A New Approach to Analysis of Polling Systems

In this paper, we consider polling systems with J stations with Poisson arrivals and general service distributions attended by a cyclic server. The service discipline at each station is either exhaustive or gated. We propose a new approach to analysis of the mean waiting times in the polling systems. The outline of our method is as follows. We first define the stochastic process Q that represents an evolution of the system state, and define three types of the performance measures W _i ,H _i and F _i , which are the expected waiting times conditioned on the system state. Then from the analysis of customers at polling instants, we find their linear functional expressions. The steady state average waiting times can be derived from the performance measures by simple limiting procedures. Their actual values can be obtained by solving J(J+1) linear equations.     

The Studies of Free Radical Cyclization Reactions Mediated by Sulfonyl Chloride (I)

A study of the free racinoal reaction of vinylcycloprelpane mediated by p-toluenesulfonyl chloride is described.     

On the stability of medial axis transform

Medial axis transform (MAT) is very sensitive to noise, in the sense that, even if a shape is perturbed only slightly, the Hausdorff distance between the MATs of the original shape and the perturbed one may be large. Recently, Choiet al. (2002) showed that MAT is stable for a class of 2D domains called weakly injective, if we view this phenomenon with the one-sided Hausdorff distance, rather than with the two-sided Hausdorff distance. In this paper, we extend this result to general 2D domains with natural boundary regularity. We also present explicit bounds for this general one-sided stability of the 2D MAT.     

Molecular dynamics simulation study of the nano-wear characteristics of alkanethiol self-assembled monolayers

A molecular dynamics (MD) simulation study of the probe-based nano-lithography of an alkanethiol self-assembled monolayer (SAM) on a metal surface was performed. The motivation of this work was to understand the nano-tribological phenomena of the nano-metric scribing process of alkanethiol molecules and gain insight into the interaction between the probe tip and the SAM-coated surface during the scribing process. The simulation results revealed that the organothiol molecules were displaced and dragged by the probe tip during scribing due to the strong interchain interactions. It was also found that the scribed pattern width was largely dependent on the tip–surface interaction induced by the probe shape rather than the tip–surface contact size. Also, the minimum load for tip–substrate contact changed with the number of molecules that interact with the probe tip. Furthermore, from the investigation of the effect of the scribing speed on the surface-damage characteristics of the chain molecules, it was found that relatively high-speed scribing could induce excessive removal of the SAM molecules from the surface. PACS 02.70.Ns; 31.15.Qg; 81.16.Nd; 68.35.Af     

Calibrated lifts of minimal submanifolds

A canonical real line bundle associated to a minimal Lagrangian submanifold in a Kähler-Einstein manifold X is known to be special Lagrangian when considered as a subset of the canonical line bundle of X with a natural Calabi-Yau structure. We first verify this result by standard moving frame computation, and obtain a uniform lower bound for the mass of compact minimal Lagrangian submanifolds in CPn. Similar correspondence is then proved for integrable G₂ and Spin(7) structures on the bundle of anti self dual 2-forms and a Spin bundle respectively of a self dual Einstein 4-manifold N constructed by Bryant and Salamon. In this case, analogues of tangent and normal bundles of certain minimal surfaces in N are calibrated, i.e., associative, coassociative, or Cayley.     

Vector Ordinal Optimization

Ordinal optimization is a tool to reduce the computational burden in simulation-based optimization problems. So far, the major effort in this field focuses on single-objective optimization. In this paper, we extend this to multiobjective optimization and develop vector ordinal optimization, which is different from the one introduced in Ref. 1. Alignment probability and ordered performance curve (OPC) are redefined for multiobjective optimization. Our results lead to quantifiable subset selection sizes in the multiobjective case, which supplies guidance in solving practical problems, as demonstrated by the examples in this paper.This paper was supported in part by Army Contract DAAD19-01-1-0610, AFOSR Contract F49620-01-1-0288, and a contract with United Technology Research Center (UTRC). The first author received additional funding from NSF of China Grants 60074012 and 60274011, Ministry of Education (China), and a Tsinghua University (Beijing, China) Fundamental Research Funding Grant, and the NCET program of China.The authors are grateful to and benefited from two rounds of reviews from three anonymous referees.     

(–)‐α‐Isosparteine copper(II) diazide

In the title complex, [Cu(N₃)₂(C₁₅H₂₆N₂)], the Cu atom is surrounded by the two N atoms of the chelating (?)‐α‐isosparteine ligand and another two N atoms from the two azide anions, forming a distorted CuN₄ tetrahedron. The two azide anions are terminally bound to the Cu^II atom, and the dihedral angle between the N_sparteine—Cu—N_sparteine and N_azide—Cu—N_azide planes is 50.0 (2)°.     

Application of SSNTDs for study of boron distribution in alloys

A study of boron behavior and its distribution in boron doped iron-, nickel- and aluminum-base alloys subjected to various treatment conditions has been performed. For this purpose a technique based on the detection of ¹⁰B(n,)⁷Li reaction products with track etch detectors has been applied. High boron enrichment of grain boundaries of both iron base and ingot nickel base alloys has been observed. After hot and then cold rolling of the latter specimens boron rearrangement along with the proper deformation of the structure took place. Striation of boron in a hot rolled aluminum alloy along the rolling direction has been observed.     

Solid phase synthesis of benzamidine-derived sulfonamide libraries

Using solid phase synthesis, a library has been constructed of benzamidine-derived sulfonamides which have strong inhibitory activity against blood coagulant thrombin. The library compounds were obtained in good yield and high purity. This revised version was published online in August 2006 with corrections to the Cover Date.     

A three‐dimensional vortex particle‐in‐cell method for vortex motions in the vicinity of a wall

A new vortex particle‐in‐cell method for the simulation of three‐dimensional unsteady incompressible viscous flow is presented. The projection of the vortex strengths onto the mesh is based on volume interpolation. The convection of vorticity is treated as a Lagrangian move operation but one where the velocity of each particle is interpolated from an Eulerian mesh solution of velocity–Poisson equations. The change in vorticity due to diffusion is also computed on the Eulerian mesh and projected back to the particles. Where diffusive fluxes cause vorticity to enter a cell not already containing any particles new particles are created. The surface vorticity and the cancellation of tangential velocity at the plate are related by the Neumann conditions. The basic framework for implementation of the procedure is also introduced where the solution update comprises a sequence of two fractional steps. The method is applied to a problem where an unsteady boundary layer develops under the impact of a vortex ring and comparison is made with the experimental and numerical literature. Copyright © 2001 John Wiley & Sons, Ltd.