Impact of the fourth‐order compact difference scheme on computational properties of 3D grids in a nonhydrostatic model

To investigate the potential of the fourth‐order compact difference scheme within the specific context of numerical atmospheric models, a linear baroclinic adjustment system is discretized, using a variety of candidates for practically meaningful staggered 3D grids. A unified method is introduced to derive the dispersion relationship of the baroclinic geostrophic adjustment process. Eight popular 3D grids are obtained by combining contemporary horizontal staggered grids, such as the Arakawa C and Eliassen grids, with optimal vertical grids, such as the Lorenz and Charney‐Phillip (CP) grids, and their time‐staggered versions. The errors produced on the 3D grids in describing the baroclinic geostrophic adjustment process relative to the differential case are compared in terms of frequency and group velocity components with the elimination of implementation error. The results show that by utilizing the fourth‐order compact difference scheme with high precision, instead of the conventional second‐order centered difference scheme, the errors in describing baroclinic geostrophic adjustment process decrease but only when using the combinations of the horizontally staggered Arakawa C grid and the vertically staggered CP or the C/CP grid, the time‐horizontally staggered Eliassen (EL) grid and vertically staggered CP or the EL/CP grid, the C grid and the vertically time‐staggered versions of Lorenz (LTS) grid or C/LTS grid, EL grid and LTS grid or EL/LTS grid. The errors were found to increase for specific waves on the rest grids. It can be concluded that errors produced on the chosen 3D grids do not universally decrease when using the fourth‐order compact difference scheme; hence, care should be taken when implementing the fourth‐order compact difference scheme, otherwise, the expected benefits may be offset by increased errors. Copyright © 2008 John Wiley & Sons, Ltd.     

Structure,adsorption and rheological properties of composites based on biocomplexes of natural origin and modified coal

The structure, adsorption and rheological properties have been studied of new composites based on biocomplexes of natural origin and modified coal with various relative compositions. Values of the fractal dimensionality of the composite sorbents have been calculated: they range from 2.26-2.78 as they do also in natural clay minerals. The rheological characteristics of the composites and the influence of their composition on structural-mechanical properties (viscosity) were calculated. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 45, No. 2, pp. 125-129, March-April, 2009.     

The metric dimension of Cayley digraphs

A vertex x in a digraph D is said to resolve a pair u, v of vertices of D if the distance from u to x does not equal the distance from v to x. A set S of vertices of D is a resolving set for D if every pair of vertices of D is resolved by some vertex of S. The smallest cardinality of a resolving set for D, denoted by dim(D), is called the metric dimension for D. Sharp upper and lower bounds for the metric dimension of the Cayley digraphs Cay(Δ:Γ), where Γ is the group Z_n1⊕Z_n2⊕?⊕Z_nm and Δ is the canonical set of generators, are established. The exact value for the metric dimension of Cay({(0,1),(1,0)}:Z_n⊕Z_m) is found. Moreover, the metric dimension of the Cayley digraph of the dihedral group D_n of order 2n with a minimum set of generators is established. The metric dimension of a (di)graph is formulated as an integer programme. The corresponding linear programming formulation naturally gives rise to a fractional version of the metric dimension of a (di)graph. The fractional dual implies an integer dual for the metric dimension of a (di)graph which is referred to as the metric independence of the (di)graph. The metric independence of a (di)graph is the maximum number of pairs of vertices such that no two pairs are resolved by the same vertex. The metric independence of the n-cube and the Cayley digraph Cay(Δ:D_n), where Δ is a minimum set of generators for D_n, are established.     

Quasiperiodic solutions of the Navier-Stokes equations induced by the quasiperiodic shape of the boundaries of a two-dimensional flow domain

Steady quasiperiodic solutions of the Navier-Stokes equations in an infinite two-dimensional layer with quasiperiodic boundaries are obtained on the Reynolds number range 0 < Re* < 200. The calculations are performed using a spectral-difference method based on the representation of the quasiperiodic solutions in the form of convergent double Fourier series. The properties of these solutions and the distinctive features of their spectra are studied and their fundamental differences from periodic solutions are shown. The possibility of applying the quasiperiodic solutions for modeling flows in fractal layers is discussed.     

Maximal speed of particles in super-Lévy process

We introduce a super-Lévy process and study maximal speed of all particles process is a measure on the set of paths.We study the maximal speed of all particles during a given time period,which turns out to be a function of the packing dimension of the time period.We calculate the Hausdorff dimension of the set of a-fast patlls in the support and the range of the historical super-lévy process.     

Representation dimension and finitely generated cohomology

We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal complexity occurring among its modules. This provides a unified approach to computing lower bounds for the representation dimension of group algebras, exterior algebras and Artin complete intersections. We also obtain new examples of classes of algebras with arbitrarily large representation dimension.     

On Hypereuclidean Manifolds

We show that the universal cover of an aspherical manifold whose fundamental groups has finite asymptotic dimension in sense of Gromov is hypereuclidean after crossing with some Euclidean space     

一类条件变分问题解的存在性

本文对一类有广泛应用价值的不规则的条件泛函极值问题的解的存在性及解的解析表示式进行了深入系统的讨论,得到了一系列在理论及应用上颇有价值的结果.对该类问题最优解的存在性的证明填补了这方面的空白.     

Free Entropy Dimensions of Some von Neumann Algebras

In this paper, we estimate the free entropy dimension of the group yon Neumann algebra L（Zt）, which is less than 1/t,2 ≤t ≤ ＋∞. This data is identical with the free dimension defined by Dykema.     

一类Moran测度的Lq-谱

此文考虑了一类Moran分形，在其生成过程中每一阶的压缩比及压缩比的个数可以是不相同的，证明了支撑在此类Moran分形上的Moran测度的L^q-谱的存在性．