We develop higher order fi nite element methods for fracture mechanics. The framework is cast within the contextof conforming fi nite elements [1]. The method [2] exploits the a priori knowledge of the singular behavior of thefi elds to construct an alternate regular solution. Solving for the alternate problem yields optimal rates of conver-gence and high order of accuracy. The ...

This paper gives double angle theorems that bound the change in an invariant subspace of an inde nite Hermitian matrix in the graded form H = D AD subject to a perturbation H ! e H = D (A + A)D. These theorems extend recent results on a de nite Hermitian matrix in the graded form (Linear Algebra Appl., 311 (2000), 45{60) but the bounds here are more complicated in that they depend on not only r...

Decentralized Finance (DeFi) has brought about decentralized applications which allow untrusted users to lend, borrow and exchange crypto-assets. Many of such fulfill the role markets or market makers, featuring complex, highly parametric incentive mechanisms equilibrate interest rates prices. This complexity makes behaviour DeFi difficult understand: indeed, ill-designed could potentially lead...

We focus on the -nite-sample behavior of heteroskedasticity-consistent covariance matrix estimators and associated quasi-t tests. The estimator most commonly used is that proposed by Halbert White. Its -nite-sample behavior under both homoskedasticity and heteroskedasticity is analyzed using Monte Carlo methods. We also consider two other consistent estimators, namely: the HC3 estimator, which ...

In this paper we characterize a class of stochastic Petri nets that can be solved using matrix geometric techniques. Advantages of such an approach are that very eecient mathematical technique become available for practical usage, as well as that the problem of large state spaces can be circumvented. We rst characterize the class of stochastic Petri nets of interest by formally deening a number...

1 of 2 DESCRIPTION We present the case of a 63-year-old lady who complained of feeling constantly tired and lethargic, and was found to have iron defi ciency anaemia. There was no history of per vaginal bleeding. Examination was normal apart from a large, mobile, fi rm, well-defi ned abdominal mass in the upper abdomen approximately 10cm in diameter. The abdominal CT scan revealed a large intra...

In this paper we extend Kalman's concept of partial realization and deene generalized partial realizations of nite matrix sequences by descriptor systems. Our deenition is in agreement with the realization theory for deterministic boundary value descriptor systems 15]. The aim of this contribution is to prove a counterpart of Kalman's main theorem of realization theory for generalized partial r...

A uni® ed review of various Kohn variational methods for scattering calculations is presented using appropriate Bloch operators. Previous expressions are generalized slightly to use either an in® nite range or a ® nite range of the scattering coordinate, or to use a basis set with non-® xed log derivative boundary conditions. A non-variationalmethod (method of moments) is used in the derivation...

The present paper summarizes the generalized ®nite element method formulation and demonstrates some of its advantages over traditional ®nite element methods to solve complex, three-dimensional (3D) structural mechanics problems. The structure of the sti€ness matrix in the GFEM is compared to the corresponding FEM matrix. The performance of the GFEM and FEM in the solution of a 3D elasticity pro...

We present a family of algorithms for computing symmetric rank-revealing VSV decompositions, based on triangular factorization of the matrix. The VSV decomposition consists of a middle symmetric matrix that reveals the numerical rank in having three blocks with small norm, plus an orthogonalmatrix whose columns span approximations to the numerical range and null space. We show that for semi-de ...