Degenerate Crossing Numbers

Let G be a graph with n vertices and e≥4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p, then they properly cross one another at p. It is shown that the number of crossing points, counted without multiplicity, is at least constant times e and that the order of magnitude of this bound cannot be improved. If, in addition, two edges are allowed to cross only at most once, then the number of crossing points must exceed constant times (e/n)⁴. The research of J. Pach was supported by NSF grant CCF-05-14079 and by grants from NSA, PSC-CUNY, BSF, and OTKA-K-60427. The research of G. Tóth was supported by OTKA-K-60427.     

Optimal choice of threshold in Two Level Processor Sharing

We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with the hyper-exponential job size distribution and with the Poisson arrival process. TLPS is a convenient model to study the benefit of the file size based differentiation in TCP/IP networks. In the case of the hyper-exponential job size distribution with two phases, we find a closed form analytic expression for the expected sojourn time and an approximation for the optimal value of the threshold that minimizes the expected sojourn time. In the case of the hyper-exponential job size distribution with more than two phases, we derive a tight upper bound for the expected sojourn time conditioned on the job size. We show that when the variance of the job size distribution increases, the gain in system performance increases and the sensitivity to the choice of the threshold near its optimal value decreases. The work was supported by France Telecom R&D Grant “Modélisation et Gestion du Trafic Réseaux Internet” no. 46129414.     

Region-based object and background extraction via active contours

In this paper, we propose a region-based model for the object and background extraction with application to the image with thick or complex boundary. Based on region information of the image, we employ two curves to extract the object and background, respectively, regardless of the boundary. The first curve is used to extract the object. Correspondingly, the second curve is used to extract the background. By employing two level set functions to represent the two curves, we propose a new region-based energy functional. In the proposed model, a distance constraint term is incorporated, which effectively avoid that the two level set functions too away from each other and keep their similar shapes well. Besides, we present a penalty term to maintain the accurate computation and stability evolution. Experiment results demonstrate the desirable performance of the proposed model with application to synthetic and real-world images.     

Sequencing mixed-model assembly lines: Survey,classification and model critique

Manufacturers in a wide range of industries nowadays face the challenge of providing a rich product variety at a very low cost. This typically requires the implementation of cost efficient, flexible production systems. Often, so called mixed-model assembly lines are employed, where setup operations are reduced to such an extent that various models of a common base product can be manufactured in intermixed sequences. However, the observed diversity of mixed-model lines makes a thorough sequence planning essential for exploiting the benefits of assembly line production. This paper reviews and discusses the three major planning approaches presented in the literature, mixed-model sequencing, car sequencing and level scheduling, and provides a hierarchical classification scheme to systematically record the academic efforts in each field and to deduce future research issues.     

An L-like model containing very large cardinals

We force and construct a model in which level by level equivalence between strong compactness and supercompactness holds, along with a strong form of diamond and a version of square consistent with supercompactness. This generalises a result due to the first author. There are no restrictions in our model on the structure of the class of supercompact cardinals. A. W. Apter’s research was partially supported by PSC-CUNY Grants and CUNY Collaborative Incentive Grants. J. Cummings’s research was partially supported by NSF Grant DMS-0400982.     

Directional convexity of level lines for functions convex in a given direction

Let be the class of functions which are holomorphic and convex in direction in the unit disk , i.e. the domain is such that the intersection of and any straight line is a connected or empty set. In this note we determine the radius of the biggest disk with the property that each function maps this disk onto the convex domain in the direction .

     

Some function classes closed under infimal convolution

It is shown that the following classes of functionsf, each defined on some subsetD of a fixed Hausdorff topological vector spaceE, are closed under the binary operation of infimal convolution: (a) the class of functionsf:D[–, ) having connectedstrict lower level sets; (b) the class of functionsf:D having compact connected lower level sets; and (c) the class of functionsf:D having compact lower level sets and for which every local minimizer is global. In (a),E need not be Hausdorff; while in (a) and (b), the word connected may be replaced by the word path-connected.     

贴体坐标系中非理想爆轰波阵面传播计算的一个问题

 研究在贴体坐标系中采用Level Set方法计算多维非理想爆轰波阵面传播问题,根据Hamiltom-Jacobi方程的Godunov差分格式,提出了非正交的贴体坐标系中Level Set函数方程的差分格式及其相应的数值方法。最后给出了几个典型数值算例,并且与解析结果进行了比较。     

Precise measurement of hyperfine coupling in CH F based on nuclear spin conversion

A new method is proposed for the experimental determination of the hyperfine coupling in molecules. The method is based on the level-crossing effect in the spin isomer conversion in alternating electric fields. An experiment performed with the ¹³CH₃F molecules has revealed the strength of the off-diagonal in K () nuclear spin-spin coupling kHz, which is only by kHz larger than the theoretical value calculated on the basis of the molecular structure. Received 25 January 2000 and Received in final form 11 May 2000     

Matrix analytic methods for a multi-server retrial queue with buffer

We present numerical methods for obtaining the stationary distribution of states for multi-server retrial queues with Markovian arrival process, phase type service time distribution with two states and finite buffer; and moments of the waiting time. The methods are direct extensions of the ones for the single server retrial queues earlier developed by the authors. The queue is modelled as a level dependent Markov process and the generator for the process is approximated with one which is spacially homogeneous above some levelN. The levelN is chosen such that the probability associated with the homogeneous part of the approximated system is bounded by a small tolerance and the generator is eventually truncated above that level. Solutions are obtained by efficient application of block Gaussian elimination.