bifurcations for near-Hamiltonian systems. In particular, for $m=2$, we use the coefficients to consider the limit cycle bifurcations of general near-Hamiltonian systems and give the existence conditions for 10, 11, 13, 15 and 16 (11, 13 and 16, respectively) limit cycles in the case that the homoclinic loop is of cuspidal type (smooth type, respectively) and their distributions. As an application, we consider a near-Hamiltonian system with a nilpotent saddle of order 2 and obtain the lower bounds of the maximal number of limit cycles.     

TBOR-shaped electro-optic modulator with dual output based on double-layer graphene

We proposed an electro-optic modulator with two-bus one-ring (TBOR) structure to improve the extinction ratio and reduce insert loss. It has a dual output compared with one-bus one-ring structure. In addition, double-layer graphene makes it possible for the modulation in the visible to mid-infrared wavelength range. It shows that this new electro-optic modulator can present two switching states well with low insertion loss, high absorption and high extinction ratio. At $\lambda =1550\text{ nm}$, when the switching states are based on the chemical potential, ${\mu }_{\mathrm{c}}=0.38\text{ eV}$ and ${\mu }_{\mathrm{c}}=0.4\text{ eV}$, the insertion losses of both output ports are less than 2 dB, the absorption of the output port coupled via a micro-ring reaches 45 dB and the extinction ratio reaches 14 dB. When the refractive index of the dielectric material is 4.2, the applied voltage will be less than 1.2 V, thus can be used in low-voltage CMOS technology.     

Energy-preserving trigonometrically fitted continuous stage Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems

Numerical Algorithms - Recently, continuous-stage Runge-Kutta-Nyström (CSRKN) methods for solving numerically second-order initial value problem $q^{\prime \prime }= f(q)$ have been proposed...     

Nb(iPrNPMe2)3Fe–PMe3: A potential high reactivity heterobimetallic catalyst for acetylene cycloadditions

Alkynes cycloaddition reactions are powerful tools for constructing cyclic molecules with optimal atom efficiency, but these reactions cannot proceed at ambient temperature without transition-metal catalysts. In this work, a heterobimetallic complex featuring an Nb–Fe triple bond, Nb(ⁱPrNPMe₂)₃Fe–PMe₃, has been evaluated as the potential catalyst for acetylene cycloaddition, using density functional theory. The calculated results show that the singlet-state (i.e. ground-state) Nb(ⁱPrNPMe₂)₃Fe–PMe₃ can be applied to benzene synthesis, but is not suitable for cyclobutadiene. Benzene can be obtained easily at room temperature and is the unique product on the singlet potential surface. The irradiation of infrared-red light can drive the excitation of singlet Nb(ⁱPrNPMe₂)₃Fe–PMe₃ to its triplet state. Both benzene and cyclobutadiene can be formed on the triplet reaction potential surface due to their low energy barriers. Therefore, Nb(ⁱPrNPMe₂)₃Fe–PMe₃ is a potential high reactivity heterobimetallic catalyst for the cyclotrimerization of alkynes. In the reaction process, the catalytic active site of Nb(ⁱPrNPMe₂)₃Fe–PMe₃ moves from niobium to iron.     

Mechanism and Stereoselectivity of the Elementometalation Process of Activated Alkyne RCCR(RCO2Me) by Cp2TaH3

The elementometalation process is a fundamental chemical step in several catalytic cycles. In this work, density functional theory computations have elucidated the detailed elementometalation mechanism of activated alkyne RCCR(RCO₂Me) by Cp₂TaH₃ and rationalized the selectivity in experimental findings. The calculated results show that in the formation process of (E)-olefin monohydride((E)-Pro), the Gibbs free energy barrier is low and the entire reaction is spontaneous and exothermic; thus, (E)-Pro can be formed easily. The formation of (Z)-η²-olefin monohydride complex ((Z)-Pro) is difficult due to its high Gibbs free energy barrier. The formation process (E)-Pro consists of the following five steps: hydride H1-shift, conformational isomerism 1, hydride H2-shift, conformational isomerism 2, and olefin coordination process. Topological analysis shows that there is a five-membered ring plane structure in the reaction pathway and that the final product (E)-Pro belongs to a typical η²-olefin monohydride complex. Our calculated results provide an explanation for experimental observations and useful insights for further development of olefin functionalization. © 2019 Wiley Periodicals, Inc.     

高效液相色谱法测定烯草酮合成废液中4-二甲氨基吡啶含量

采用高效液相色谱法测定烯草酮合成废液中4-二甲氨基吡啶含量,使用BDS Hypersil C18不锈钢柱(250mm×4.6mm),以甲醇∶水∶磷酸=60∶39.75∶0.25为流动相,使用紫外检测器,在波长254nm下进行测定。实验测定4-二甲氨基吡啶加标回收率为97.7%,变异系数为3.33%,线性相关系数为0.9994。