Asymptotic expansions for the location invariant moment-type estimator

In this paper, based on moment-type and location invariant Hill estimators, a new kind of location invariant moment-type extreme value index estimator is proposed. The weak and strong consistency of the estimator are discussed. The asymptotic expansion of the estimator and its distribution are also considered under second order regularly varying conditions. The asymptotic normality is employed to construct the confidence interval. Monte Carlo simulations are performed to compare the Hill estimator and the moment estimator in terms of mean squared error.     

Domain decomposition methods for the neutron diffusion problem

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, simplified transport (S_PN$S{P}_N$) or diffusion approximations are often used. The MINOS solver developed at CEA Saclay uses a mixed dual finite element method for the resolution of these problems, and has shown his efficiency. In order to take into account the heterogeneities of the geometry, a very fine mesh is generally required, and leads to expensive calculations for industrial applications. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose here two domain decomposition methods based on the MINOS solver. The first approach is a component mode synthesis method on overlapping subdomains: several eigenmodes solutions of a local problem on each subdomain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is an iterative method based on a non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each subdomain with the interface conditions given by the solutions on the adjacent subdomains estimated at the previous iteration. Numerical results on parallel computers are presented for the diffusion model on realistic 2D and 3D cores.     

一类修正的DY共轭梯度法及其全局收敛性

本文提出了一类求解无约束优化问题的修正DY共轭梯度法.算法采用新的迭代格式,每步迭代都可自行产生一个充分下降方向.采用Wolfe线搜索时,证明了全局收敛性.数值实验结果验证了算法是有效的.     

Edge-fault-tolerant bipanconnectivity of hypercubes

This paper shows that for any two distinct vertices u and v with distance d in the hypercube Q_n (n?3) with at most faulty edges and each vertex incident with least two fault-free edges, there exist fault-free uv-paths of length ? in Q_n for every ? with d+4???2ⁿ-1 and . This result improves some known results on edge-fault bipanconnectivity of hypercubes. The proof is based on the recursive structure of Q_n.     

Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations

This paper is concerned with the error behaviour of linear multistep methods applied to singularly perturbed Volterra delay-integro-differential equations. We derive global error estimates of A(α)$A(\alpha )$-stable linear multistep methods with convergent quadrature rule. Numerical experiments confirm our theoretical analysis.     

Evolutions of Polygons in the Study of Subdivision Surfaces

We employ the theory of evolving n-gons in the study of subdivision surfaces. We show that for subdivision schemes with small stencils the eigenanalysis of an evolving polygon, corresponding either to a face or to the 1-ring neighborhood of a vertex, complements in a geometrically intuitive way the eigenanalysis of the subdivision matrix. In the applications we study the types of singularities that may appear on a subdivision surface, and we find properties of the subdivision surface that depend on the initial control polyhedron only.     

Wavelet-Based Multiresolution with

Multiresolution methods are a common technique used for dealing with large-scale data and representing it at multiple levels of detail. We present a multiresolution hierarchy construction based on subdivision, which has all the advantages of a regular data organization scheme while reducing the drawback of coarse granularity. The -subdivision scheme only doubles the number of vertices in each subdivision step regardless of dimension n. We describe the construction of 2D, 3D, and 4D hierarchies representing surfaces, volume data, and time-varying volume data, respectively. The 4D approach supports spatial and temporal scalability. For high-quality data approximation on each level of detail, we use downsampling filters based on n-variate B-spline wavelets. We present a B-spline wavelet lifting scheme for -subdivision steps to obtain small or narrow filters. Narrow filters support adaptive refinement and out-of-core data exploration techniques.     

Derivative Free Inclusion Methods for Polynomial Zeros

Two iterative methods for the simultaneous inclusion of complex zeros of a polynomial are presented. Both methods are realized in circular interval arithmetic and do not use polynomial derivatives. The first method of the fourth order is composed as a combination of interval methods with the order of convergence two and three. The second method is constructed using double application of the inclusion method of Weierstrass’ type in serial mode. It is shown that its R-order of convergence is bounded below by the spectral radius of the corresponding matrix. Numerical examples illustrate the convergence rate of the presented methods     

h-p Spectral Element Method for Elliptic Problems on Non-smooth Domains Using Parallel Computers

We propose a new h-p spectral element method to solve elliptic boundary value problems with mixed Neumann and Dirichlet boundary conditions on non-smooth domains. The method is shown to be exponentially accurate and asymptotically faster than the standard h-p finite element method. The spectral element functions are fully non-conforming for pure Dirichlet problems and conforming only at the vertices of the elements for mixed problems, and hence, the dimension of the resulting Schur complement matrix is quite small. The method is a least-squares collocation method and the resulting normal equations are solved using preconditioned conjugate gradient method with an almost optimal preconditioner. The algorithm is suitable for a distributed memory parallel computer. The numerical results of a number of model problems are presented, which confirm the theoretical estimates.     

Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures

We analyze, both analytically and numerically, the dynamical behavior of the N-soliton train in the Manakov system with perturbations due to an external potential. The perturbed complex Toda chain model has been employed to describe adiabatic interactions within the N Manakov-soliton train. Simulations performed demonstrate that external potentials can play a stabilizing role to provide bound state regime of the train propagation. We also present new stationary and travelling wave solutions to equations describing Bose–Fermi mixtures in an elliptic external potential. Precise conditions for the existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases.