Intersection homology of stratified fibrations and neighborhoods

We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include regular neighborhoods in PL stratified spaces.     

PL fibrator properties of partially aspherical manifolds

Approximate fibrations form a useful class of maps. By definition fibrators provide instant detection of maps in this class, and PL fibrators do the same in the PL category. This paper formalizes a natural concept of partial asphericity and establishes fibrator properties of certain partially aspherical closed manifolds. One consequence is that any connected sum of aspherical PL manifolds with residually finite fundamental groups is a codimension-(2n−2) PL fibrator.     

Uniqueness of PL Minimal Surfaces

Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some ambiguity, we sharpen the definition of PL minimal surfaces, and prove a technical lemma on the Plateau problem in the hyperbolic space.     

On the geometry of paths generated by PL homotopy methods

PL homotopy methods are effective numerical methods for highly nonlinear problems. It is widely believed that the feasibility of a PL homotopy method depends on the nondegeneracy condition that the zero set (or the fixed point set in the case of finding fixed points instead of zeroes) of the PL approximation of the homotopy does not intersect the triangulation's skeletons of co-dimensions two and above. This paper shows that, although the sections of the PL approximation's zero set tracked by the PL homotopy method are of dimension one (while other sections may have higher dimensions), the paths generated by the pivoting method are potentially and essentially of dimension two. It makes pathcrossing a safe thing. Thus, this paper first sets up the without exception feasibility of PL homotopy methods geometrically.This work is supported in part by the Foundation of Zhongshan University Advanced Research Centre.     

Joint logistics and financial services by a 3PL firm

Integrated logistics and financial services have been practiced by third party logistics (3PL) firms for years; however, the literature has been silent on the value of 3PL firms as credit providers in budget-constrained supply chains. This paper investigates an extended supply chain model with a supplier, a budget-constrained retailer, a bank, and a 3PL firm, in which the retailer has insufficient initial budget and may borrow or obtain trade credit from either a bank (traditional role) or a 3PL firm (control role). Our analysis indicates that the control role model yields higher profits not only for the 3PL firm but also for the supplier, the retailer, and the entire supply chain. In comparison with a supplier credit model where the supplier provides the trade credit, the control role model yields a better performance for the supply chain as long as the 3PL firm’s marginal profit is greater than that of the supplier. We further demonstrate that, for all players, both the control role and supplier credit models can outperform the classic newsvendor model without budget constraint.     

平滑的PL和分位点过程之间距离的渐近分布(英文)

在随机右删失情况下,我们证明了基于平滑ＰＬ估计和平滑ＰＬ分位点估计的Ｂａｈａｄｕｒ－Ｋｉｅｆｅｒ型过程的弱极限定理     

关于向量标号单纯算法的基本理论——对《解法》一书的若干意见

§1.引言 在《非线性方程组的数值解法》(简称解法)的第七章和第四章中,有些论述不够妥当. 考虑到一些院校已经或准备选用它作为计算数学专业研究生和高年级学生的教材和参考书,影响较大,故将自己的意见提出来,与作者和读者商榷.     

基于直觉模糊集的电子商务第三方物流选择

论文分析了电子商务第三方物流供应商的特点,提出电子商务第三方物流选择评估指标系统。由于指标评估的不确定性、语言描述性,以及信息的不完全性,引入直觉模糊集恰当地刻画已有信息关于相应决策指标的支持、反对,以及不确定状态,提出直觉模糊集的均衡数量集中函数以及均衡数量离散函数,并在此基础上,定义直觉模糊集合成函数,建立基于直觉模糊集的综合评估方法。并通过实例说明该模型的有效性。     

PL embeddings ofPL manifolds into some Euclidean spaces

The main result in this paper is the following: Theorem.Assume that W is a k-connected compact PL n-manifold with boundary, BdW is (k–1)-connected, k1(BdW is 1-connected for k=1), 0h2k, 2n–h>5and there exists a normal block (n-h-1)-bundle vover W, then

左截断右删失下乘积限过程的振动模的强极限定理

本文在左截断右删失模型下获得了乘积限过程和累积失效率过程的振动模和Ｌｉｐｓｃｈｉｔｚ－１２模的强一致收敛的精确速度．作为定理的应用，推导了各种核密度估计和失效率估计的强一致收敛的精确速度．     

A geometrical interpretation of the without-exception feasibility of PL homotopy methods

PL homotopy methods are effective methods to locate zerces (or fixed points) of highly nonlinear mappings. Due to the lexicographical system, the methods are feasible without exceptions. This paper presents a geometrical interpretation of the without-exception feasibility.An invited talk at the 13th International Symposium on Mathematical Programming, Aug. 29–Sep. 2, 1988, Tokyo. The work is supported in part by the Foundation of Zhongshan University, Advanced Research Centre and in part by the National Natural Science Foundation of China.     

Codimension Two PL Embeddings of Spheres with Nonstandard Regular Neighborhoods

For a given polyhedron K(?)M,the notation RM(K)denotes a regular neigh- borhood of K in M.The authors study the following problem:find all pairs(m,k) such that if K is a compact k-polyhedron and M a PL m-manifold,then R_M(f(K))≌R_M(g(K))for each two homotopic PL embeddings f,g:K→M.It is proved that R_S~(k 2)(S~k)(?)S~k×D~2 for each k(?)2 and some PL sphere S~k(?)S~(k 2)(even for any PL sphere S~k(?)S~(K 2)having an isolated non-locally flat point with the singularity S~(k-1)(?) S~(k 1)such thatπ_1(S~(k 1)-S~(k-1))(?)Z).     

Mapping fibrations

We present a fibration theorem for mappings from C ⁿ to C ^p , withn <p that resembles the Milnor fibration theorem for isolated complete intersection singularities which is due to H. Hamm.     

Three-dimensional conical fibrations

The investigation of conical fibrations initiated by M. Artin and D. Mumford, and by A. N. Tyurin (for the case of a nonsingular degeneracy divisor) is extended to the general case. The main results are: a canonical birational model is found for varieties of a given type; the cohomology groups are computed for the canonical models.Translated from Matematicheskie Zametki, Vol. 21, No. 6, pp. 745–758, June, 1977.The author thanks V. A. Iskovskikh, without whose substantial participation, this paper would not have appeared.     

Skew Hopf fibrations

We introduce class F_R(S²⁺¹) of analytic fibrations of sphere S²ⁿ⁺¹,n1, by great circles for which there exists a tensor R, with the algebraic properties of a curvature tensor, such that 1) for almost everyx (R ²ⁿ +2 there exists a unique plane )x, Ofith the condition R (x, u, x)=x ² u, (u x, u (); 2) for planes spanned by fibers condition R(x, u x)=x ² u, (u x, u, x () is fulfiled. We show that F_R(S²ⁿ⁺¹) consists of skew Hopf fibrations (for n=1 see Rzh. Mat. 1987, 11A822). This implies a negative answer to the conjecture expressed in Rzh. Mat. 1972, 11A559 that this class consists of Hopf fibrations. The proof is based on the following result: skew Hopf fibrations are characterized, in the class of all analytic fibrations of a sphere by great circles, by the property that for any pair of orthogonal fibers the great three-dimensional sphere containing them inherits a skew Hopf fibration.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 101–104, 1990.