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1.
Summary The members of the power divergence family of statistics
all have an asymptotically equivalent χ2 distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the
speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX
2 statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated)
expansions. 相似文献
2.
Shi Ping LU Wei Gao GE 《数学学报(英文版)》2005,21(6):1309-1314
Thc main aim of this paper is to use the continuation theorem of coincidence degree theory for studying the existence of periodic solutions to a kind of neutral functional differential equation as follows:(x(t)-^n∑i=1cix(t-ri))″=f(x(t))x′+g(x(t-τ))+p(t).In order to do so, we analyze the structure of the linear difference operator A : C2π→C2π, [Ax](t) =x(t)-∑^ni=1cix(t-ri)to determine some flmdamental properties first, which we are going to use throughout this paper. Meanwhile, we also prove some new inequalities which are useful for estimating a priori bounds of periodie solutions. 相似文献
3.
This paper is concerned with the divergence points with fast growth orders of the partial quotients in continued fractions.
Let S be a nonempty interval. We are interested in the size of the set of divergence points
$
E_\varphi (S) = \left\{ {x \in [0,1):{\rm A}\left( {\frac{1}
{{\varphi (n)}}\sum\limits_{k = 1}^n {\log a_k (x)} } \right)_{n = 1}^\infty = S} \right\},
$
E_\varphi (S) = \left\{ {x \in [0,1):{\rm A}\left( {\frac{1}
{{\varphi (n)}}\sum\limits_{k = 1}^n {\log a_k (x)} } \right)_{n = 1}^\infty = S} \right\},
相似文献
4.
V. M. Dil’nyi 《Ukrainian Mathematical Journal》2008,60(9):1477-1482
We present an equivalent definition of functions analytic in the half-plane ℂ+ = {z: Re z > 0} for which
5.
Suppose z
1, z
2, ... z
n are complex numbers with absolute values more than 1 and Arg z
j Arg z
k for j k where Arg w stands for the argument of the complex number w in [0,2). In this note we show that
6.
For positive integersn, m and realp≥1, let
Upper and lower bounds for this quantity are derived, extending results of Brown and Spencer forB
1(n,n), corresponding to the Gale-Berlekamp switching problem. For a Minkowski spaceM of dimensionm, define
a quantity investigated by Dvoretzky and Rogers. 相似文献
7.
We prove a general theorem on the zeros of a class of generalised Dirichlet series. We quote the following results as samples.
Theorem A.Let 0<θ<1/2and let {a
n
}be a sequence of complex numbers satisfying the inequality
for N = 1,2,3,…,also for n = 1,2,3,…let α
n
be real and |αn| ≤ C(θ)where C(θ) > 0is a certain (small)constant depending only on θ. Then the number of zeros of the function
in the rectangle (1/2-δ⩽σ⩽1/2+δ,T⩽t⩽2T) (where 0<δ<1/2)is ≥C(θ,δ)T logT where C(θ,δ)is a positive constant independent of T provided T ≥T
0(θ,δ)a large positive constant.
Theorem B.In the above theorem we can relax the condition on a
n
to
and |aN| ≤ (1/2-θ)-1.Then the lower bound for the number of zeros in (σ⩾1/3−δ,T⩽t⩽2T)is > C(θ,δ) Tlog T(log logT)-1.The upper bound for the number of zeros in σ⩾1/3+δ,T⩽t⩽2T) isO(T)provided
for every ε > 0.
Dedicated to the memory of Professor K G Ramanathan 相似文献
8.
V. Zh. Dumanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(1):26-42
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
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