Integrated Density of States for the Periodic Schrödinger Operator in Dimension Two

No Abstract. .submitted 30/04/04, accepted 26/07/04     

A Priori Error Estimates for a Single-Phase Quasilinear Stefan Problem in one Space Dimension

Fixing the free boundary with the help of a Landau-type transformation,a finite element Galerkin method is applied to a single-phasequasilinear Stefan problem in one space dimension. Optimal errorestimates both for semidiscrete and fully discrete Galerkinapproximations are derived.     

Dimension Estimates of Earthquake Epicentres and Hypocentres

Summary. We use the Hill estimator to estimate the correlation dimension of epicentres and hypocentres from four earthquake catalogues: Wellington micro earthquakes, New Zealand catalogue, Kanto micro earthquakes, and the Japanese (JMA) catalogue. We wanted to determine if the fracturing process is fractal, and whether it is different in the four selected regions. We found that the spatial pattern of tabulated shallow events in Japan is more tightly clustered than in New Zealand, while for deeper events the spatial pattern is similar. In both regions, tabulated shallow events are more clustered than tabulated deeper events. It may appear that if one had a sufficiently large amount of data (enabling one to look at sufficiently small interpoint distances), the dimension of the epicentres and hypocentres would appear to be two or three, respectively; however, this may not be a true reflection of the fracturing process. Estimates that indicate that the fracturing tends ultimately to fill the entire space are probably caused by measurement errors in hypocentre locations. Similarly, for large values of interpoint distances, the power law exponent tends to be underestimated because of the boundary effect. When these two effects are sufficiently severe, they tend to merge, and it is difficult to determine power law exponents. These biases are not peculiar to the estimation procedure we have used. Received June 29, 1995; second revision received March 24, 1997; third revision received November 24, 1997     

Upper and Lower Hausdorff Dimension Estimates for Invariant Sets of k — 1 — Endomorphisms

For a special class of non–injective maps on Riemannian manifolds upper and lower bounds for the Hausdorff dimension of invariant sets are given in terms of the singular values of the tangent map. The upper estimation is based on a theorem by Douady and Oesterlé and its generalization to Riemannian manifolds by Noack and Reitmann , but additionally information about the noninjectivity is used. The lower estimation can be reached by modifying a method, derived by Shereshevskij for geometric constructions on the real line (also described by Barreira , for similar constructions in general metric spaces. The upper and lower dimension estimates for k — 1 — endomorphisms can for instance be applied to Julia sets of quadratic maps on the complex plane.     

一类分形函数及其维数估计

本文作者首先借助于b进制分数及无穷级数构造了一类分形函数,然后研究了这些函数图象的分形维数及其Hoelder性质,得到了一些维数结果。     

Lyapunov Functions in Dimension Estimates of Attractors of Dynamical Systems

We discuss relations between the Lyapunov dimension and the topological, Hausdorff, and fractal dimensions of attractors. For the Henon and Lorenz systems, explicit formulas characterizing the Lyapunov dimension of their attractors are obtained. Bibliography: 23 titles.     

Upper and Lower Bounds on the Dimension of Superspline Spaces

Upper and lower bounds are provided on the dimension of bivariate polynomial superspline spaces which are defined by enforcing smoothness conditions across the interior edges of the underlying triangulation. The results generalize known bounds for classical spline spaces. As an example of the usefulness of such bounds, we show how they can be applied to analyze a new macroelement.     

Capacity Density of Subanalytic Sets in Higher Dimension

We show that capacity density exists for subanalytic sets in any dimension. Moreover, we state connections between capacity density and volume density for subanalytic sets.      

M-矩阵最小特征值的上界估计

利用M-矩阵最小特征值与非负矩阵谱半径之间的关系,结合矩阵的迹分两种情况给出M-矩阵最小特征值的上界序列,并且给出数值例子加以说明.     

Logarithmic Estimates for the Density of Hypoelliptic Two-Parameter Diffusions

We consider a hypoelliptic two-parameter diffusion. We first prove a sharp upper bound in small time (s, t)[0, 1]² for the L^p-moments of the inverse of the Malliavin matrix of the diffusion process. Second, we establish the behaviour of2² log p_s, t(x, y), as ↓0, where x is the initial condition of the diffusion, = , and p_s, t(x, y) is the density of the hypoelliptic two-parameter diffusion.     

Sharp Dimension Estimates for the Attractors of the Regularized Damped Euler System

Doklady Mathematics - A regularized damped Euler system in two-dimensional and three-dimensional setting is considered. The existence of a global attractor is proved and explicit estimates of its...     

Decorrelation Estimates for a 1D Tight Binding Model in the Localized Regime

In this article, we prove decorrelation estimates for the eigenvalues of a 1D discrete tight-binding model near two distinct energies in the localized regime. Consequently, for any integer n ≥ 2, the asymptotic independence for local level statistics near n distinct energies is obtained.     

局部熵高维重分形谱的上界估计

We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.     

Estimates for the Upper Bounds of the First Eigenvalue on Submanifolds

ＥｓｔｉｍａｔｅｓｆｏｒｔｈｅＵｐｐｅｒＢｏｕｎｄｓｏｆｔｈｅＦｉｒｓｔＥｉｇｅｎｖａｌｕｅｏｎＳｕｂｍａｎｉｆｏｌｄｓ祁锋，于霖泉，雒秋明ＥｓｔｉｍａｔｅｓｆｏｒｔｈｅＵｐｐｅｒＢｏｕｎｄｓｏｆｔｈｅＦｉｒｓｔＥｉｇｅｎｖａｌｕｅｏｎＳｕｂｍａｎｉ...     

Estimates for the real taylor coefficients in one function class

Considering the class {ie48-01} of analytic functions {ie48-02} in the unit disk with a _m,n ε ℝ and the nonvanishing nth divided difference [F(z);z ₀, ⋯, z _n ] for all z ₀, ℝ, z _n ∈ E we establish that {ie48-03}, where {ie48-04}. If n is an odd number then {ie48-05}.     

An Upper Bound for the w-Weak Global Dimension of Pullbacks

Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}.     

A New Upper Bound for the Dimension of Trace Codes

We shall derive a new non-trivial upper bound for the dimensionof trace codes connected to algebraic-geometric codes. Furthermore,we shall deduce their true dimension if certain conditions aresatisfied.