Computation of the inverse Laplace Transform based on a Collocation method which uses only real values

We develop a numerical algorithm for inverting a Laplace transform (LT), based on Laguerre polynomial series expansion of the inverse function under the assumption that the LT is known on the real axis only. The method belongs to the class of Collocation methods (C-methods), and is applicable when the LT function is regular at infinity. Difficulties associated with these problems are due to their intrinsic ill-posedness. The main contribution of this paper is to provide computable estimates of truncation, discretization, conditioning and roundoff errors introduced by numerical computations. Moreover, we introduce the pseudoaccuracy which will be used by the numerical algorithm in order to provide uniform scaled accuracy of the computed approximation for any x with respect to ex . These estimates are then employed to dynamically truncate the series expansion. In other words, the number of the terms of the series acts like the regularization parameter which provides the trade-off between errors. With the aim to validate the reliability and usability of the algorithm experiments were carried out on several test functions

Naturally graded Zinbiel algebras with nilindex n - 3

We present the classification of a subclass of n-dimensional naturally graded Zinbiel algebras. This subclass has the nilindex n − 3 and the characteristic sequence (n − 3, 2, 1). In fact, this result completes the classification of naturally graded Zinbiel algebras of nilindex n − 3

Early changes in brain structure correlate with language outcomes in children with neonatal encephalopathy.

Global patterns of brain injury correlate with motor, cognitive, and language outcomes in survivors of neonatal encephalopathy (NE). However, it is still unclear whether local changes in brain structure predict specific deficits. We therefore examined whether differences in brain structure at 6 months of age are associated with neurodevelopmental outcomes in this population. We enrolled 32 children with NE, performed structural brain MR imaging at 6 months, and assessed neurodevelopmental outcomes at 30 months. All subjects underwent T1-weighted imaging at 3 T using a 3D IR-SPGR sequence. Images were normalized in intensity and nonlinearly registered to a template constructed specifically for this population, creating a deformation field map. We then used deformation based morphometry (DBM) to correlate variation in the local volume of gray and white matter with composite scores on the Bayley Scales of Infant and Toddler Development (Bayley-III) at 30 months. Our general linear model included gestational age, sex, birth weight, and treatment with hypothermia as covariates. Regional brain volume was significantly associated with language scores, particularly in perisylvian cortical regions including the left supramarginal gyrus, posterior superior and middle temporal gyri, and right insula, as well as inferior frontoparietal subcortical white matter. We did not find significant correlations between regional brain volume and motor or cognitive scale scores. We conclude that, in children with a history of NE, local changes in the volume of perisylvian gray and white matter at 6 months are correlated with language outcome at 30 months. Quantitative measures of brain volume on early MRI may help identify infants at risk for poor language outcomes

Leibniz Algebras Whose Semisimple Part is Related to sl2

In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras sl1 2⊕sl2 2⊕· · ·⊕sls 2⊕R, where R is a solvable radical. The classifications of such Leibniz algebras in the cases dimR = 2, 3 and dimI 6= 3 have been obtained. Moreover, we classify Leibniz algebras with L/I ∼= sl1 2⊕sl2 2 and some conditions on ideal I = id < [x, x] | x ∈ L