“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).     

Size effects on tensile and fatigue behaviour of polycrystalline metal foils at the micrometer scale

Tensile and fatigue properties of as-rolled and annealed polycrystalline Cu foils with different thicknesses at the micrometer scale were investigated. Uniaxial tensile testing results showed that with decreasing foil thickness the uniform elongation decreases for both as-rolled and annealed foils, whereas the yield strength and ultimate tensile strength increase for as-rolled foils, but decrease for the annealed foils. For both the as-rolled or annealed foils, bending fatigue resistance decreases with decreasing the foil thickness. Deformation and fatigue damage behaviour of the free-standing foils were characterised as a function of foil thickness. In addition, the fatigue strength of various small-scale Cu foils was compared to understand the physical mechanisms of size effects on mechanical properties of the metallic material at micrometer scales.     

Addition of multiwalled carbon nanotube and graphene nanosheet in cobalt oxide film for enhancement of capacitance in electrochemical capacitors

In order to enhance the capacitance of electrochemical capacitors, multiwalled carbon nanotubes (MWCNTs) and graphene nanosheets (GNS) were added to cobalt oxide (Co₃O₄) paste. The composite film based on Co₃O₄/MWCNT/GNS (95:4:1 wt%) exhibited a capacitance of 294 F/g while the capacitance of Co₃O₄/MWCNT (95:5 wt%) and pure Co₃O₄ film is 205 and 163 F/g, respectively. The enhanced capacitance of Co₃O₄/MWCNT/GNS composite film was attributed to the electrochemical contributions of the Co₃O₄ nanoparticle attached to the GNS as well as their significantly increased specific surface areas by MWCNTs. Furthermore, the composite films showed faradaic redox capacitive behavior to double-layer capacitive behavior due to the different nanostructures of the composites.     

Coupling effects of depletion interactions in a three-sphere colloidal system

In a three-sphere system, the middle sphere is acted upon by two opposite depletion forces from the other two spheres. It is found that, in this system, the two depletion forces are coupled with each other and result in a strengthened depletion force. So the difference of the depletion forces of the three-sphere system and its corresponding two two-sphere systems is introduced to describe the coupling effect of the depletion interactions. The numerical results obtained by Monte-Carlo simulations show that this coupling effect is affected by both the concentration of small spheres and the geometrical confinement. Meanwhile, it is also found that the mechanisms of the coupling effect and the effect on the depletion force from the geometry factor are the same.