大跨桥梁参数识别响应面方法中的近似函数及样本选取

以某大跨斜拉桥实验室物理模型设计参数与动力特性之间复杂的隐式关系为对象,分析响应面模型中近似函数和试验样本对回归模型精度的影响。首先推导多项式和径向基函数响应面模型的建模方法,然后基于斜拉桥三维空间模型的有限元动力分析,比较分析完全二阶多项式与几种径向基函数模型在设计域和扩展设计域内以及噪声污染情况下的回归精度。最后对几种少量样本的试验设计方法和响应面试验设计方法进行了分析。结果表明,径向基函数模型各方面性能优于多项式模型,响应面实验设计方法优于其他方法,少量样本可采用D优化设计,较多样本情况下以中心复合设计较佳。     

Decay rates for the energy of a singular nonlocal viscoelastic system

This work deals with decay rates for the energy of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. We prove the decay rates for the energy of a singular one‐dimensional viscoelastic system with a nonlinear source term and nonlocal boundary condition of relaxation kernels described by the inequality $g_i^{\prime }\left(t\right)\le ?H\left(g_i\left(t\right)\right),\left(i=1,2\right)$ for all t ≥ 0, with H convex.     

Irreducible polynomials from a cubic transformation

Let $R(x)=g(x)/h(x)$ be a rational expression of degree three over the finite field ${\mathbb{F}}_q$. We count the irreducible polynomials in ${\mathbb{F}}_q[x]$, of a given degree, that have the form $h{(x)}^{\mathrm{deg}f}\cdot f(R(x))$ for some $f(x)\in {\mathbb{F}}_q[x]$. As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017.