A very simple and eÆcient nite element method is introduced for two and three dimensional viscous incompressible ows using the vorticity formulation. The method relies on recasting traditional nite element method in the spirit of the high order accurate nite di erence methods introduced by the authors in [10]. Optimal accuracy of arbitrary order can be achieved using standard nite element or sp...

The article discusses the thesis that German verb sollen expresses a special type of modality occupies an intermediate position between necessity and possibility, i.e. weak ontological necessity. expressed by can be characterized as follows: points to correlation state aff airs P with certain logic development events, not only possible, but salient in some respect. This is diff erence this “cla...

The main purpose of this work is to investigate the solutions, periodic character and study global asymptotic behavior so- lutions following rational di↵erence equation x_(n+1) = x_(n-2)*x_(n-6) / x_(n-3)*(±1 ± x_(n-2)*x_(n-6)) with a non-zero real numbers initial conditions.

The Newtonian divided-di¤erence operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil...

We develop a fourth order accurate finite di↵erence method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson [J. Sci. Comput. 52 (2012)]. The proposed method discretizes the anisotropic e...

A benchmark problem on atmospheric sound propagation over irregular terrain has been solved using a stable fourth-order accurate nite di erence approximation of a highdelity acoustic model. A comparison with the parabolic equation method and ray tracing methods is made. The results show that ray tracing methods can potentially be unreliable in the presence of irregular terrain.

ÐThe unsteady ̄ow of blood in a straight, long, rigid pipe, driven by an oscillatory pressure gradient is studied. Three di€erent non±newtonian models for blood are considered and compared. One of them turns out to o€er the best ®t of experimental data, when the rheological parameters are suitably ®xed. Numerical results are obtained by a spectral collocation method in space and the implicit tr...

6.1 A Basic Statistical Method in Hypothesis Testing. In chapter 4 we encountered our …rst problems in statistical inference. One dealt with the problem of sample size. The other was a problem of a statistical test of hypothesis. It dealt with the problem of whether two samples arose from the same distribution function or whether there was a shift and essentially a di¤erence in means between th...

Transforms of linear operators on bivariate generating functions can be used for constructing explicte solutions to certain generalized q di¤erence equations. The method is applied to counting intersecting pairs of lattice paths with weighted turns, a re…nement of the q-Narayana numbers.

An initial value problem with piecewise constant coe cients is considered. The accuracies for both nite di erence methods and the pseudospectral method are analyzed, and a modi cation of the initial value problem is suggested. The modi ed problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method at integ...