Synthesis of a Tweezer—like Bis（Phenylthiapropoxy）calix[4]—arene as a Cation／π Enhanced Sensor for Ion—Selective Electrodes

Two novel 25,27-dihydroxy-26,28-bis(3-phenylthiapropxy)-calix[4]arene(3) and 25,27-dihydroxy-26,28-bis(3-phenylthiapropoxy)-5,11,17,23-tetra-tert-butylcalix[4] arene (4) were synthesized for the evaluation of their ion-selectivity in ion-selective electrodes(ISEs).ISEs based on 3 and 4 as neutral ionophores were prepared,and their selectivity coefficients for Ag^ (lg KAg,M^pot)were investigated against other alkali metal,alkaline-earth metal,aluminum,thallium(Ⅰ）,Lead and some transition metal ions using the separate solution method (SSM).These ISEs showed excellent Ag^ seletivity over most of the interfering cations examined,except for Hg^2 and Fe^2 having relative smaller interference(lg KAg,M^pot≤-2.1).     

Positivity preserving finite element approximation

We consider finite element operators defined on ``rough' functions in a bounded polyhedron in . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of . We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.

     

高能强子–强子碰撞中喷注性质的蒙特卡洛研究

在喷注“圆锥判定法”的基础上,对高能强子–强子碰撞中产生的喷注(微喷注)的性质进行了蒙特卡洛研究.采用以喷注动量为z轴的“喷注坐标系”,给出了表征喷注性质的各物理量在新坐标系中的分布情况.结果表明,圆锥判定法能够作为一种有效手段来对高能强子–强子碰撞和相对论重离子碰撞中发生的硬和半硬过程开展实验研究.由有喷注事件和无喷注事件的多重数分布可以看到,E_t=2GeV是用圆锥法确定喷注的合理的横能截断值.     

Laser-hole boring into overdense plasmas measured with soft X-Ray laser probing

A laser self-focused channel formation into overdense plasmas was observed using a soft x-ray laser probe system with a grid image refractometry (GIR) technique. 1.053 &mgr;m laser light with a 100 ps pulse duration was focused onto a preformed plasma at an intensity of 2x10(17) W/cm (2). Cross sections of the channel were obtained which show a 30 &mgr;m diameter in overdense plasmas. The channel width in the overdense region was kept narrow as a result of self-focusing. Conically diverging density ridges were also observed along the channel, indicating a Mach cone created by a shock wave due to the supersonic propagation of the channel front.     

A posteriori error estimates by recovered gradients in parabolic finite element equations

This paper considers a posteriori error estimates by averaged gradients in second order parabolic problems. Fully discrete schemes are treated. The theory from the elliptic case as to when such estimates are asymptotically exact, on an element, is carried over to the error on an element at a given time. The basic principle is that the elliptic theory can be extended to the parabolic problems provided the time-step error is smaller than the space-discretization error. Numerical illustrations confirming the theoretical results are given. Our results are not practical in the sense that various constants can not be estimated realistically. They are conceptual in nature. AMS subject classification (2000)  65M60, 65M20, 65M15     

Error estimates for a Galerkin method for a class of model equations for long waves

The Galerkin method, together with a second order time discretization, is applied to the periodic initial value problem for $$\frac{\partial }{{\partial t}}(u - (a(x)u_x )_x ) + (f(x,u))_x = 0$$ . Heref(x, ·) may be highly nonlinear, but a certain cancellation effect is assumed for∫f(x, u) _x u. Optimal order error estimates inL ₂,H ₁, andL _∞ are derived for a general class of piecewise polynomial spaces.     

Stability and analyticity in maximum-norm for simplicial Lagrange finite element semidiscretizations of parabolic equations with Dirichlet boundary conditions

Stability and analyticity estimates in maximum-norm are shown for spatially discrete finite element approximations based on simplicial Lagrange elements for the model heat equation with Dirichlet boundary conditions. The bounds are logarithm free and valid in arbitrary dimension and for arbitrary polynomial degree. The work continues an earlier study by Schatz et al. [5] in which Neumann boundary conditions were considered. Received November 1998 / Revised version received August 11, 1999 / Published online July 12, 2000     

Curing theory of A_f-A_g type free radical polymerization (I)──Distribution function and its invariant property

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