Applications of Mathematics最新文献

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Anisotropic viscoelastic body subjected to the pulsating load 受脉动载荷作用的各向异性粘弹性体

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 2023-09-14 DOI: 10.21136/AM.2023.0256-22

Jozef Sumec, Mária Minárová, L’uboš Hruštinec

Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later on, a simply supported straight concrete beam reinforced by the steel fibres is taken as an investigated domain. The reinforcement is considered and dealt as scattered within the beam. Material characteristics are determined in line with the theory of the reinforcement. Sinusoidal load is taken as the action, stress reaction function is observed. By exploitation of the Fourier transform within the stress-strain relation analysis, both time and frequency interpretation of the constitutive relation can be performed.

研究了各向异性材料固相连续介质力学的本构方程。首先，研究了任意变形载荷作用下的天气性一维Maxwell模型。导出了应力与应变关系的显式。在此基础上，对三维空间的显式本构方程进行了数学处理。随后，以钢纤维加固的简支直混凝土梁为研究对象。钢筋被认为是分散在梁内的。材料特性是根据钢筋理论确定的。以正弦载荷为作用，观察应力反应函数。利用应力-应变关系分析中的傅里叶变换，可以实现本构关系的时间和频率解释。

引用次数: 0

Inexact Newton-type method for solving large-scale absolute value equation Ax − |x| = b 求解大规模绝对值方程 Ax - |x| = b 的非精确牛顿式方法

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 2023-08-31 DOI: 10.21136/AM.2023.0171-22

Jingyong Tang

Newton-type methods have been successfully applied to solve the absolute value equation Ax − |x| = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique, which is well-defined and easy to implement. We prove that the proposed method has global and local superlinear convergence under the condition that the interval matrix [A − I, A + I] is regular. This condition is much weaker than those used in some Newton-type methods. Numerical results show that our method has fairly good practical efficiency for solving large-scale AVEs.

牛顿型方法已成功应用于求解绝对值方程 Ax - |x| = b（用 AVE 表示）。这类方法通常在每次迭代中精确求解线性方程组。然而，对于大规模的 AVE，精确求解相应的系统可能代价高昂。本文提出了一种求解 AVE 的非精确牛顿型方法。在每次迭代中，所提出的方法只能近似地求解相应的系统。此外，它采用了一种新的线搜索技术，定义明确且易于实现。我们证明，在区间矩阵 [A - I, A + I] 规则的条件下，所提出的方法具有全局和局部超线性收敛性。这一条件比某些牛顿型方法所使用的条件要弱得多。数值结果表明，我们的方法在求解大规模 AVE 时具有相当好的实用效率。

引用次数: 0

Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory 用特罗特理论对具有诺顿或特雷斯卡摩擦的非线性开尔文-沃依格粘弹性薄板的瞬态响应进行渐近建模

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 2023-07-21 DOI: 10.21136/AM.2023.0013-23

Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht, Thibaut Weller

We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical data of the problem, the asymptotic analysis of its unique solution leads to different limit models whose properties are detailed. We highlight the appearance of an additional state variable that allows us to write these limit systems of equations in the same form as the genuine problem.

我们研究了由非线性开尔文-伏依格特材料制成的粘弹性薄板的动态响应，该薄板沿其具有诺顿或特雷斯卡摩擦力的横向边界的一部分与刚体发生双边接触。我们选择直接使用作用于可变空间的算子半群收敛的特劳特理论。根据问题的物理和几何数据的各种相对行为，对其唯一解的渐近分析导致了不同的极限模型，并详细介绍了这些模型的特性。我们强调了附加状态变量的出现，它使我们能够以与真正问题相同的形式写出这些极限方程组。

引用次数: 0

Inverse rate-dependent Prandtl-Ishlinskii operators and applications 逆速率相关Prandtl-Ishlinskii算子及其应用

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 2023-02-09 DOI: 10.21136/AM.2023.0231-22

Mohammad Al Janaideh, Pavel Krejčí, Giselle Antunes Monteiro

In the past years, we observed an increased interest in rate-dependent hysteresis models to characterize complex time-dependent nonlinearities in smart actuators. A natural way to include rate-dependence to the Prandtl-Ishlinskii model is to consider it as a linear combination of play operators whose thresholds are functions of time. In this work, we propose the extension of the class of rate-dependent Prandtl-Ishlinskii operators to the case of a whole continuum of play operators with time-dependent thresholds. We prove the existence of an analytical inversion formula, and illustrate its applicability in the study of error bounds for inverse compensation.

在过去的几年中，我们观察到对速率相关滞后模型的兴趣增加，以表征智能执行器中复杂的时间相关非线性。将速率依赖性纳入Prandtl-Ishlinskii模型的一种自然方法是将其视为游戏算子的线性组合，其阈值是时间的函数。在这项工作中，我们提出了将率相关的Prandtl-Ishlinskii算子类扩展到具有时间相关阈值的游戏算子的整个连续体的情况。证明了解析反演公式的存在性，并说明了其在逆补偿误差界研究中的适用性。

引用次数: 0

Exact controllability of linear dynamical systems: A geometrical approach 线性动力系统的精确可控性:一种几何方法

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 2016-01-01 DOI: 10.21136/AM.2016.0427-15

M. García-Planas

In recent years there has been growing interest in the descriptive analysis of complex systems, permeating many aspects of daily life, obtaining considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems it is of interest to study the exact controllability; this measure is defined as the minimum set of controls that are needed in order to steer the whole system toward any desired state. In this paper, we focus the study on the obtention of the set of all B making the system (A, B) exact controllable.

近年来，人们对复杂系统的描述性分析越来越感兴趣，这些系统渗透到日常生活的许多方面，在描述其结构和动力学特性方面取得了相当大的进展。然而，很少有人致力于研究发生在它们身上的动力学的可控性。具体地说，对于复杂系统，研究精确的可控性是很有意义的;这个度量被定义为将整个系统引导到任何期望状态所需的最小控制集。本文主要研究了所有B的集合的注意性，使系统(A, B)精确可控。

引用次数: 5

A stability result for a class of nonlinear integrodifferential equations with L1 kernels 一类具有L1核的非线性积分微分方程的稳定性结果

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 2008-01-01 DOI: 10.4064/AM35-4-2

P. Cannarsa, D. Sforza

We study the generation of analytic semigroups in the L-2 topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimensions, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type estimates for degenerate parabolic operators.

研究了L-2拓扑上可在空间域边界简并的二阶散度椭圆算子生成解析半群的问题。我们的结果在两个空间维度上成立，保证了相应演化问题的解支持分部积分。因此，本文为导出退化抛物算子的Carleman型估计提供了依据。

引用次数: 13

Efficient robust estimation of time-series regression models 时间序列回归模型的有效鲁棒估计

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 2007-10-01 DOI: 10.2139/ssrn.1068624

P. Čížek

The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.

本文研究了一类基于两步最小加权二乘(2S-LWS)估计的鲁棒回归估计，该估计采用由初始鲁棒拟合得到的回归残差的经验分布或分位数函数确定的数据自适应权值。与许多现有的两步鲁棒方法一样，所提出的2S-LWS估计器保持了初始鲁棒估计的鲁棒性。然而，与现有方法相反，在温和条件下，2S-LWS的一阶渐近行为完全独立于初始估计。我们提出了在横截面和时间序列数据中都表现良好的数据自适应加权方案，并证明了结果过程的渐近正态性和效率。一个模拟研究在有限的样本中证明了这些理论性质。

引用次数: 11

70th birthday of Vratislav Horálek 弗拉季斯拉夫70岁生日Horálek

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 1996-01-01 DOI: 10.21136/am.1996.134323

V. Beneš, I. Saxl

引用次数: 0

Combining the preconditioned conjugate gradient method and a matrix iterative method 将预条件共轭梯度法与矩阵迭代法相结合

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 1996-01-01 DOI: 10.21136/am.1996.134311

J. Zítko

Summary. The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated . The initial approxima tion for conjugate gradient is constructed as a result o f a matrix iteration method after 77i steps . The behaviour o f the error vector for such a combined method is studied and special numerical tests and conclusions are made.

总结。研究了求解具有正定矩阵的线性代数方程组的预条件共轭梯度法。采用矩阵迭代法，经过77i步，构造了共轭梯度的初始近似。对这种组合方法的误差矢量特性进行了研究，并进行了专门的数值试验和结论。

引用次数: 5

Reissner-Mindlin model for plates of variable thickness. Solution by mixed-interpolated elements 变厚板的Reissner-Mindlin模型。混合插值元解法

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics

Pub Date : 1996-01-01 DOI: 10.21136/am.1996.134313

I. Hlavácek

Hard clamped and hard simply supported elastic plate is considered. The mixed finite element analysis combined with some interpolation, proposed by Brezzi, Fortin and Stenberg, is extended to the case of variable thickness and anisotropic material.

考虑硬夹紧、硬简支弹性板。将Brezzi, Fortin和Stenberg提出的结合插值的混合有限元分析推广到变厚度和各向异性材料的情况。

引用次数: 3

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