关于三维Minkowski空间中直线汇的一些注记

本文研究了三维Minkowski空间中直线汇的一些性质,特别是关于类时线汇的性质．讨论了线汇基本元素的存在性,并证明了关于三维Minkowski空间中类时线汇的配分参数的一个结果,推广了苏步青1927年的—个成果．     

Approximation by a class of modified Szász-Durrmeyer operators

We modify Szász-Durrmeyer operators by means of three-diagonal generalized matrix which overcomes a difficulty in extending a Berens-Lorentz result to the Szász-Durrmeyer operators for second order of smoothness. The direct and converse theorems for these operators inL _p are also presented by Ditzian-Totik modulus of smoothness.This project is supported by Zhejiang Provincial Foundation of China.     

Equisingularity classes of birational projections of normal singularities to a plane

Given a birational normal extension O of a two-dimensional local regular ring (R,m), we describe all the equisingularity types of the complete m-primary ideals J in R whose blowing-up X=BlJ(R) has some point Q whose local ring OX,Q is analytically isomorphic to O.     

非球面塑料透镜注射型芯工艺探讨

本文来自于作者的实践。介绍了加工方法及测量问题。重点叙述了加工中的一些关键,同时也提供了国内外在这方面的进展情况。     

Radio-Frequency Hexamethyldisiloxane Plasma Deposition: A Comparison of Plasma- and Deposit-Chemistry

This study reports on the effect of input power to hexamethyldisiloxane (HMDSO) plasmas. The power dependence of the plasma-phase species and of the surface chemistry (of the deposits) has been investigated. Neutral and positive molecular species were detected within the plasma using mass spectrometry (MS). Secondary ion mass spectrometry (SIMS) was used to probe the molecular structure of the deposits. The elemental composition of the surface was determined by XPS and the deposition rate was monitored using a vibrating quartz crystal microbalance. Neutral and cationic molecules of mass greater than HMDSO were detected in the plasma. Their formation through ion-molecule reactions is proposed. Changes in the relative concentration of plasma-phase species follow those seen in molecular species detected at the deposit surface. Thus, we believe that the molecular structure of the deposits can be related to the species present in the plasma. While traditionally the dominant mechanism in deposit formation is assumed to be free radical combinations, we propose other possibilities involving cations with the aim of putting forward a new perspective on plasma polymerization mechanisms and thereby stimulating discussion.     

Rescaled mean spherical approximation structure factor for an aqueous suspension of polystyrene spheres

Rescaled mean spherical approximation (RMSA) has been used to calculate the structure factor for the aqueous suspension of polystyrene macroions with the interaction potential taken according to Derjaguin and Landau (1941) and Verwey and Overbeek (1948) (DLVO) model. The effects of charge over the macroion and size on the surface potential and therefore, the structure factor have been studied. The breakdown of the DLVO potential with an excess charge over the macroion (⩾800e) has been reported. The oscillation in the first peak height of structure factor versus wave vector curve with size has been correlated with the Debye length.     

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH3 on Pt(1 0 0) coupled by diffusion

The Lombardo–Imbihl–Fink (LFI) ODE model of the NO+NH₃ reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH₃ and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH₃ and H.     

Surface Nitridation of Molybdenum by Laser-promoted Reaction

l.IntroductionowingtotheirpromisingproPertiesandPOtentialapplications,transitionmetalni-trideshavedrawngreatattentionandthepreparationandinvestigationofthesecom-poundshavebeenasubjectbothofscientificandoftechnologicalinterest.Transitionmetalnitridescombineadvantagesofexce1lenthardness,highmeltingPOint,goodchemi-calstabilityandhigheIectricalconductivity[11,henceoverlaySofthesecompoundshavefoundwideappIicationsinvariousfie1ds.Molybdenumnitrides,inparticular,havealsoemergedasverypromisingcandi…     

A partial differential equation which describes an interatomic surface

In this work we present a first-order partial differential equationwhich defines the topology of single ‘atomic entities’in multiatomic systems. Such an equation, obtained by R. F.W. Bader, is here analysed and discussed from a general mathematicalpoint of view; a method is then proposed for defining the initialor boundary condition. With this contribution we would liketo promote and stimulate a more detailed analysis which goesbeyond practical purposes and basic mathematical analysis inorder to have a deeper understanding of the theory behind theequation and its consequences for practical applications.     

A hybrid finite-element–volume-of-fluid method for simulating free surface flows and interfaces

A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume-of-fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid-size-dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM-VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break-up of a capillary jet and the coalescence collision of two liquid drops.