人行荷载下梁式结构振动分析的DQ-IQ混合法

为了评估人行荷载作用下梁式结构的振动舒适度，利用微分求积-积分求积，即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程，首先利用IQ法离散与时间相关的Dirac函数，再利用DQ法把控制方程转化为二阶常系数微分方程，最后利用Newmark算法求解微分方程。以某钢结构连廊为例，利用DQ法计算结构自振频率并与解析解进行对比，结果验证了节点选取和边界条件施加的合理性，再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应，计算结果表明，DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。     

A Flexible Framework for Cubic Regularization Algorithms for Nonconvex Optimization in Function Space

We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework.     

Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equation

The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained.     

三次Gauss和及二项指数和的混合均值

我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式.     

Multifunctional land‐use value mapping and space type classification: A case study of Puge County,China

Land exhibits diverse functions under the combined influence of natural and human forces. A production–living–ecology functional classification system was constructed by integrating land, ecosystem, and landscape functions. The land functional value was calculated by systematically integrating ecosystem service value assessments. The primary and secondary functions, as well as combinations of different land‐use types, were determined using vertical and horizontal comparison methods. The production–living–ecology ranges were then delineated in Puge County, which is a typical mountain county in China. The production–living–ecology functions identified were well connected with the current land‐use types. The “production–living–ecology” space in Puge County showed obvious multifunctionality and agglomeration. The function identification system proposed in this paper integrated multiple methods, overcame the difficulty of direct quantitative identification of land functions. The methods used to map and quantify land function will enhance our ability to understand and model land system changes and adequately inform policies and planning. Summary for Managers

• The function valuation method constructed in this paper could be used to reflect the multifunctionality and importance of land use and provide guidance and a quantitative basis for regional development planning.
• The spatial classification results provided in this paper could offer a valuable reference for the land management department to scientifically formulate land use planning.
• Under the goal of creating a group‐type urban development pattern and constructing an ecological protection pattern in Puge County, the hotspot analysis results of this paper can provide decision‐making tools and alternative spatial plans.

     

Lyapunov inequalities for nabla Caputo boundary value problems

ABSTRACT

We will establish uniqueness of solutions to boundary value problems involving the nabla Caputo fractional difference under two-point boundary conditions and give an explicit expression for the Green's functions for these problems. Using the Green's functions for specific cases of these boundary value problems, we will then develop Lyapunov inequalities for certain nabla Caputo BVPs.     

Group divisible 3‐designs with block size four and group type 1ns1

In this article, we mainly consider the existence problem of a group divisible design GDD $\left(3,4,n+s\right)$ of type $1^n{s}^1$. We present two recursive constructions for this configuration using candelabra systems and construct explicitly a few small examples admitting given automorphism groups. As an application, several new infinite classes of GDD $\left(3,4,n+s\right)$s of type $1^n{s}^1$ are produced. Meanwhile a few new infinite families on candelabra quadruple systems with group sizes being odd and stem size greater than one are also obtained.     

Birnbaum‐Saunders distribution: A review of models,analysis, and applications

Birnbaum and Saunders introduced a two‐parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix‐variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research.