辅助函数法应用举例

本文给出用辅助函数法解题的若干例子。由此可以看出辅助函数法应用的一斑。例1 已知acosθ bsinθ=c,acosφ bsinφ=c((θ-φ)/2≠kπ,k为整数)。求证a/cos(θ φ)/2=b/sin(θ φ)/2=c/cos(θ-φ)/2 证明作辅助函数f=(x,y)=ax by-c,则点P(cosθ,sinθ),Q(cosφ,sinφ)在直线f(x,y)=0上,此时直线方程为ax by=c,由两点式可得 (y-sinθ)/(x-cosθ) =(sinθ-sinφ)/(cosθ-cosφ) ∴xcos[(θ φ)/2] ysin[(θ φ)/2] =cos[(θ-φ)/2],     

Calibration study of the X-T relation for the BESⅢ drift chamber

Offline calibration plays an important role in BES offline data processing. In order to achieve good spatial and momentum resolution, it is necessary to implement high precision offline calibration for the BES drift chamber. This paper studies the time-to-distance relations, which are important calibration constants for track reconstruction. The parameterization of the time-to-distance relation, studies of left-right asymmetry and studies of variation with entrance angle are performed. The impact of dead channels on the time-to-distance relation is given special attention in order to reduce the shift in measured momentum for tracks passing near dead cells. Finally we present the resolutions for barrel Bhabha events(|cos θ|< 0.8) from a J/ψ data set taken in 2012. The average spatial resolution is 123 μm and the momentum resolution for 1.548 Ge V/c Bhabha tracks is 11.9 Me V/c.