Upper bounds of Schubert polynomials

Science China Mathematics - Let w be a permutation of {1, 2, …, n}, and let D(w) be the Rothe diagram of w. The Schubert polynomial ${\mathfrak{S}_w}\left(x \right)$ can be realized as the...     

Existence and Uniqueness of Solutions to Time-delays Stochastic Fractional Differential Equations with Non-Lipschitz Coefficients

In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations.     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

原位氧化还原沉淀水热合成法制备LixMn2O4尖晶石

Li xMn2O4尖晶石是新一代的锂离子二次电池正极材料 [1], 其合成方法对材料的电化学性质影响很大[2].常规合成大多采用高温固相反应法, 此法具有反应温度高, 反应时间长, 容易产生缺陷和产物不纯净等缺点, 导致所合成的锂离子二次电池正极材料的性能较差. 目前用水热合成法制备电池正极材料Li xMn2O4尖晶石尚未见文献报道. 本文在常规水热合成法的基础上采用原位氧化还原沉淀水热合成法 [3]制备前驱物, 该法合成条件更温和, 而且使材料的综合性能得到了改善和提高. 