Inverse Problems for Identification of Memory Kernels in Viscoelasticity

Inverse problems for identification of the memory kernel in the linear constitutive stress–strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.     

Linear Viscoelasticity of Liquid-Crystalline Polymers

A linear (small-amplitude) periodic shear deformation of anisotropic viscoelastic liquids obeying the Akay–Leslie rheological model is considered. The frequency dependences of the real and imaginary components of the complex shear modulus and complex normal-stress coefficient are determined. A comparison between calculation results and test data on the shear flow of poly(-benzylglutamate) in m-cresol is carried out. It is stated that, if the material is characterized by some initial orientation, both components of the complex shear modulus contain a multiplier which depends on the degree of the initial orientation and increases the values of the components compared with those for an initially isotropic material. The model predicts that, in a periodic shear flow, the components of shear and normal stresses are constant and, like the components of shear modulus, are independent of deformation frequency. If the parameter d ₀ of the Akay–Leslie model is equal to zero, the values of its other parameters can be determined from experimental results on periodic shear flow.     

On Some Steady-state Moving Boundary Problems in the Linear Theory of Viscoelasticity

Three steady-state moving boundary problems in the linear theoryof viscoelasticity are considered when the inertia terms aretaken into account. Attention is directed to the dimensionlessparameter = V/L where V is the speed of the boundary, is therelaxation time of the medium, and L is a length associatedwith the geometry of the problem. When is small the problemsare recognized as having a singular perturbation character andthe method of matched asymptotic expansions is used. The problemsare (i) a semi-infinite crack moving steadily in a clamped viscoelasticstrip, (ii) a finite length crack moving in an infinite viscoelasticmedium, and (iii) a steady rolling cylinder on a visco-elastichalf-space.     

Sequential Identification of Linear Dynamic Systems with Memory

This paper presents a sequential estimator for some unknown parameters in stochastic linear systems with memory. As examples stochastic differential equations with time delayed drift are considered. Based on the maximum likelihood method, we construct an estimation procedure with given accuracy in the sense of the L _p -norm (p 2). It is shown, that this procedure works also in certain cases, when the normalized information matrix of the observed process is asymptotically degenerated. The almost surely consistency of the proposed estimators and the asymptotic behavior of the length of observations are derived.     

A New Class of Kernels Leading to an Arbitrary Decay in Viscoelasticity

A new assumption on the relaxation in a viscoelastic problem ensuring uniform stability in an arbitrary rate is established. This assumption replaces a usual condition and allows for a much wider class of kernels. As consequences several earlier results are extended and improved.     

Local Linear Smoothers Using Asymmetric Kernels

This paper considers using asymmetric kernels in local linear smoothing to estimate a regression curve with bounded support. The asymmetric kernels are either beta kernels if the curve has a compact support or gamma kernels if the curve is bounded from one end only. While possessing the standard benefits of local linear smoothing, the local linear smoother using the beta or gamma kernels offers some extra advantages in aspects of having finite variance and resistance to sparse design. These are due to their flexible kernel shape and the support of the kernel matching the support of the regression curve.     

Structure of Viability Kernels for Some Linear Differential Games

A convenient form of necessary and sufficient conditions of viability for differential games with linear dynamics is proposed. These conditions are utilized to construct maximal viable subsets of state constraints, viability kernels, in two illustrative two-dimensional examples. These examples demonstrate the relative simplicity of the structure of the viability kernels. It was found that the boundaries of the viability kernels consist of segments of the boundary of the state constraint and of lines defined by the first integrals of the governing equations as the players use extremal constant controls. It is conjectured that such a structure holds in high dimensional cases too.     

Time-Irreversibility and Existence and Uniqueness of Solutions of Problems in Linear Viscoelasticity

We study a problem of linear viscoelasticity for the case where the relation between the Cauchy stress and strain tensors is described by a linear integral relation. Theorems on the existence and uniqueness of a solution of the problem are proved.     

粘弹性本构模型的准静力位移识别

对一类边界条件，建立粘弹性准静力位移与本构参数的显式关系，给出优化识别的叠代格式，从二阶微分模型出发，识别粘弹性本构模式，讨论了信息误差对反演结果的影响     

Local Linear Estimation of Jump-Diffusion Models by Using Asymmetric Kernels

This article addresses the problem of nonparametric estimation of the first and second infinitesimal moments by using the local linear method of the underlying jump-diffusion models. The motivation behind the study is to use the asymmetric kernels instead of standard kernel smoothing. The basic idea relies on replacing the symmetric kernel by asymmetric kernel and provides a new way of obtaining the nonparametric estimation for jump-diffusion models. We prove that the estimators based on the local linear method for jump-diffusion models are consistent and asymptotically follow normal distribution under the condition of recurrence and stationarity.     

关于等价嵌入于存贮线性有限自动机问题

本文应用模的手段研究域上线性有限自动机等价嵌入于其中存贮类型的问题,分别得到可等价嵌入的一个充分条件与不可等价嵌入的一个充要条件。     

On Weighted Kernels of Two Posets

A recent result of Aharoni Berger and Gorelik (Order 31(1), 35–43, 2014) is a weighted generalization of the well-known theorem of Sands Sauer and Woodrow (Theory Ser. B 33(3), 271–275, 1982) on monochromatic paths. The authors prove the existence of a so called weighted kernel for any pair of weighted posets on the same ground set. In this work, we point out that this result is closely related to the stable marriage theorem of Gale and Shapley (Amer. Math. Monthly 69(1), 9–15, 1962), and we generalize Blair’s theorem by showing that weighted kernels form a lattice under a certain natural order. To illustrate the applicability of our approach, we prove further weighted generalizations of the Sands Sauer Woodrow result.     

On the Theory of Generalized Toeplitz Kernels

A new proof of the integral representation of the generalized Toeplitz kernels is given. This proof is based on the spectral theory of the corresponding differential operator that acts in the Hilbert space constructed from a kernel of this sort. A theorem on conditions that should be imposed on the kernel to guarantee the self-adjointness of the operator considered (i.e., the uniqueness of the measure in the representation) is proved.     

On Cellular Covers with Free Kernels

In this paper we show that every cotorsion-free and reduced abelian group of any finite rank (in particular, every free abelian group of finite rank) appears as the kernel of a cellular cover of some cotorsion-free abelian group of rank 2. This situation is the best possible in the sense that cotorsion-free abelian groups of rank 1 do not admit cellular covers with free kernel except for the trivial ones. This work is motivated by an example due to Buckner?CDugas, and recent results obtained by Fuchs?CG?bel, and G?bel?CRodríguez?CStrüngmann.     

线性连续衰退记忆系统的可分性

为逼近建模和辨识问题的需要,讨论线性时变连续有界输入有界输出稳定衰退记忆系统的不同子类．从衰退记忆系统的子类包括概周期系统,渐近周期系统,渐近强周期系统,找到了LTV系统的可分子空间即渐近强周期系统．     

On Marcinkiewicz Integral Operators with Rough Kernels

This paper is devoted to the study on the L^p-mapping properties of Marcinkiewicz integral operators with rough kernels along “polynomial curves” on The boundedness of the Marcinkiewicz integrals for some fixed 1 < p < ∞ are obtained under some size conditions, which essentially improve or extend some well-known results.