共查询到20条相似文献,搜索用时 15 毫秒
1.
A. E. Rudenok 《Differential Equations》2009,45(2):159-167
We suggest a new approach to studying the isochronism of the system where p n and q n are homogeneous polynomials of degree n. This approach is based on the normal form and its analog in polar coordinates. We prove a theorem on sufficient conditions for the strong isochronism of a center and a focus for the reduced system and obtain examples of centers with strong isochronism of degrees n = 4, 5. The present paper is the first to give examples of foci with strong isochronism for the system in question.
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${{dx} \mathord{\left/ {\vphantom {{dx} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = - y + p_n (x,y),{{dy} \mathord{\left/ {\vphantom {{dy} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = x + q_n (x,y),$
${{dX} \mathord{\left/ {\vphantom {{dX} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = - Y + XS(X,Y),{{dY} \mathord{\left/ {\vphantom {{dY} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = X + YS(X,Y)$
2.
V. V. Zhuk 《Journal of Mathematical Sciences》2009,157(4):592-606
Let
be the Fejér kernel, C be the space of contiuous 2π-periodic functions f with the norm
, let
be the Jackson polynomials of the function f, and let
be the Fejér sums of f. The paper presents upper bounds for certain quantities like
which are exact in order for every function f ∈ C. Special attention is paid to the constants occurring in the inequalities obtained. Bibliography: 14 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 90–114. 相似文献
3.
We give criteria for a sequence (X
n
) of i.i.d.r.v.'s to satisfy the a.s. central limit theorem, i.e.,
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4.
In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ(f)(x)=(∫0^∞│∫│1-y│≤t Ω(x,x-y)/│x-y│^n-p f(y)dy│^2dt/t1+2p)^1/2 are investigated.It is proved that if Ω∈ L∞(R^n) × L^r(S^n-1)(r〉(n-n1p'/n) is an odd function in the second variable y,then the operator μΩ^ρ is bounded from L^p(R^n) to L^p(R^n) for 1 〈 p ≤ max{(n+1)/2,2}.It is also proved that,if Ω satisfies the L^1-Dini condition,then μΩ^ρ is of type(p,p) for 1 〈 p ≤ 2,of the weak type(1,1) and bounded from H1 to L1. 相似文献
5.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
6.
Vito Lampret 《Central European Journal of Mathematics》2010,8(3):488-499
Zeta-generalized-Euler-constant functions,
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