The paper proves estimates for the partial derivatives of the solution to a time-fractional diffusion equation, posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is less regular than in the well-known case of classical diffusion.

A wavelet-based method for the numerical simulation of acoustic and elastic wave propagation is developed. Using a displacement-velocity formulation and treating spatial derivatives with linear operators, the wave equations are rewritten as a system of equations whose evolution in time is controlled by first-order derivatives. The linear operators for spatial derivatives are implemented in wave...

Two exponential wave integrator Fourier pseudospectral (EWI-FP) methods are presented and analyzed for the long-time dynamics of Dirac equation with small potentials characterized by ??(0,1] a dimensionless parameter. Based on (symmetric) temporal derivatives in phase space followed applying discretization spatial derivatives, EWI-FP explicit spectral accuracy second-order time any fixed ?=?0. ...

We numerically investigate the pulsatile flow and heat transfer of a micropolar fluid through a Darcy-Forchhmeir porous channel in the presence of wall transpiration. We use the central difference approximations for the spatial derivatives, whereas the time integration has been performed by employing the three steps explicit Runge-Kutta method to obtain the numerical solution. It i...

We consider nonautonomous quasilinear parabolic equations satisfying certain symmetry conditions. We prove that each positive bounded solution u on RN × (−∞, T ) decaying to zero at spatial infinity uniformly with respect to time is radially symmetric around some origin in RN . The origin depends on the solution but is independent of time. We also consider the linearized equation along u and pr...

We carried out a study of the expression patterns of seven developmental regulatory genes (Lef1, Lhx2, Lhx9, Lhx5, Lmo3, Lmo4, and Prox1), in combination with topological position, to identify the medial pallial derivatives, define its major subdivisions, and compare them between mouse and chicken. In both species, the medial pallium is defined as a pallial sector adjacent to the cortical hem a...

Using ambient atmosphere instead of pure nitrogen environment enabled efficient recording of room temperature fluorescence from single molecules of porphycenes, chromophores with a high triplet formation efficiency. Double hydrogen transfer between two chemically identical trans tautomers has been demonstrated for parent porphycene and three alkyl derivatives by the analysis of spatial patterns...

The theory of zero-crossing detection is extended to include the first and second spatial derivative of the gaussian distribution. On the premise that phase contains a considerable proportion of the information content in an unknown signal, we show that phase can be extracted from the first and second derivatives of an appropriate filter. It is shown that the spatial gradient of phase can be us...

In the recent years there has been an increased interest in the pyridazinone ring system. Many investigations indicated that the presence of at least one aryl group, one or two electron donor atoms and/or an NH group in a special spatial arrangement is necessary for anticonvulsant activity. Many investigations indicated that the presence of at least one aryl group, one or two electron donor ato...