I is well recognised that people can derive meaning from and experience positive psychological changes even in the most adverse circumstances surrounding illness and trauma. Although many different theories of ‘posttraumatic growth’ (PTG) exist in the literature (see Zoellner & Maercker, 2006), there is consensus that when people experience an event as traumatic or highly stressful, their globa...

We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T . Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes interpolation, generalized sampling with prefiltering, and the projectors encountered in wavelet theory. We claim that we can predict the L-...

Abstract: A complete characterization is given of closed shift-invariant subspaces of L2(IR) which provide a specified approximation order. When such a space is principal (i.e., generated by a single function), then this characterization is in terms of the Fourier transform of the generator. As a special case, we obtain the classical Strang-Fix conditions, but without requiring the generating f...

We consider a family of explicit compact schemes for advection in one dimension. The order is arbitrarily high. These stencils may be called Strang’s stencils after the seminal work of Strang [J. Math. Phys., 41 (1962), pp. 147–154]. We prove that odd order schemes are stable in all Lq under CFL one. The strategy of the proof is similar to the one of Thomée [J. Differential Equations, 1 (1965),...

Attention has recently been directed to the possible lethal effect of aerosol sympathomimetic agents in the treatment of bronchial asthma (Speizer, Doll, Heaf and Strang, 1968), death being attributed to an excitatory action on the heart. Animal studies indicate that practolol (I.C.I. 50,172, Eraldin) specifically blocks cardiac beta-adrenergic receptors, preventing arrhythmias or other alterat...

We study the n-simplex nonconforming Crouzeix-Raviart element in approximating the n-dimensional second-order elliptic boundary value problems and the associated eigenvalue problems. By using the second Strang Lemma, optimal rate of convergence is established under the discrete energy norm. The error bound is also valid for the eigenfunction approximations. In addition, when eigenfunctions are ...

Finite element multiwavelets were constructed by Strela and Strang [12]. They simultaneously achieve higher regularity and short support. However, these multiwavelets are not orthogonal with respect to translates. In this notes, we introduced an alternate Sobolev type inner product in which the scaling functions are orthogonal to their translates. We then derive a simple version of the decompos...

Every teacher of linear algebra should be familiar with the matrix singular value decomposition (or SVD). It has interesting and attractive algebraic properties, and conveys important geometrical and theoretical insights about linear transformations. The close connection between the SVD and the well known theory of diagonalization for symmetric matrices makes the topic immediately accessible to...

Abstract In this paper, we establish the optimal convergence for a second-order exponential-type integrator from Hofmanová & Schratz (2017, An KdV equation. Numer. Math., 136, 1117–1137) solving Korteweg–de Vries equation with rough initial data. The scheme is explicit and efficient to implement. By rigorous error analysis, show that provides accuracy in $H^\gamma $ data $H^{\gamma +4}$ any...