电影《极限空间》的亮点

文章认为,电影《极限空间》获得了巨大成功,其中充满了亮点,包括奇异的电影剧情、人物之间复杂而又有趣味的关系情结,以及令人回味的趣味逻辑谜题。它以独特的叙事方式和视角,引发了人们对当下生存状态不同程度的解读与反思。

On Inverse Limits of Normal δθ-refinable Spaces

This paper proves the following results: Le t X= lim ←｛X σ,π σ ρ,Λ｝,｜Λ｜=λ, and every p rojection π σ: X→X σ be an open and onto mapping. (A) If X is λ-paracompact and every X σ is normal and δθ-refinable, then X is normal and δθ-refinable; (B) If X is hereditarily λ-pa racompact and every X σ is hereditarily normal and hereditarily δθ- refinable, then X is hereditarily normal and hereditarily δθ-refiable .

Characteristic Functions over C*-Probability Spaces

Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.

Quasi Fast Completeness and Inductive Limits of Webbed Spaces

Let (E,ζ)= indlim (E n ,ζ n ) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E n ,ζ n ). We introduce a property which is weaker than fast completeness, quasi-fast completeness, and prove that for inductive limits of strictly webbed spaces, quasi-fast completeness implies that ( DST ). By using De Wilde’s theory on webbed spaces,we also give some other conditions for ( DST ). These results improve relevant earlier results.

THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES

Let X be a complex Banach space without the analytic Radon-Nikodym property. The author shows that G = {f∈H∞(D,X) there exists∈＞ 0, such that for almost allθ∈[0, 2], lim sup f(reiθ) - f(seiθ)≥∈ } is a dense open subset of H∞(D, X). It is also shown that for every open subset B of T, there exists F∈H∞ (D, X), such that F has boundary values everywhere on Bc and F has radial limits nowhere on B. When A is a measurable subset of T with positive measure, there exists f∈H∞ (D, X), such that f has nontangential limits almost everywhere on Ac and f has radial limits almost nowhere on A.

A SCATTERING MATRIX MODEL OF SEMICONDUCTOR SUPERLATTICES IN MULTIDIMENSIONAL WAVE-VECTOR SPACE AND ITS DIFFUSION LIMIT

The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.

Fluctuation limits of strongly degenerate branching systems

Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.

Chaotic dynamics and coexistence in a three species interaction model

This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of dynamical systems we prove that the trajectories of system are bounded and that open subsets of parameters exist, such that the system in the first octant has at most two singularities. For an open subset of the parameters space, the system is shown to have an invariant compact set and this is a topologically transitive attractor set. Finally, we find another open set in the parameters space, such that the system has two limit cycles each contained in different invariant planes. The work is completed with a numeric simulation showing the attractor is a strange attractor.

The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space

We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schr¨odinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.

Asymptotic limit of the Gross-Pitaevskii equation with general initial data

This paper mainly concerns the mathematical justification of the asymptotic limit of the GrossPitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.

Reconstructing the neutrally-buoyant particle flow near a singular corner

The correction of buoyancy effects is tackled for particles moving close to a singular corner in creeping flow conditions.A few density-mismatched particle trajectories are used to reconstruct the dynamics of a neutrally-buoyant particle all over the target domain.We propose to take advantage of the dissipative dynamics of density-mismatched particles in order to probe the target domain.Thereafter,we retrieve the neutrally-buoyant particle flow all over the domain by reconstructing the phase space of the density-mismatched particulate flow and taking the limit of the particle-to-fluid density ratio tending to one.The robustness of such an approach is demonstrated by deliberately ill-conditioning the reconstruction operator.In fact,we show that our algorithm well performs even when we rely on qualitatively-different density-mismatched orbit topologies or on bundles of close trajectories rather than homogeneously distributed orbits.Potential applications to microfluidics and improvements of the proposed algorithm are finally discussed.