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1.
A. M. Zubkov 《Mathematical Notes》1977,22(5):906-914
Let
where 1,..., n are independent random variables and the
are functions (e.g., taking the values 0 and 1). For cases when almost all the summands forming are equal to 0 with a probability close to 1, estimates from above and below are obtained for the quantity P{=0}, as well as upper estimates for the distance in variation between the distribution , and the distribution of the approximating sum of independent random variables.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 745–758, November, 1977.The author is grateful to V. G. Mikhailov for numerous discussions of the results of this paper and for his help in carrying out the tedious auxiliary calculations. 相似文献
2.
We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH
0 (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH
0. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :
相似文献
3.
Rudolf Wegmann 《Constructive Approximation》1994,10(2):179-186
Letf be a function analytic in the unit diskD. If the rangef(D) off is contained in a rectangleR with sidesa andb withba such thatf(D) touches both small sides ofR, then the supremum norm of the derivative satisfies f b·(b/a). We derive tight bounds for the best possible function in this estimate. In particular, we show that
for small .Communicated by Dieter Gaier. 相似文献
4.
E. G. Emel'yanov 《Journal of Mathematical Sciences》1987,38(4):2090-2098
In the class F1 of functions f(), regular and univalent in the annulus ={<||<1} and satisfying the conditions ¦f()¦ < 1 and f() 0 for , ¦f()¦=1 ¦¦=1, for f(l)=1, one finds the set of the values D(A)=f(A): f for an arbitrary fixed point A. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 82–92, 1985. 相似文献
5.
С. Г. Мерзляков 《Analysis Mathematica》1989,15(1):3-16
A=(a
ij)
i
j=1
— k-o ,a
ij
. :
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