Layered Orthorhombic Nb2O5@Nb4C3Tx and TiO2@Ti3C2Tx Hierarchical Composites for High Performance Li‐ion Batteries

Engineering electrode nanostructures is critical in developing high‐capacity, fast rate‐response, and safe Li‐ion batteries. This study demonstrates the synthesis of orthorhombic Nb₂O₅@Nb₄C₃T_x (or @Nb₂CT_x) hierarchical composites via a one‐step oxidation —in flowing CO₂ at 850 °C —of 2D Nb₄C₃T_x (or Nb₂CT_x) MXene. The composites possess a layered architecture with orthorhombic Nb₂O₅ nanoparticles decorated uniformly on the surface of the MXene flakes and interconnected by disordered carbon. The composites have a capacity of 208 mAh g^?1 at a rate of 50 mA g^?1 (0.25 C) in 1–3 V versus Li⁺/Li, and retain 94% of the specific capacity with 100% Coulombic efficiency after 400 cycles. The good electrochemical performances could be attributed to three synergistic effects: (1) the high conductivity of the interior, unoxidized Nb₄C₃T_x layers, (2) the fast rate response and high capacity of the external Nb₂O₅ nanoparticles, and (3) the electron “bridge” effects of the disordered carbon. This oxidation method was successfully extended to Ti₃C₂T_x and Nb₂CT_x MXenes to prepare corresponding composites with similar hierarchical structures. Since this is an early report on producing this structure, there is much room to push the boundaries further and achieve better electrochemical performance.     

Infinitely many homoclinic orbits for a class of second‐order damped differential equations

We investigate the existence and multiplicity of homoclinic orbits for the second‐order damped differential equations For Equation 1 where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, and W, we get infinitely many homoclinic orbits for superquadratic, subquadratic and concave–convex nonlinearities cases by using fountain theorem and dual fountain theorem in critical point theory. These results generalize and improve some existing results in the literature. Copyright © 2015 JohnWiley & Sons, Ltd.     

ON DISCRETE PHENOMENA IN THE MIXED PROBLEM

On discrete phenomena in uniqueness of the initial value problem, F. Treves studied an interesting example and proved that the Oauohy problem \[\left\{ \begin{array}{l} {L_p}u = {u_{xx}} - {x^2}{u_{tt}} + p{u_t} = 0,t \ge 0;\u(x,0) = {u_t}(x,0) = 0, \end{array} \right.\] has non-triyial solutions if and only if p = 3, 5, …. Wang Guang-ymg and others proved that the Oauohy problem \[\left\{ \begin{array}{l} {L_p}u = 0,t \ge 0;\u(x,0) = {\varphi _1}(x);{u_t}(x,0) = {\varphi _2}(x), \end{array} \right.\] and Goursat problem \[\left\{ \begin{array}{l} {L_p}u = 0,t \ge \frac{{{x^2}}}{2};\u(x,\frac{{{x^2}}}{2}) = {\varphi _3}(x), \end{array} \right.\] both have a unique solution if and only if p≠1, 3, 5, …. In this paper, we discuss in detail the equation Lvu = 0 for discrete phenomena. We prove that solution of the mixed problem \[\left\{ \begin{array}{l} {L_p}u = 0,x \ge 0,t \ge 0,\u(x,0) = \varphi (x),\{u_t}(x,0) = \psi (x),\u(0,t) = 0 \end{array} \right.\] is not only existent but also unique, for р≠3, 7, 11，…，neither existence nor uniqueness could be proved in this problem, for p = 3, 7, 11，….，more precisely, only under some compatibility condition can the solution exist for the equation \({L_p}u = 0\).     

一锅反应合成1—三甲硅氧基烯丙基膦酸酯

1-三甲硅氧基膦酸酯是一类具有显著生物活性的有机硅磷化合物。具有药效长、毒性低等特点,采用含P—O—Si键的亚磷酸酯与羰基化合物反应的方法进行合成,反应条件温和,产率比较高,但需要先制备化学性质活泼的含硅基亚磷酸酯,而且反应要在惰性气体下进行,实施有所不便。本文直接采用三烷基亚磷酸酯(1)、α、β-不饱和醛(2)与三甲基氯硅烷进     

具重特征的偏微分方程柯西问题的离散现象

1.引言 众所周知,人们对主型方程,即无重实特征的线性偏微分方程,已有了很好的了解,而对远较主型方程复杂得多的具重特征方程却认识得较少,目前大体上还只停留在个别例子的水平上。грушпн,в.в.首先举例指出重特征方程在解的光滑性问题中有所谓离散现象,即方程中的参量取一些离散的例外值时,解突然失去了光滑性。接着Treves,F.在类似的例子中发现了这种离散现象也出现在Cauchy问题解的唯一性问题中,王光寅等对Treves例子的离散现象作了进一步的深刻揭示。Menikoff,A.曾讨论了以下Treves例子为特例的更广泛一类的重特征方程     

Design,synthesis and evaluation of lactoside-derived galectin-3 inhibitors

Based on docking computation, a panel of lactoside derivatives have been designed as galectin-3 inhibitors. Suitable functional group modifications at C′-3 of methyl lactoside were predicted to supply some additional π–cation, π…H–O, and hydrogen bond interactions between the designed substrates and galectin-3 residues. The selected compounds, giving higher TotalScore in docking calculations, were thus synthesized, and their binding affinities toward galectin-3 were evaluated with SPR assay.     

A Robust,Freestanding MXene‐Sulfur Conductive Paper for Long‐Lifetime Li–S Batteries

Freestanding, robust electrodes with high capacity and long lifetime are of critical importance to the development of advanced lithium–sulfur (Li–S) batteries for next‐generation electronics, whose potential applications are greatly limited by the lithium polysulfide (LiPS) shuttle effect. Solutions to this issue have mostly focused on the design of cathode hosts with a polar, sulfurphilic, conductive network, or the introduction of an extra layer to suppress LiPS shuttling, which either results in complex fabrication procedures or compromises the mechanical flexibility of the device. A robust Ti₃C₂T_x/S conductive paper combining the excellent conductivity, mechanical strength, and unique chemisorption of LiPSs from MXene nanosheets is reported. Importantly, repeated cycling initiates the in situ formation of a thick sulfate complex layer on the MXene surface, which acts as a protective membrane, effectively suppressing the shuttling of LiPSs and improving the utilization of sulfur. Consequently, the Ti₃C₂T_x/S paper exhibits a high capacity and an ultralow capacity decay rate of 0.014% after 1500 cycles, the lowest value reported for Li–S batteries to date. A robust prototype pouch cell and full cell of Ti₃C₂T_x/S paper // lithium foil and prelithiated germanium are also demonstrated. The preliminary results show that Ti₃C₂T_x/S paper holds great promise for future flexible and wearable electronics.     

含氮烃基膦酸的合成(Ⅳ)——以环丁砜作溶剂直接合成N-烃基-α-氨基苄基膦酸

具有生物活性的 α-氨基烃基膦酸的合成有过报道^[1], 而氮烃基-α-氨基烃基膦酸的合成报道较少. 应用醛、苄胺与亚磷酸酯反应后在强酸条件下水解得到取代的 α-氨基烃基膦酸^{[2, 3]}.IssIeib用三甲基硅基膦酸与席夫碱加成然后再水解^[4]. 这些方法尽管得到相应的膦酸产物,但它的水解却需要较长时间。     

非线性奇性椭圆边值问题解的存在性

设X=(x_1,x_2,…,X_n)∈R~n,E_0是半空间x_n≥0.Ω(?)E_o是有界的光滑区域,(?)Ω=S_1US_2,此处S_1在超平面X_n=0上,而S_2整个地位于X_n>0上.讨论非线性奇性椭圆边值问题     

直接催化氧化苯制苯酚的研究简介

由苯直接羟基化制苯酚有几种催化反应,包括阳极氧化法、N2O氧化法、H2O2氧化法、O2直接氧化法,这些反应均具有良好的原子经济性和环境效益。