Quasi‐optimal preconditioners for finite element approximations of diffusion dominated convection–diffusion equations on (nearly) equilateral triangle meshes

The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a finite element approximation to diffusion‐dominated convection–diffusion equations. We consider a model setting in which the structured finite element partition is made by equilateral triangles. Under such assumptions, if the problem is coercive and the diffusive and convective coefficients are regular enough, then the proposed preconditioned matrix sequences exhibit a strong eigenvalue clustering at unity, the preconditioning matrix sequence and the original matrix sequence are spectrally equivalent, and under the constant coefficients assumption, the eigenvector matrices have a mild conditioning. The obtained results allow to prove the conjugate gradient optimality and the generalized minimal residual quasi‐optimality in the case of structured uniform meshes. The interest of such a study relies on the observation that automatic grid generators tend to construct equilateral triangles when the mesh is fine enough. Numerical tests, both on the model setting and in the non‐structured case, show the effectiveness of the proposal and the correctness of the theoretical findings. Copyright © 2014 John Wiley & Sons, Ltd.     

Synthesis of some three-qubit gates and their implementation in a three spins system coupled with Ising interaction

The synthesis of the Toffoli gate, Fredkin gate, three-qubit Inversion-on-equality gate and D(α) gate, as well as their implementation in a three spins system coupled with Ising interaction are investigated. The sequences of the control pulse and the drift process to implement these gates are given. It is revealed that the implementation of some three-qubit gates in a circular spin chain is much better than in a linear spin chain, and every two measurements of the quantum computation complexity are not always consistent. It is significant to directly study the implementation of the multi-qubit gates and even more complicated components of quantum information processing without resorting to their synthesis.     

Efficient sampling in approximate dynamic programming algorithms

Dynamic Programming (DP) is known to be a standard optimization tool for solving Stochastic Optimal Control (SOC) problems, either over a finite or an infinite horizon of stages. Under very general assumptions, commonly employed numerical algorithms are based on approximations of the cost-to-go functions, by means of suitable parametric models built from a set of sampling points in the d-dimensional state space. Here the problem of sample complexity, i.e., how “fast” the number of points must grow with the input dimension in order to have an accurate estimate of the cost-to-go functions in typical DP approaches such as value iteration and policy iteration, is discussed. It is shown that a choice of the sampling based on low-discrepancy sequences, commonly used for efficient numerical integration, permits to achieve, under suitable hypotheses, an almost linear sample complexity, thus contributing to mitigate the curse of dimensionality of the approximate DP procedure.     

New technical developments in magnetic resonance imaging of epilepsy

Within the last several years a number of technical developments have been made in magnetic resonance imaging (MRI) that can potentially impact clinical and research MR imaging applications in epilepsy. These include developments in instrumentation and in pulse sequences. Advances in instrumentation include higher capacity gradient systems and multiple receiver coils as directed to brain imaging. Advances in pulse sequence include use of fast or turbo-spin-echo techniques, variants of echo-planar imaging, and sequences such as fluid-attenuation inversion recovery (FLAIR) targeted to specific applications of brain imaging. The purpose of this paper is to review several of these developments.     

Metric,Fractal Dimensional and Baire Results on the Distribution of Subsequences

Let X be a locally compact metric space. One important object connected with the distribution behavior of an arbitrary sequence x on X is the set M( x ) of limit measures of x . It is defined as the set of accumulation points of the sequence of the discrete measures induced by x . Using binary representation of reals one gets a natural bijective correspondence between infinite subsets of the set ℕ of positive integers and numbers in the unit interval I = 〈0, 1]. Hence to each sequence x = (x_n)_n∈ℕ ∈ X^ℕ and every a I there corresponds a subsequence denoted by a x . We investigate the set M(a x ) for given x with emphasis on the behavior for “typical” a in the sense of Baire category, Lebesgue measure and Hausdorff dimension.     

Spectral assignment of poly(vinyl acetate) by one and two dimensional NMR spectroscopy: Revisited

Poly(vinyl acetate) (PVA) prepared by photopolymerization was studied by a combination of one and two dimensional NMR spectroscopy. The ¹³C{¹H} and ¹H NMR spectra of the homopolymer (PVA) were assigned to the configurational pentads (CH region) and tetrads (CH₂ region). These assignments were substantiated by the use of two dimensional heteronuclear single quantum correlation (HSQC), heteronuclear single quantum correlation‐total correlation spectroscopy (HSQC‐TOCSY) and double quantum filtered correlation spectroscopy (DQFCOSY) experiments. The results obtained by the analysis of the area under the resonance signals confirmed that PVA obeys Bernoullian statistics. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 551–556, 1999     

Convexity of degree sequences

We explore the convexity of the set of vectors consisting of degree sequences of subgraphs of a given graph. Results of Katerinis and Fraisse, Hell and Kirkpatrick concerning vertex deleted f‐factors are generalized. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 147–156, 1999     

On the complete convergence of sums of negatively associated random variables

This paper extends results on complete convergence in the law of large numbers for subsequences to the case of negatively associated nonidentically distributed random variables. Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 411–420, September, 2000.     

Extended Well-Posedness Properties of Vector Optimization Problems

In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness.