On the Crossing Number of <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> □ <Emphasis Type="Italic">P</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

Crossing numbers of graphs are in general very difficult to compute. There are several known exact results on the crossing number of the Cartesian products of paths, cycles or stars with small graphs. In this paper we study cr(K_m □ P_n), the crossing number of the Cartesian product K_m □ P_n. We prove that for m ≥ 3,n ≥ 1 and cr(K_m □ P_n)≥ (n − 1)cr(K_m+2 − e) + 2cr(K_m+1). For m≤ 5, according to Klešč, Jendrol and Ščerbová, the equality holds. In this paper, we also prove that the equality holds for m = 6, i.e., cr(K₆ □ P_n) = 15n + 3. Research supported by NFSC (60373096, 60573022).     

解高阶抛物型方程的高精度显式差分格式

1 引言 1960年,Saul’ev在文中讨论了如下的高阶(2m阶)抛物型方程 μ/t=(-1)~(m 1)~2mμ/x~(2m) (1)(其中m为正整数),提出了一类含极因子α的两层差分格式。当α=0时为显式格式,其稳定性条件为,r=△t/(△x)~(2m)<1/2~(2m-1),△t,△x分别为时间及空间步长。随后,文[2],[3]利用     

莱茵衣藻(Chlamydomonas reinhardtii)中叶绿素b生物合成的遗传控制研究进展

光合作用是植物生理学研究的重要领域.莱茵衣藻是用于研究光合作用遗传的重要模式植物.本文以叶绿素b的合成途径为线索,阐述了以莱茵衣藻为工具,对合成途径各调控酶及其编码基因的研究成果.重点讨论对比了有关叶绿素b合成的不同观点,对于CAO基因与CBN1基因这两个叶绿素b的主控基因进行了分析,提出要弄清叶绿素b的合成途径,首先要弄清两基因是否为同源基因.用“点滴试法”与彩色数字成像法对莱茵衣藻色素调节基因突变株进行检测和分析,通过筛选调控基因相关突变株,就可为莱茵衣藻中叶绿素b生物合成相关基因调控机制的研究尊定基础.     

Three‐Dimensional Multilayer Assemblies of MoS2/Reduced Graphene Oxide for High‐Performance Lithium Ion Batteries

Three‐dimensional (3D) multilayer molybdenum disulfide (MoS₂)/reduced graphene oxide (RGO) nanocomposites are prepared by a solution‐processed self‐assembly based on the interaction using different sizes of MoS₂ and GO nanosheets followed by in situ chemical reduction. 3D multilayer assemblies with MoS₂ wrapped by large RGO nanosheets and good interface are observed by transmission electron microscopy. The interaction of Na⁺ ions with oxygen‐containing groups of GO is also investigated. The measurement of lithium ion batteries (LIBs) shows that MoS₂/RGO anode nanocomposite with a weight ratio of MoS₂ to GO of 3:1 exhibits an excellent rate performance of 750 mAh g^?1 at 3 A g^?1 outperforming many previous studies and a high reversible capacity up to ≈1180 mAh g^?1 after 80 cycles at 100 mA g^?1. Good rate performance and high capacity of MoS₂/RGO with 3D unique layered‐structures are attributed to the combined effects of continuous conductive networks of RGO, good interface facilitating charge transfer, and strong RGO sheets preventing the volume expansion. Results indicate that 3D multilayer MoS₂/RGO prepared by a facile solution‐processed assembly can be developed to be an excellent nanoarchitecture for high‐performance LIBs.     

Oleylamine‐Assisted Phase‐Selective Synthesis of Cu2−xS Nanocrystals and the Mechanism of Phase Control

Environmentally friendly Cu_2?x S compounds exist in many different mixed phases in nature, while their nanoscale counterparts can be pure phase with interesting localized surface plasmon resonance properties. Because of the complexity of composition and phase, controllable synthesis of Cu_2?x S nanocrystals becomes an important scientific issue in colloidal chemistry. In this work, a hot‐injection method is developed to synthesize Cu_2?x S nanocrystals by injecting a sulfur precursor into a copper precursor using oleylamine and octadecene as solvents. By varying the reaction parameters (temperature, volume ratio of oleylamine/octadecene, molar ratio of Cu/S in the precursors), hexagonal CuS, monoclinic Cu_1.75S, and rhombohedral Cu_1.8S, nanocrystals can be selectively synthesized, providing a platform to illustrate the mechanism of crystal phase control. The crystal phase control of Cu_2?x S nanocrystals is oleylamine‐determined by controlling the molar ratio of Cu/S in the reaction precursors as well as the ratio of Cu_2?x S clusters/Cu⁺ in the subsequent reaction. More importantly, temperature plays an important role in varying the molar ratio of Cu/S and Cu_2?x S clusters/Cu⁺ in the reaction system, which significantly influences the crystal phase of the resulting Cu_2?x S nanocrystals. The understanding into crystal control provides a guideline to realize reproducible phase‐selective synthesis and obtain well‐defined high‐quality materials with precise control.     

Nanochemoprevention by encapsulation of (-)-epigallocatechin-3-gallate with bioactive peptides/chitosan nanoparticles for enhancement of its bioavailability

Nanochemoprevention by oral consumption was developed by the encapsulation of (-)-epigallocatechin-3-gallate (EGCG) with nanoparticles that were electrostatically assembled from bioactive caseinophosphopeptides and chitosan, which was highly biocompatible and able to enhance the bioavailability of EGCG.     

Organic photoresponse materials and devices

Organic photoresponse materials and devices are critically important to organic optoelectronics and energy crises. The activities of photoresponse in organic materials can be summarized in three effects, photoconductive, photovoltaic and optical memory effects. Correspondingly, devices based on the three effects can be divided into (i) photoconductive devices such as photodetectors, photoreceptors, photoswitches and phototransistors, (ii) photovoltaic devices such as organic solar cells, and (iii) optical data storage devices. It is expected that this systematic analysis of photoresponse materials and devices could be a guide for the better understanding of structure-property relationships of organic materials and provide key clues for the fabrication of high performance organic optoelectronic devices, the integration of them in circuits and the application of them in renewable green energy strategies (critical review, 452 references).     

High Performance Phototransistors of a Planar Conjugated Copolymer

A planar conjugated copolymer named HXS‐1 was applied in thin film phototransistors. Similar to organic field‐effect transistors using V_G to control the source‐drain current, in phototransistors, the light is used to substitute V_G as an independent variable to control the output of the transistors to realize light detection and signal magnification in a single organic device. All devices exhibited high performance with an on/off ratio up to 4.6 × 10⁴ (the highest on/off ratio of organic or polymer phototransistors), which could be assigned to i) the wide absorption features of HXS‐1 in the whole UV‐vis range, ii) the ideal HOMO energy level of HXS‐1 (5.21 eV) to align with Au electrodes (5.2 eV) and iii) the high mobility of the polymer thin films (∼0.06 cm²/Vs). Moreover, the devices, both under continuous operation conditions and long term measurement conditions, exhibited excellent stability, indicating potential applications of the devices in polymer‐based optoelectronics.

     

Highly active Pd/WO3-CNTs catalysts for formic acid electrooxidation and study of the kinetics

The new Pd/WO₃-CNTs catalysts are prepared for formic acid electrooxidation in direct formic acid fuel cells (DFAFCs). According to XRD, TEM, and HRTEM results, WO₃ particles are covered or overlapped with Pd particles, which have a uniform and narrow size distribution due to the highly dispersion of WO₃-CNTs. The electrochemical results show significantly enhanced electrocatalytic performances for formic acid oxidation on Pd/WO₃-CNTs catalysts, especially its dramatically improved stability and excellent tolerance to CO poisoning, which is mainly ascribed to the interaction between Pd and WO₃. Therefore, Pd/WO₃-CNTs catalysts show the great potential as less expensive and more efficient electrocatalyst for DFAFCs. Additionally, the kinetic parameters such as the charge transfer parameter and the diffusion coefficient of formic acid electrooxidation on 20 %Pd/20 %WO₃-CNTs were obtained.

The new Pd/WO₃-CNTs catalysts are prepared and studied in the oxidation of formic acid, and the significantly enhanced electrocatalytic performances, especially its dramatically improved stability and excellent tolerance to CO poisoning show great potential as less expensive and more efficient electrocatalyst for the direct formic acid fuel cells.     

基于不同时间步长时域非结构有限体积法模拟声-弹性耦合问题

介绍一种改进的时域非结构有限体积法(FVM),并将其应用于声-弹性耦合问题.在流体与固体介质中分别求解声波动方程与弹性波方程,根据交界面上的力平衡与质点振速连续条件考虑二者的相互作用.同时考虑双线性四边形单元的线性变化项及常数项,并结合常应变三角形单元处理混合网格问题.分别对三角形单元和四边形单元进行色散分析,给出声波动方程的稳定性条件.在不同介质中采用不同时间步长,提高计算效率.求解弹性波问题、声-弹性耦合问题,结果表明,改进后的方法求解声-弹性耦合问题是有效和准确的,并且具有良好的数值稳定性.