Inverse Anisotropic Curvature Flow from Convex Hypersurfaces

In this paper, we study the inverse anisotropic curvature flow from strictly convex hypersurfaces. We show the long-time existence and the convergence to the Wulff shape after rescaling, under certain conditions on the general speed functions.     

一个寻找外围节点的算法

指出了著名的用于降低稀疏矩阵带宽的Gibbs-Poole-Stockmeyer方法中所找到的伪外围节点的偏心距可能远小于图的直径.由此提出了一个寻找外围节点的算法,证明了其正确性和有效性.     

张拉结构初始几何形状确定的形函数方法

提出了一个确定张拉结构初始几何形状的形状函数.基于该形状函数,通过对结构边界控制点的插值确定张拉结构的初始形状.该结构形状可随结构的双向张力比和边界控制点的坐标而进行自动调整.从而给出了几何上可行,力学上合理的高精度张拉曲面.通过有限元方法检查,大量例子表明该方法确定的初始形状对于实际常用边界及双向等拉或不等拉张结构均十分理想,误差很小.     

Inverse Iteration: An Alternative Form

Rayleigh quotient inverse iteration (RQI) is examined from the standpoint of incremental vectors. By choosing such a vector orthogonal to the eigenvector iterate at the mth step, χ_m, a system of linear equations is derived; solving the system is shown to be equivalent to RQI. The residual norm converges to zero for Hermitian matrices, and the coefficient matrix does not in general converge to a singular matrix as it does in RQI. Furthermore, the procedure described produces successive vector iterates whose norms do not in general become large (when m→∞) as they do with RQI.     

Uniqueness For An Inverse Boundary Value Problem For Dirac Operators

The uniqueness of both the inverse boundary value problem and inverse scattering problem for Dirac equation with a magnetic potential and an electrical potential are proved. Also, a relation between the Dirichlet to Dirichlet map for the inverse boundary value problem and the scattering amplitude for the inverse scattering problem is given     

Stability For a Multidimensional Inverse Spectral Theorem

We consider the eigenvalue problem in Ω

Where Ω is a bounded domain in R^d with smooth boundary,a nd q is a bounded, measurable function on Ω The eigenvalue problem has discrete spectrum; we denote by and a nondecreasing sequence of eigenvalue and corresponding (orthonormal) eigenfunctions. It is known ([N–S–U]) that knowledge of the eigenvalues and the boundary values of the normal derivatives of the corresponding eigenfunctions is sufficient to uniquely determine a coefficient, q.     

Solvability of the Inverse Problem of Finding Thermal Conductivity

We study the inverse problem of finding the coefficient of thermal conductivity of the heat equation (along with the solution). As the overdetermination condition we take the values of the solution at the final time. Existence of a regular solution is proven.     

An Inverse Problem for Maxwell’s Equations in Anisotropic Media

The authors consider Maxwell's equations for an isomagnctic anisotropic and inhomogeneous medium in two dimensions, and discuss an inverse problem of determining the permittivity tensor (ε1ε2ε2ε3) and the permeabilityμin the constitutive relations from a finite number of lateral boundary measurements. Applying a Carlcman estimate, the authors prove an estimate of the Lipschitz type for stability, provided thatε1,ε2,ε3,μsatisfy some a priori conditions.     

An Inverse Phaseless Problem for Electrodynamic Equations in an Anisotropic Medium

Doklady Mathematics - For the system of electrodynamics equations with anisotropic permittivity, the inverse problem of determining the permittivity is studied. It is supposed that the permittivity...     

Inverse Problems of Finding the Absorption Parameter in the Diffusion Equation

Mathematical Notes - The paper is devoted to the study of inverse problems of finding, together with a solution u(x, t) of the diffusion equation $${u_t} - \Delta u + [c(x,t) + a{q_0}(x,t)]u =...     

求矩阵Jordan标准形的一种新法

讨论了一种求不变因子的方法,利用不变因子与初等因子之间的关系,给出了一种求矩阵Jordan标准形的新方法.     

T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product

In this paper,we investigate the tensor similarity and propose the T-Jordan canonical form and its properties.The concepts of the T-minimal polynomial and the T...     

Numerical Projection Method For Inverse Fourier Transform And Its Application

Numerical projection method of the Fourier transform inversion from data given on a finite interval is proposed. It is based on an expansion of the solution into a series of eigenfunctions of the Fourier transform. The number of terms of the expansion depends on the length of the data interval. Convergence of the solution of the method is proved. The projection method for the case of the sine Fourier transform and the set of the odd Hermite functions being its eigenfunctions are examined and applied to numerical Fourier filtering.     

On Free Inverse Semigroups

Using techniques of Rewriting Theory, we present a new proof of the known theorem of Munn that FIX , the free inverse semigroup on X, is isomorphic to birooted word-trees on X.     

Micro-Mechanical Modelling of Anisotropic Time-Dependent Healing Effects in Rubber-like Materials

Filler-reinforced rubber-like materials demonstrate deformation induced softening, known as the Mullins effect. This softening can be reversible in a certain range (healing). The previously introduced concept of network evolution (NE) explains the Mullins effect as the result of a filler-polymer network rearrangement [1]. It is assumed that debonding of polymer chain segments from rigid aggregates does not effect the number of active segments. Furthermore, debonded chains are still active as a part of a longer chain. Now, considering the entropic vibration of polymer chains, entanglement of chains to the rough aggregate surfaces is assumed. This process inverse to the NE leads to a micro-mechanical model of time-dependent recovery of the deformation induced softening. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)