On almost sure max-limit theorems of complete and incomplete samples from stationary sequences

Let M _n denote the partial maximum of a strictly stationary sequence (X _n ). Suppose that some of the random variables of (X _n ) can be observed and let [(M)tilde]_ntilde M_n stand for the maximum of observed random variables from the set {X ₁, ..., X _n }. In this paper, the almost sure limit theorems related to random vector ([(M)tilde]_ntilde M_n , M _n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.     

空间几何角度下看代入法求条件极值

通过具体实例,借助matlab作图,阐述了代入法求条件极值的几何含义和理论依据,指出了这种解法容易遗漏极值点的原因,并根据代入法的使用限制归纳了三种常见的代入形式,为学习者正确使用代入法提供参考.     

基于主成分的改进雷达图及其在综合评价中的应用

本文从可视化角度出发,在总结传统可视化方法因优点与不足的基础上,将主成分分析、因子分析与雷达图结合,改进了传统的可视化方法。并将新的可视化方法引入到综合评价中,提出了一种基于雷达图面积的综合评价模型,实例验证该种方法切实有效。     

Numerical method for the inverse heat transfer problem in composite materials with Stefan-Boltzmann conditions

In this paper, one specific kind of heat transfer problem with nonlinear Stefan-Boltzmann conditions are considered in a three dimensional multi-layer domain. Theoretical results for forward and inverse problems are presented. Numerical simulations of specific models from applications are provided to demonstrate the heat transfer process in the composite materials of forward problem. One reconstruction method is proposed to find the corrosion part, and the numerical examples show that the reconstruction algorithm is effective.     

On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G（2, 5）

Let s ： S2 → G（2, 5） be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G（2, 5）. It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions.     

A class of nonlinear integrodifferential impulsive periodic systems of mixed type and optimal controls on Banach space

A class of nonlinear integrodifferential impulsive periodic systems of mixed type on Banach space is considered. Existence of periodic PC-mild solutions is proved. Existence of periodic optimal pairs of systems governed by nonlinear impulsive integrodifferential equations of mixed type is also presented. An example is given for demonstration.     

Carbon cloth supported lithiophilic carbon nanotubes@Ag skeleton for lithium anode via ultrafast Joule heating method

Journal of Solid State Electrochemistry - Regulating lithium deposition and stripping behavior during cycles is critical for constructing high-performance and stable lithium metal anodes (LMAs)....     

Activating Bi p-orbitals in Dispersed Clusters of Amorphous BiOx for Electrocatalytic Nitrogen Reduction

Catalytic strategies based on main group metals are significantly less advanced than those of transition metal catalysis, leaving untapped areas of potentially fruitful research. We here demonstrate an effective approach for the modulation of Bi 6p energy levels during the construction of atomically dispersed clusters of amorphous BiO_x. Bi oxidation state is proposed to strongly affects the nitrogen fixation activity, with the half-occupied p_z orbitals of the Bi²⁺ ions being highly efficient toward electron injection into the inert N₂ molecule. With sufficient catalytic sites to adsorb and activate N₂, the bonding between N₂ and catalyst is able to be in situ identified. The catalyst shows an outstanding Faraday efficiency (≈30 %) and high yield (≈113 μg h⁻¹ mg⁻¹_cat) in NH₃ production, outperforming most of the existing catalysts in aqueous solution. These results lay the basis for developing the potential of p-block elements for catalysis of multi-electron reactions.     

Correlating Polysulfide Solvation Structure with Electrode Kinetics towards Long-Cycling Lithium–Sulfur Batteries

Lithium–sulfur (Li−S) batteries are promising due to ultrahigh theoretical energy density. However, their cycling lifespan is crucially affected by the electrode kinetics of lithium polysulfides. Herein, the polysulfide solvation structure is correlated with polysulfide electrode kinetics towards long-cycling Li−S batteries. The solvation structure derived from strong solvating power electrolyte induces fast anode kinetics and rapid anode failure, while that derived from weak solvating power electrolyte causes sluggish cathode kinetics and rapid capacity loss. By contrast, the solvation structure derived from medium solvating power electrolyte balances cathode and anode kinetics and improves the cycling performance of Li−S batteries. Li−S coin cells with ultra-thin Li anodes and high-S-loading cathodes deliver 146 cycles and a 338 Wh kg⁻¹ pouch cell undergoes stable 30 cycles. This work clarifies the relationship between polysulfide solvation structure and electrode kinetics and inspires rational electrolyte design for long-cycling Li−S batteries.     

Symmetry-Broken Intermolecular Charge Separation of Cationic Radicals

A quadrupolar compound Pyr-BA with two pyrrole-type nitrogen atoms doped externally was prepared in this work. In high contrast with other π ionic radicals, its cationic radical Pyr-BA ⋅ ⁺ undergoes unusual symmetry-broken charge separation (SB-CS), generating the mixed valence complex of Pyr-BA^+1−q ⋅⋅⋅ Pyr-BA^+1+q , where q is the degree of charge transfer. Variable-temperature (VT) single-crystal analysis, absorption and EPR experiments all confirmed that aggregation and lower temperature would help to facilitate this SB-CS process. Gibbs energy calculations and gauge-including magnetically induced current simulation both validate that, for Pyr-BA ⋅ ⁺ , SB-CS behavior is more favorable than the conventional dimerization mode. To the best of our knowledge, this is the first study that shows solid single-crystal evidence for spontaneous SB-CS between identical ionic radicals. Such a unique phenomenon is of great significance both in terms of fundamental aspects and uncharted material science.