The twisted T -adic exponential sum associated with xd + λx is studied. If λ = 0, then an explicitarithmetic polygon is proved to be the Newton polygon of the C-function of the twisted T-adic exponential sum.It give...The twisted T -adic exponential sum associated with xd + λx is studied. If λ = 0, then an explicitarithmetic polygon is proved to be the Newton polygon of the C-function of the twisted T-adic exponential sum.It gives the Newton polygons of the L-functions of twisted p-power order exponential sums.展开更多
Based on the definition of second order moment and the approximate three-dimensional analytical formula for probe detected laser beam passing through a cat-eye optical lens with center shelter and oblique detector, th...Based on the definition of second order moment and the approximate three-dimensional analytical formula for probe detected laser beam passing through a cat-eye optical lens with center shelter and oblique detector, the analytical expression of the encirclement power ratio of the cat-eye effect reflected light under far-field condition has been deduced. Variable laws of light intensity at the return place and encirclement power ratio are performed by numerical calculation, and are analyzed physically. The results show that the light intensity at the return place decreases monotonically with the increases of the diameter, incidence angle, tilted angle of the detector and the center shelter ratio, but the relationships between these parameters and the encirclement power ratio are all nonmonotonic. The reasonable choice of the focal shift size would result in the largest light intensity at the return place and the largest erirclenent power ratio.展开更多
Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its...Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10671015)
文摘The twisted T -adic exponential sum associated with xd + λx is studied. If λ = 0, then an explicitarithmetic polygon is proved to be the Newton polygon of the C-function of the twisted T-adic exponential sum.It gives the Newton polygons of the L-functions of twisted p-power order exponential sums.
文摘Based on the definition of second order moment and the approximate three-dimensional analytical formula for probe detected laser beam passing through a cat-eye optical lens with center shelter and oblique detector, the analytical expression of the encirclement power ratio of the cat-eye effect reflected light under far-field condition has been deduced. Variable laws of light intensity at the return place and encirclement power ratio are performed by numerical calculation, and are analyzed physically. The results show that the light intensity at the return place decreases monotonically with the increases of the diameter, incidence angle, tilted angle of the detector and the center shelter ratio, but the relationships between these parameters and the encirclement power ratio are all nonmonotonic. The reasonable choice of the focal shift size would result in the largest light intensity at the return place and the largest erirclenent power ratio.
基金supported by the National Natural Science Foundation of China(No.11171161)the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education Ministry(No.2012940)
文摘Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.
