Formulation of a Hysteretic Restoring Force Model. Application to Vibration Isolation

This article focuses on the formulation of a hysteretic model used as anisolator restoring force model. The proposed model is based on operatorgoverning input and output functions that depend on the deflection andthe restoring force of the isolator. First, the mathematical formulationis demonstrated, then the hysteretic model proposed is applied toisolators having different types of behavior. The model parameters aresought using the experimental force-deflection loop of each of theisolators studied. Next, the transient response of a flexible structuremounted on an all-metal isolator is predicted by coupling the firstorder differential equation of the restoring force and the second orderdifferential equations of the structure's motion. The experimentalinvestigation validates the proposed hysteretic model applied to theall-metal mount.     

Nontangential Limit of the Weyl m-Functions for the Ergodic Schrödinger Equation

This paper deals with the spectral and qualitative problems associated with the one-dimensional ergodic Schrödinger equation. Let A ₂ be the set of those energies for which the real projective flow admits an invariant linear measure with square integrable density function. On this set we calculate the directional derivative of the Floquet coefficient and prove the existence of a nontangential limit of the Weyl m-functions in the L ¹-topology. In particular, we verify that the known Dieft–Simon inequality for the derivative of the rotation number obtained from Kotani's theory is in fact an equality. In the bounded orbit case we deduce the uniform boundedness of the Weyl m-functions and obtain necessary and sufficient conditions to assure their uniform convergence.     

Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

A Newton type iterative inverse method for heat-conduction problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.     

One approximate solution of the Nekrasov problem

An approximate solution ω = A[ω, μ] of the nonlinear integral Nekrasov equation is obtained by successive replacement of the kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point μ₁ = 3 of the linearized equation ω = μL[ω] but at the point μ = 1 at which operator A[ω, μ], remaining nonlinear in ω, is linear in μ. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 50–56, November–December, 2007.     

椭圆截面曲线管道内二次流动的Galerkin解

推导了任意空间曲线直角坐标系内的张量流体力学方程．采用Galerkin方法和计算机符号运算技术求解了椭圆截面螺旋管道（电括弯管、扭管）内的二次流动．计算结果表明了Galerkin方法的适用和有效性，克服了振动法的小参数局限．对所得结果的分析揭示了椭圆截面螺旋管道内流动的特性，给出了k,r和Re较大情况的研究结论．     

A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

The aim of this paper is to establish a well‐posedness result for a boundary value problem of transmission‐type for the standard and generalized Brinkman systems in two Lipschitz domains in , the former being bounded, and the latter, its complement in . As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L²‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.     

G-Frame and Riesz Sequences in Hilbert Spaces

G-frames generalize frames in Hilbert spaces. The literatures show that g-frames and frames share many similar properties, while they behave differently in redundancy and perturbation properties. Interestingly, g-frames have been extensively studied, but g-frame sequences have not. This problem is nontrivial since a g-frame and a frame both involve all vectors in the same Hilbert space, while a g-frame sequence and a frame sequence do not. They involve different linear spans. Using the synthesis and Gram matrix methods, we in this paper characterize g-frame sequences and g-Riesz sequences; obtain the Pythagorean theorem for g-orthonormal systems. These results recover several known results and lead to some new results on g-frames.     

Consistency check on the fundamental and alternative flux operators in loop quantum gravity

There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the literature, we check their consistency by the graphical calculus. Our calculation based on the original Brink graphical method is obviously simpler than the algebraic calculation. It turns out that our consistency check fixes the regulating factor κreg of the Ashtekar-Lewandowski volume operator as1/2, which corrects its previous value in the literature.