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A shadow of a subset A of Rn is the image of A under a projectiononto a hyperplane. Let C be a closed nonconvex set in Rn suchthat the closures of all its shadows are convex. If, moreover,there are n independent directions such that the closures ofthe shadows of C in those directions are proper subsets of therespective hyperplanes then it is shown that C contains a copyof Rn2. Also for every closed convex set B minimalimitations C of B are constructed, that is, closed subsetsC of B that have the same shadows as B and that are minimalwith respect to dimension. 相似文献
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Simple Zeros of the Riemann Zeta-Function 总被引:1,自引:0,他引:1
Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26. 相似文献
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This paper concerns a Markov operator T on a space L1, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:
- a the existence of invariant probabilitydensities (IPDs)
- b the existence of strictly positive IPDs,and
- c the existence and uniqueness of IPDs.
- b the existence of strictly positive IPDs,and
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应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统. 相似文献
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A new scheme for plasma electron injection into an acceleration phase of a plasma wake field is presented. In this scheme, a single, short electron pulse travels through an underdense plasma with a sharp, localized, downward density transition. Near this transition, a number of background plasma electrons are trapped in the plasma wake field, due to the rapid wavelength increase of the induced wake wave in this region. The viability of this scheme is verified using two-dimensional particle-in-cell simulations. To investigate the trapping and acceleration mechanisms further, a 1D Hamiltonian analysis, as well as 1D simulations, has been performed, with the results presented and compared. 相似文献