THE SOLUTION OF _b－EQUATION OF （P，Q）－FORMS AND IT＇S L~P＆HOLDER ESTIMATES ON A STEIN MANIFOLD

ＴＨＥＳＯＬＵＴＩＯＮＯＦ_ｂ－ＥＱＵＡＴＩＯＮＯＦ（Ｐ，Ｑ）－ＦＯＲＭＳＡＮＤＩＴ＇ＳＬ￣Ｐ＆ＨＯＬＤＥＲＥＳＴＩＭＡＴＥＳＯＮＡＳＴＥＩＮＭＡＮＩＦＯＬＤ￥ＷｕＸｉａｏｑｉｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉｍｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｇｅＸｉａ?..     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

偶极子在径向非均匀介质中的电磁场分布

提出了柱状多层介质中的磁偶极子在任意介质层中的电磁场的递推算法，给出了磁偶极子产生的电磁波在柱状多层介质中的反射、透射系数和广义反射系数，从而得到了任意介质层中满足各层界面边界条件的电磁场解析表达式．     

Synthesis methods of multiple phase-cycled SSFP images to reduce the band artifact and noise more reliably

The band artifact in steady-state free precession can be reduced by synthesizing the multiple images obtained through different phase increments of successive radiofrequency pulses. Even though the complex summation method was reported to be effective in reducing the band artifact, it has the pitfalls of intensity abnormality and sensitivity to the phase abnormality. Two new methods have been developed for more reliable reduction of the band artifact than the complex summation method. One method is to sum the complex images partially and to take the maximum intensity of the partially summed images. The other method is to sum the free induction decay (FID) and primary echo components of the Fourier series that are obtained through Fourier analysis of the complex base images. Both proposed methods were compared with other magnitude (maximum intensity projection, spectrally decomposed synthesis, sum-of-squares, nonlinear averaging) and complex-based (complex summation, magnitude-weighted complex summation) methods experimentally at 3 T for the phantom and volunteer's head imaging. Both proposed methods were confirmed to maintain the advantage of the complex summation in reducing both the dark and bright band artifacts while reducing the intensity abnormality and sensitivity to the phase abnormality from that of the complex summation method over a wide range of flip angles and relaxation times.     

A study of time over threshold (TOT) technique for plastic scintillator counter

A new charge measurement method, time over threshold (TOT), has been used in some gas detectors lately. Here TOT is studied for TOF system, made of plastic scintillator counter, which can simplify the electronics of the system. The signal characteristics are measured and analyzed with a high quality oscilloscope, including noise, pedestal, signal amplitude, total charge, rise time and the correlation between them. The TOT and charge are related and can be fitted by some empirical formula. The charge measurement resolution by TOT is given and this will help the design of TOF electronics.     

A localization argument for characters of reductive Lie groups

This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by Schmid (in: Deformation Theory and Symplectic Geometry, Mathematical Physics Studies, Vol. 20, Kluwer Academic Publishers, Dordrecht, 1997, pp. 259-270).A corresponding problem in the compact group setting was solved by Berline et al. (Heat Kernels and Dirac Operators, Springer, Berlin, 1992) by an application of the theory of equivariant forms and particularly the fixed point integral localization formula. This article (besides its representation-theoretical significance) provides a whole family of examples where it is possible to localize integrals to fixed points with respect to an action of a noncompact group. Moreover, a localization argument given here is not specific to the particular setting considered in this article and can be extended to a more general situation.There is a broadly accessible article (Libine, A Localization Argument for Characters of Reductive Lie Groups: An Introduction and Examples, 2002, math.RT/0208024) which explains how the argument works in the case, where the key ideas are not obstructed by technical details and where it becomes clear how it extends to the general case.     

Modularity and Total Ellipticity of Some Multiple Series of Hypergeometric Type

We collect some new evidence for the validity of the conjecture that every totally elliptic hypergeometric series is modular invariant and briefly discuss a generalization of such series to Riemann surfaces of arbitrary genus.     

平面运动学位似运动Steiner公式的推广

对单参数闭平面复意义位似运动，给出了Muller提出的Steiner公式和混合面公式的表达式。利用推广的Steiner公式得到了位似运动的Holditch定理．作为特例，给出了Muller位似比h≡1时的结果。