Variational formulations of time-dependent PDEs in space and time yield (d + 1)-dimensional problems to be solved numerically. This increases the number unknowns as well storage amount. On other hand, this approach enables adaptivity model reduction w.r.t. both type variables. In paper, we show that matrix oriented techniques can significantly reduce computational timings for solving arising li...

In this issue, instead of a review new books or textbooks on transport and transportation, paying tribute to the oeuvres our predecessors, journal reproduces bibliographic article first appeared more than century ago in «Zheleznodorozhnoe delo» [Rail Business]. The editors hope that it will help get an idea how concise, meaningful and, modern terms, informative reviews scientific literature wer...

Modifications to the standard finite element mass matrix are considered with the aim of preserving the positivity of the discrete solution. The approach is used in connection with calculating the initial time derivative values for parabolic equations and in connection with nonlinear Petrov-Galerkin schemes for hyperbolic equations in one space dimension. The extension of the ideas to unstructur...

We develop further the integration procedure in the generalised invariant formalism , and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A ...

We combine multiple word representations based on semantic clusters extracted from the (Brown et al., 1992) algorithm and syntactic clusters obtained from the Berkeley parser (Petrov et al., 2006) in order to improve discriminative dependency parsing in the MSTParser framework (McDonald et al., 2005). We also provide an ensemble method for combining diverse cluster-based models. The two contrib...

A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to the twistor and/or Killing equations. These lead to the notions of twistor and Killing spinor initial data. These notions are used to obtain a characterisatio...

Using a decomposition of the global error into a locally created part and a propagating component, we derive residual-based two-sided local a posteriori error bounds for the locally created component of the global error for Petrov-Galerkin approximations of symmetric positive systems in the sense of Friedrichs. The performance of the a local error indicators is illustrated by a series of numeri...