生态平衡制约下离散尺度结构种群的最优收获

研究基于扩展Leslie投影矩阵的离散尺度结构种群模型的最优收获问题,约束条件包括生态平衡和开发成本等.运用凸优化理论证明了最优收获策略的存在性,导出了最优收获模式,应用模型参数给出了收获比率.结论显示:最优策略具有两阶段结构.     

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

The construction and approximation of feedforward neural network with hyp erb olic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.     

Cauchy-type integral formula and Plemelj formula of hypermonogenic functions on unbounded domains

In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries.     

Dirac方程的特征函数的迹公式

本文研究具有周期有限带位势的Dirac算子, 利用Dirac算子与单值算子的交换性,定义Bloch函数和乘子曲线, 进而获得揭示Bloch函数与位势间内在关系的Dubrovin-Novikov型公式; 通过复球面上的留数计算, 最终分别得到相应于谱带左端点、右端点以及双侧端点的特征函数的迹公式.     

关于广义三项指数和的四次幂均值

The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.     

Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions

This paper deals with the stability analysis of a class of uncertain switched systems on non-uniform time domains. The considered class consists of dynamical systems which commute between an uncertain continuous-time subsystem and an uncertain discrete-time subsystem during a certain period of time. The theory of dynamic equations on time scale is used to study the stability of these systems on non-uniform time domains formed by a union of disjoint intervals with variable length and variable gap. Using the concept of common Lyapunov function, sufficient conditions are derived to guarantee the asymptotic stability of this class of systems on time scale with bounded graininess function. The proposed scheme is used to study the leader–follower consensus problem under intermittent information transmissions.