〈I〉型三角剖分下非张量积连续小波基的构造

多维非张量积小波是近年小波研究领域中的热点问题之一 ,它们与多维张量积小波相比具有更多的优势 .关于高维张量积、非张量积小波 ,目前已有一些很好的工作 (见文[2 ] [3 ] [4 ] ) ,但关于样条小波 ,还有许多问题有待于研究 .本文针对〈I〉型三角剖分下的二维线性元空间 ,讨论其具有紧支集和对称性的半正交样条小波基 .给定 x1 x2 平面上的〈I〉型三角剖分 (图 1 ( a)所示 ) ,记 j=( j1 ,j2 ) ,| j| =j1 + j2 ,πm= { 0≤ |j|≤ mCj1j2 xj11 xj22 ,Cj1,j2 是任意实数 }为次数不超过 m的代数多项式全体 .引入剖分尺度为 1的线性元空间 V0…     

On the duration of the total eclipse of a satellite of a body

This paper solves the problem of the duration of the total eclipseof a satellite of a body, provided that (a) the body is sphericalin shape and the mass distribution inside the body is sphericallysymmetrical; (b) the satellite is a very small object; (c) thesatellite's orbit around a body is circular and the satellitecan pass through the centre of its shadow; (d) a source of lightis the source of the conical body's shadow (umbra) and it doesnot change its apparent position in the sky; (e) there are noperturbations on the satellite's orbit. The solution presentedrepresents the general discussion of the problem based on utilizationof some parts of the theory of contraction mappings.     

激光等离子体2660紫外探针及干涉系统

成功地在六路高功率Nd玻璃激光装置上建立了2660紫外激光探针和适合紫外波段的Normaski干涉仪,首次将可见波长的连续激光应用于紫外干涉仪中靶成像调整和光路准直。利用该紫外光干涉仪,在铜柱状靶(φ500μm)上测量了厚等离子体中高达0.6n。的电子密度。     

Sharp estimates in terms of moduli of smoothness for compound cubature rules

Summary In 1980 Dahmen-DeVore-Scherer introduced a modulus of continuity which turns out to reflect invariance properties of compound cubature rules effectively. Accordingly, sharp error bounds are derived, the existence of relevant counterexamples being a consequence of a quantitative resonance principle, established previously.     

On the density of the space of continuous and uniformly continuous functions

For X a metrizable space and (Y,ρ) a metric space, with Y pathwise connected, we compute the density of (C(X,(Y,ρ)),σ)—the space of all continuous functions from X to (Y,ρ), endowed with the supremum metric σ. Also, for (X,d) a metric space and (Y,‖⋅‖) a normed space, we compute the density of (UC((X,d),(Y,ρ)),σ) (the space of all uniformly continuous functions from (X,d) to (Y,ρ), where ρ is the metric induced on Y by ‖⋅‖). We also prove that the latter result extends only partially to the case where (Y,ρ) is an arbitrary pathwise connected metric space.To carry such an investigation out, the notions of generalized compact and generalized totally bounded metric space, introduced by the author and A. Barbati in a former paper, turn out to play a crucial rôle. Moreover, we show that the first-mentioned concept provides a precise characterization of those metrizable spaces which attain their extent.     

Coxeter complexes and graph-associahedra

Given a graph Γ, we construct a simple, convex polytope, dubbed graph-associahedra, whose face poset is based on the connected subgraphs of Γ. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.     

On extremally disconnected topological groups

We introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set implies the existence of a P-point in ω^∗. Thus it is consistent with ZFC that there is no extremally disconnected topological group containing a countable discrete nonclosed subset.     

Dirac and Lagrangian reductions in the canonical approach to the first-order form of the Einstein-Hilbert action

It is shown that the Lagrangian reduction, in which solutions of equations of motion that do not involve time derivatives are used to eliminate variables, leads to results quite different from the standard Dirac treatment of the first-order form of the Einstein-Hilbert action when the equations of motion correspond to the first class constraints. A form of the first-order formulation of the Einstein-Hilbert action which is more suitable for the Dirac approach to constrained systems is presented. The Dirac and reduced approaches are compared and contrasted. This general discussion is illustrated by a simple model in which all constraints and the gauge transformations which correspond to first class constraints are completely worked out using both methods to demonstrate explicitly their differences. These results show an inconsistency in the previous treatment of the first-order Einstein-Hilbert action which is likely responsible for problems with its canonical quantization.     

下料问题的优化模型及其快速算法

结合生产实际中具体的下料问题,本文建立了该类问题的优化模型,并提出下料方式的遴选三准则,即高利用率优先准则,长度优先准则和时间优先准则.运用本文的算法对一维下料的利用率高达99.6%,机器时间4秒.对二维的利用率为98.9%,机器时间约7秒.     

General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.