Sensitivity analysis for discrete optimal control problems

We present local sensitivity analysis for discrete optimal control problems with varying endpoints in the case when the customary regularity of boundary conditions can be violated. We study the behavior of the optimal solutions subject to parametric perturbations of the problem.     

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.     

皮革中甲醛含量测量不确定度评估

依据GB/T 19941-2005标准,测定了皮革中的甲醛含量,对测量结果的不确定度来源进行了分析和评定,并计算出合成不确定度和有效自由度,最后根据JJF1059规范要求给出了甲醛测量不确定度表达式.     

浅析二阶齐次线性变系数微分方程的一个可积类型

本文讨论了二阶齐次线性变系数微分方程的特殊形式，给出了这种微分方程的一个可积类型．     

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.     

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.     

A study of the fluorescent properties of spin-coated sodium salicylate thin films

Thin films of sodium salicylate were deposited by spin coating from a solution prepared by dissolving sodium salicylate in methanol. The films were characterized by X-ray photoelectron spectroscopy, X-ray diffraction, scanning electron microscopy, UV-visible spectroscopy and spectrofluorometry. The films were crystalline with a strong blue fluorescence peak at an emission wavelength of 419.3 nm. The influence of solution concentration, spin speed and annealing temperature on the fluorescence intensity was studied. Optimum results were obtained with a solution whose concentration was 2.5 M. It was found that lower spin speed resulted in higher fluorescence intensity. Moreover, the fluorescence intensity decreased as the annealing temperature was increased. The durability of the films over a period of 30 days was also investigated, and films annealed at higher temperatures were found to be less degraded with time.