Isospectral Flat 3-Manifolds

A well-known problem about Riemannian manifolds asks whether the isospectral manifolds are isometric. We settle this problem for compact flat 3-manifolds.     

Set-Indexed Conditional Empirical and Quantile Processes Based on Dependent Data

We consider a conditional empirical distribution of the form F_n(C x)=∑ⁿ_t=1 ω_n(X_t−x) I{Y_tC} indexed by C , where {(X_t, Y_t), t=1, …, n} are observations from a strictly stationary and strong mixing stochastic process, {ω_n(X_t−x)} are kernel weights, and is a class of sets. Under the assumption on the richness of the index class in terms of metric entropy with bracketing, we have established uniform convergence and asymptotic normality for F_n(· x). The key result specifies rates of convergences for the modulus of continuity of the conditional empirical process. The results are then applied to derive Bahadur–Kiefer type approximations for a generalized conditional quantile process which, in the case with independent observations, generalizes and improves earlier results. Potential applications in the areas of estimating level sets and testing for unimodality (or multimodality) of conditional distributions are discussed.     

Distributions of the high temperature and the high pressure inside a single acoustically driven bubble

The physical circumstances inside an acoustically driven single gas bubble in water has been intensively explored during the past few years. Starting from the results obtained for a typical case in a well known early paper (Wu, C. C., Roberts, P. H., Phys. Rev. Lett., 1993, 70(22): 3424) and introducing successively several corrections to the physical model, this paper computes in corresponding order the temporal and spatial distributions of significant physical parameters, including the temperature and the pressure, in the bubble around the moment of the bubble’s violent collapse, until expectations in consistence with the present points of view are procured. For the peak temperature our results agree with the prevailing belief that in a typical stable single bubble it is of the order of ten thousand degrees.     

A network model for airline cabin crew scheduling

Airline crew scheduling problems have been traditionally formulated as set covering problems or set partitioning problems. When flight networks are extended, these problems become more complicated and thus more difficult to solve. From the current practices of a Taiwan airline, whose work rules are relatively simple compared to many airlines in other countries, we find that pure network models, in addition to traditional set covering (partitioning) problems, can be used to formulate their crew scheduling problems. In this paper, we introduce a pure network model that can both efficiently and effectively solve crew scheduling problems for a Taiwan airline using real constraints. To evaluate the model, we perform computational tests concerning the international line operations of a Taiwan airline.     

匹配数与控制数相等的图的结构性质

我们分别用γ(G)，β(G)和α(G)表示图G的控制数、匹配数和覆盖数，对任意连通图，有γ(G)≤β(G)≤α(G)成立，1998年，Randerath和Volkmann给出了控制数等于覆盖数的图的特征，本文首先证明了匹配数与控制数相等的图其最小度不超过2，而后给出了最小度为2的图的结构性质。     

无穷级拟亚纯映射的充满圆及Borel方向

对于平面上的K-拟亚纯映射，文献^[1]里证明了有限正级K-拟亚纯映射必定存在充满圆序列及Borel方向；本文进一步证明了对于平面上无穷级K-拟亚纯映射也存在充满圆序列及Borel方向．     

On Harpers' Result Concerning the Bandwidths of Graphs

In this paper, we improve the result by Harper on the lower bound of the bandwidth of connected graphs. In addition, we prove that considerating the interior boundary and the exterior boundary when estimating the bandwidth of connected graphs gives the same results.     

Polynomials with Critical Values on Intervals

For polynomials P(z) with real coefficients having a fixed leading coefficient and satisfying the conditions P(z) ∈ [?1, 1] for z ∈ [?1, 1] and P(z) ∈ [?1, 1] if P′(z) = 0, we obtain new covering theorems, a Bernshtein-type inequality, and inequalities for the coefficients. The proofs are based on the use of univalent conformal mappings.     

关于正方形序列覆盖正方形的注记

本文研究正方形序列覆盖正方形问题中涉及的一个函数的下界问题·设{Q_i}为闭正方形序列, f(x)=sup{a:Q为正方形,其边长为a,{Q_i}覆盖{Q},本文给出了f(x)的若干下界.     

Interior Point Methods for Second-Order Cone Programming and OR Applications

Interior point methods (IPM) have been developed for all types of constrained optimization problems. In this work the extension of IPM to second order cone programming (SOCP) is studied based on the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear objective function over the direct product of quadratic cones, rotated quadratic cones, and an affine set. It is described in detail how to convert several application problems to SOCP. Moreover, a proof is given of the existence of the step for the infeasible long-step path-following method. Furthermore, variants are developed of both long-step path-following and of predictor-corrector algorithms. Numerical results are presented and analyzed for those variants using test cases obtained from a number of application problems.