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981.
The finite motion of a massive scalar particle in the gravitational field of a microcosmic black hole with weak relativistic approximation is discussed. In the Schwarzschild field, using the condition for balance σ=0, we obtain the relation between the produced and captured amplitudes for particles. In the Kerr field we show that the attenuation depends on the moment of the black hole and the attenuation process becomes an exciting one when ωh. 相似文献
982.
983.
The sound generated by the unsteady motion of a vortex filament moving over a flat boundary with a sharp flow impedance discontinuity is studied theoretically. Theoretical results show that the vortex filament undergoes significant accelerating or decelerating motions and radiates sound at the instant when it moves across the plane of impedance discontinuity. The accelerations and decelerations of the vortex filament are shown to be the major mechanisms of sound generation. The sound so produced has a large low-frequency content such that the change in the flow impedance affects only the sound generation process but not the subsequent sound propagation to the far field. 相似文献
984.
985.
986.
987.
By the extremal number
ex(n; t) = ex(n; {C
3, C
4, . . . , C
t
}) we denote the maximum size (that is, number of edges) in a graph of order n > t and girth at least g ≥ t + 1. The set of all the graphs of order n, containing no cycles of length ≥ t, and of size ex(n; t), is denoted by EX(n; t) = EX(n; {C
3, C
4, . . . , C
t
}), these graphs are called EX graphs. In 1975, Erdős proposed the problem of determining the extremal numbers ex(n; 4) of a graph of order n and girth at least 5. In this paper, we consider a generalized version of this problem, for t ≥ 5. In particular, we prove that ex(29; 6) = 45, also we improve some lower bounds and upper bounds of ex
u
(n; t), for some particular values of n and t. 相似文献
988.
We consider a situation in which a manufacturer has to select the product(s) to sell as well as the selling price and production quantity of each selected product. There are two substitutable products in the consideration set, where product 2 has a higher quality and reservation price than that of product 1. By considering the cannibalization effect that depends on the selling price of each product, the manufacturer needs to evaluate the profit function associated with three different product line options: sell both products or only one of the 2 products. In order to examine the impact of costs, capacity, and competition on the optimal product line selection, optimal price, and optimal production quantity analytically, we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal. 相似文献
989.
In this note, we prove some results of Hua in short intervals. For example, each sufficiently large integer N satisfying some congruence conditions can be written aswhere \( U = N\tfrac{1}{2} - \eta + \varepsilon \) with \( \eta = \frac{2}{{\kappa \left( {K + 1} \right)\left( {{K^2} + 2} \right)}} \) and \( K = {2^{k - 1}},k\geqslant 3. \)
相似文献
$ \left\{ {\begin{array}{*{20}{c}} {N = p_1^2 + p_2^2 + p_3^2 + p_4^2 + {p^k}}, \hfill \\ {\left| {{p_j} - \sqrt {N/5} } \right| \leqslant U,\left| {p - {{\left( {N/5} \right)}^{\tfrac{1}{k}}}} \right|\leqslant UN - \tfrac{1}{2} + \tfrac{1}{k},j = 1,2,3,4,} \hfill \\ \end{array} } \right. $
990.