This paper describes the procedure of Gas gain uniformity measurement for ME1/2 Cathode Strip Chambers, a method of data processing and it' s result.
It is shown that, the diameter and height of the CNS,18cm - 22cm and 30cm - 36cm respectively, is necessary, if the 58Ni coating or supermirror coating with m=2 is adopted. The reasonable size of CNS has been suggested.
The leakage gamma ray of iron spheres is measured by high pure Germanium(HPGe) detector. Comparing with the BC-501A scintillator detector, four characteristic gamma rays: 846.77, 1238.282, 1771.351 and 2212.933keV caused by inelastically scattered neutrons are coincident with the BC-501 A scintillator detector. It shows that the measurements by BC-501 A scintillator detector are accurate and credible.
The error propagation in two-filtermethod was also studied and it was found that the influence of uncertaintyof diffusion coefficient D and sampling flow rate q on the result of determ-ination of ~(222)Rn decreases significantly with the decreaae of the parameterμ(μ=O.06πDL/q,where L is the length of sampling tube).
The result show: the risetime, FWHM and fall time of the single φ80mm × 800μm PIN detector is respectively 23,62,94ns; With the numbers of PIN detectors increasing, the time respond is slower; When the number of PIN detectors is six,the risetime,FWHM and fall time is respectively 40,306,652ns.
In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations.
In this paper, we prove three types of rigidity results related to CAT(-1) spaces, namely the rigidity of the isometric actions on CAT(-1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles.
This extends the results and simplifies the proof for the classical orbit structure description of  and , which applies whenF=Z.
A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsYα, α a simple root, in the opposite Borel subalgebra.
The result generalizes and implies the classical "branching rules" that describe the restriction of an irreducible representation of the symmetric groupSn toSn-1.
Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions of bounded variation (where the result is known) and elements of mixed norm spaces.
We use interpolation methods to prove a new version of the limiting case of the Sobolev embedding theorem, which includes the result of Hansson and Brezis-Wainger for Wnk/k as a special case.
The weighted inequalities allow us to transfer the result to the ergodic case, when the operator is induced by a mean bounded, invertible, positive groups.