Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

光照和氮素对外来植物凤眼莲生长和生理特性的影响

通过研究不同光照和氮素营养处理的外来植物凤眼莲的生长、生物量分配、硝酸还原酶活性、游离氨基酸以及可溶性蛋白质含量变化，探讨其对环境适应性的生理学机制。凤眼莲表现出极强的可塑性，随光照和氮素营养的增加，凤眼莲生长速率明显加快，氮素代谢关键酶硝酸还原酶活性上升。根部吸收的硝酸根离子大部分运输到叶片中还原，氮素同化效率高。氨基酸含量和可溶性蛋白质含量呈现明显的变化，叶片可溶性蛋白质含量与根冠生物量分配显著相关。本研究表明风眼莲对光照和氮素表现出很强的适应性，其快速生长和高可塑性依赖于对环境变化的牛理响廊。     

Global axisymmetric classical solutions of full compressible magnetohydrodynamic equations with vacuum free boundary and large initial data

In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.     

Studies on photochromic benzimidazol[1,2a]pyrrolidin-2-ones from the condensation of 2-methyl-3-benzothienylethylidene-(isopropylidene)succinic anhydride with 1,2-diaminobenzenes

Novel photochromic benzimidazol[1,2a]pyrrolidin-2-ones, which give thermally stable highly coloured photochromes, have been synthesised by condensation of 2-methyl-3-benzothienylethylidene(isopropylidene)succinic anhydride with 1,2-diaminobenzene and its 4,5-dimethyl and 4,5-dimethoxy derivatives. The photochromic properties are reported.     

Fabrication and electrochemical performance of nickel ferrite nanoparticles as anode material in lithium ion batteries

Nano-sized nickel ferrite (NiFe₂O₄) was prepared by hydrothermal method at low temperature. The crystalline phase, morphology and specific surface area (BET) of the resultant samples were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) and nitrogen physical adsorption, respectively. The particle sizes of the resulting NiFe₂O₄ samples were in the range of 5–15 nm. The electrochemical performance of NiFe₂O₄ nanoparticles as the anodic material in lithium ion batteries was tested. It was found that the first discharge capacity of the anode made from NiFe₂O₄ nanoparticles could reach a very high value of 1314 mAh g⁻¹, while the discharge capacity decreased to 790.8 mAh g⁻¹ and 709.0 mAh g⁻¹ at a current density of 0.2 mA cm⁻² after 2 and 3 cycles, respectively. The BET surface area is up to 111.4 m² g⁻¹. The reaction mechanism between lithium and nickel ferrite was also discussed based on the results of cycle voltammetry (CV) experiments.     

Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers

This paper considers the problems of the chaos synchronization and chaos-based secure communication when the observer matching condition is not satisfied. An auxiliary drive signal vector which may satisfy the observer matching condition is constructed. By using the drive signals of original system, a step-by-step sliding mode observer is considered to obtain the exact estimates of the auxiliary drive signals and their derivatives. A reduced-order observer is designed to asymptotically estimate the states of the drive system. By using the estimates of states and the derivatives of the auxiliary signals, an information signal recovery method which does not use any derivative information of original drive system is developed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.     

Time-domain investigation of the tunneling modes in photonic heterostructure containing single-negative materials

We present a theoretical investigation into the energy transport and transient wave propagation in metamaterial tunneling structures consisting of ??-negative (ENG) and ??-negative (MNG) materials. It is proved that a conjugated matched ENG/MNG bilayer and a (zero-index-material doped) photonic crystal heterostructure can work as a sub-wavelength resonator at tunneling frequency. The tunneling modes need a certain time to achieve the steady state and the charge up characteristic time increases (nearly) exponentially with the thickness of the structures. Under the steady state, the wave in the single-negative-material structures is not evanescent, but a hybrid of a traveling wave and a reactive standing wave. The phase difference between the electric field and the magnetic field varies with the position and time. The investigation of transient wave propagation in the metamaterial tunneling structures will help us to understand the interaction process between wave and metamaterial and to design special functional apparatus.     

Approximation formulas for Landauʼs constants

In this paper, we establish approximation formulas for evaluating Landau?s constants.