On C1-class local diffeomorphisms whose periodic points are nonuniformly expanding

Using a sifting-shadowing combination, we prove in this paper that an arbitrary C¹-class local diffeomorphism f of a closed manifold M ⁿ is uniformly expanding on the closure ${\mathrm{Cl}_{M^n}(\mathrm{Per}(f))}$ of its periodic point set Per(f), if it is nonuniformly expanding on Per(f).     

On σ(·, W)-Holomorphic Functions and Theorems of Vitali-Type

The aim of this paper is to give some criterions for holomorphy of F-valued σ(F, W)-holomorphic functions which are bounded on bounded sets in a domain D of Fréchet spaces E (resp. ${\mathbb{C}^n}$ ) where ${W \subset F'}$ defines the topology of Fréchet space F. Base on these results we consider the problem on holomorphic extension of F-valued σ(F, W)-holomorphic functions from non-rare subsets of D and from subsets of D which determines uniform convergence in H(D). As an application of the above, some theorems of Vitali-type for a locally bounded sequence ${\{f_i\}_{i \in \mathbb{N}}}$ of Fréchet-valued holomorphic functions are also proved.     

“韩信点兵”问题新解

对"韩信点兵"问题的解法进行新解,给出了较孙子定理简便的求同余式组最小正整数解的一种递推公式解法.     

The Existence and Multiplicity of Solutions for Second-order Impulsive Differential Equations on the Half-line

In this paper, we consider the existence and multiplicity of solutions for a class of nonlinear impulsive problem on the half-line. By using a variational method and a variant fountain theorem, we obtain some new criteria to guarantee that the impulsive problem has at least one solution and infinitely many solutions respectively. We extend and improve some recent results.     

Valorization of Rice Straw via Hydrotropic Lignin Extraction and Its Characterization

Rice straw hydrotropic lignin was extracted from p-Toluene sulfonic acid (p-TsOH) fractionation with a different combined delignification factor (CDF). Hydrotropic lignin characterization was systematically investigated, and alkaline lignin was also studied for the contrast. Results showed that the hydrotropic rice straw lignin particle was in nanometer scopes. Compared with alkaline lignin, the hydrotropic lignin had greater molecular weight. NMR analysis showed that β-aryl ether linkage was well preserved at low severities, and the unsaturation in the side chain of hydrotropic lignin was high. H units and G units were preferentially degraded and subsequently condensed at high severity. High severity also resulted in the cleavage of part β-aryl ether linkage. ³¹P-NMR showed the decrease in aliphatic hydroxyl groups and the increasing carboxyl group content at high severity. The maximum weight loss temperature of the hydrotropic lignin was in the range of 330–350 °C, higher than the alkaline lignin, and the glass conversion temperature (T_g) of the hydrotropic lignin was in the range of 107–125 °C, lower than that of the alkaline lignin. The hydrotropic lignin has high β-aryl ether linkage content, high activity, nanoscale particle size, and low T_g, which is beneficial for its further valorization.     

Standard Systems of Discrete Differentiable Dynamical Systems

The theory of Liao standard systems of difference equations for discrete differentiable dynamical systems over compact manifolds has been developed. Some relations between the topological structures of their phase portraits and that of their corresponding linear systems have been presented as well.     

A Nonstandard Finite Difference Scheme for Solving One Dimensional Nonlinear Heat Transfer

A nonstandard finite difference scheme is developed to solve an initial-boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. Not only does the scheme satisfy the positivity condition, but it is also stable for large values of the equation parameters.     

Convergence in Law to Operator Fractional Brownian Motions

In this paper, we provide two approximations in law of operator fractional Brownian motions. One is constructed by Poisson processes, and the other generalizes a result of Taqqu (Z. Wahrscheinlichkeitstheor. Verw. Geb. 31:287–302, 1975).