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11.
s个几乎相等的素数的k次方和(Ⅰ) 总被引:1,自引:0,他引:1
孟宪萌 《纯粹数学与应用数学》2002,18(1):5-12
假定pθ‖k,当p=2,2|k时,γ=θ 2;其它情况时,γ=θ 1。而R=П(p-1)|kp^γ。本文在GRH(广义Riemann假设下),证明了当s=2^k 1,1≤k≤11时,任何足够大的整N≡s(modR)都可以表示为s个几乎相等的素数的k次方程。 相似文献
12.
借助于环论的方法研究了具有交换自同构群的有限群,提出了一种新的自同构构作技术,并用之证明了这样的非交换有限群具有非循环的中心子群,以及其每个极大子群的中心子群也都非循环. 相似文献
13.
Roger M. Bialy Dr. Monsur M. Ali Prof. Dr. Yingfu Li Prof. Dr. John D. Brennan 《Chemistry (Weinheim an der Bergstrasse, Germany)》2020,26(22):5085-5092
We report a method to detect proteins via suppression of rolling circle amplification (RCA) by using an appropriate aptamer as the linear primer (denoted as an aptaprimer) to initiate RCA. In the absence of a protein target, the aptaprimer is free to initiate RCA, which can produce long DNA products that are detected via binding of a fluorescent intercalating dye. Introduction of a target causes the primer region within the aptamer to become unavailable for binding to the circular template, inhibiting RCA. Using SYBR Gold or QuantiFluor dyes as fluorescent probes to bind to the RCA reaction product, it is possible to produce a generic protein-modulated RCA assay system that does not require fluorophore- or biotin-modified DNA species, substantially reducing complexity and cost of reagents. Based on this modulation of RCA, we demonstrate the ability to produce both solution and paper-based assays for rapid and quantitative detection of proteins including platelet derived growth factor and thrombin. 相似文献
14.
L. A. Beklaryan 《Mathematical Notes》2002,71(3-4):305-315
In [1] G. Margulis proved Ghys's conjecture stating the validity of the following analog of the Tits alternative: either the group
of homeomorphisms of the circle possesses a free subgroup with two generators or there is an invariant probabilistic measure on S
1
. In the present paper, we prove the following strengthening of Margulis's statement: an invariant probabilistic measure for a group
exists if and only if the quotient group
does not contain a free subgroup with two generators (here
is some specific subgroup of G defined in a canonical way). We also formulate and prove analogs of the Tits alternative for groups
of homeomorphisms of the line. 相似文献
15.
We define an S1-Euler characteristic, S
1(X), of a circle action on a compact manifold or finite complex X. It lies in the first Hochschild homology group HH
1(G) where G is the fundamental group of X. This S
1(X) is analogous in many ways to the ordinary Euler characteristic. One application is an intuitively satisfying formula for the Euler class (integer coefficients) of the normal bundle to a smooth circle action without fixed points on a manifold. In the special case of a three-dimensional Seifert fibered space, this formula is particularly effective. 相似文献
16.
In the paper we give the best possible estimate for the minimal number of unit circles determined by n points passing through an arbitrarily chosen point. 相似文献
17.
Ferenc Fodor 《Geometriae Dedicata》1999,74(2):139-145
Dense packings of n congruent circles in a circle were given by Kravitz in 1967 for n = 2,..., 16. In 1969 Pirl found the optimal packings for n 10, he also conjectured the dense configurations for 11 n 19. In 1994, Melissen provided a proof for n = 11. In this paper we exhibit the densest packing of 19 congruent circles in a circle with the help of a technique developed by Bateman and Erdös. 相似文献
18.
Zaqueu Coelho 《Transactions of the American Mathematical Society》2004,356(11):4427-4445
For a minimal circle homeomorphism we study convergence in law of rescaled hitting time point process of an interval of length 0$">. Although the point process in the natural time scale never converges in law, we study all possible limits under a subsequence. The new feature is the fact that, for rotation numbers of unbounded type, there is a sequence going to zero exhibiting coexistence of two non-trivial asymptotic limit point processes depending on the choice of time scales used when rescaling the point process. The phenomenon of loss of tightness of the first hitting time distribution is an indication of this coexistence behaviour. Moreover, tightness occurs if and only if the rotation number is of bounded type. Therefore tightness of time distributions is an intrinsic property of badly approximable irrational rotation numbers.
19.
We consider quadratic diophantine equations of the shape
for a polynomial Q(X1, ..., Xs) Z[X1, ..., Xs] of degree 2.Let H be an upper bound for the absolute values of the coefficientsof Q, and assume that the homogeneous quadratic part of Q isnon-singular. We prove, for all s 3, the existence of a polynomialbound s(H) with the following property: if equation (1) hasa solution x Zs at all, then it has one satisfying
For s = 3 and s = 4 no polynomial bounds s(H) were previouslyknown, and for s 5 we have been able to improve existing boundsquite significantly. 2000 Mathematics Subject Classification11D09, 11E20, 11H06, 11P55. 相似文献
20.
Let S=G/K be a strongly irreducible, simply connected, compact symmetric space and let
be its group of isometries. We classify the symmetric spaces among these that admit free, isometric circle actions. The existence of such actions is important in constructing examples of manifolds with positive sectional curvature. 相似文献