The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of for a class planar self-affine sets. also show that sets with decreasing gaps have 0 or 1 exhibit an example set in plane whose is smaller than its projection onto \(x\)-axis, showing may increase under Lipschitz mappings. Moreover, closed sets, we Hausdorff upper bound quasi-l...

We introduce a class of functions in high dimensions which have themaximum effective dimension, then prove that generalized Sobol’sequences provide theO(N−1) convergence rate for the integration of this class of functions. An important consequence is that high-dimensional problems for which quasi-Monte Carlo outperforms Monte Carlo are not necessarily of low-effective dimension. © 2005 Elsevier...

We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Π2 in the Borel hierarchy. ...

In this paper we prove that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is equal to one. We also discuss dimension spectrums of these categories. 2000 Math. Subj. Class. 18E30, 14F05.

The quasi-neutral limit of one-fluid Euler-Poisson systems leads to incompressible Euler equations. It was widely studied in previous works. In this paper, we deal with the a two-fluid system. This presents different feature since it compressible We justify for global smooth solutions near constant equilibrium states one space dimension. Specifically, prove existence by establishing uniform ene...

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

Let X be a geodesic metric space with H1(X) uniformly generated. If X has asymptotic dimension one then X is quasi-isometric to an unbounded tree. As a corollary, we show that the asymptotic dimension of the curve graph of a compact, oriented surface with genus g ≥ 2 and one boundary component is at least two.

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...