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1.
Summary.
With denoting the -th partial
sum of ${\rm e}^{z}$, the exact rate of convergence of the zeros of the
normalized partial sums, , to the Szeg\"o curve
was
recently studied by Carpenter et al. (1991), where
is defined by
Here, the above results are generalized to the convergence of
the zeros and poles of certain sequences of normalized Pad\'{e}
approximants
to , where is the associated Pad\'{e} rational approximation to .
Received February 2, 1994 相似文献
2.
Summary. We study here in detail the location of the real and complex zeros of the partial sums of and , which extends results of Szeg? (1924) and Kappert (1996).
Received November 9, 2000 / Published online August 17, 2001 相似文献
3.
Maosheng Xiong 《Finite Fields and Their Applications》2012,18(5):933-945
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases in Ma et al. (2011) [14], Ding et al. (2011) [5], Wang et al. (2011) [20]. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special case. We make extensive use of standard tools in number theory such as characters of finite fields, the Gauss sums and the Jacobi sums to transform the problem of finding the weight distribution into a problem of evaluating certain character sums over finite fields, which on the special case is related with counting the number of points on some elliptic curves over finite fields. Other cases are also possible by this method. 相似文献
4.
研究均值为零非退化的独立同分布的随机变量序列正则和收敛性,在适当条件下,获得了自正则和精确渐近性的一般结果. 相似文献
5.
Antonio R. Vargas 《Constructive Approximation》2014,40(2):219-239
We are interested in studying the asymptotic behavior of the zeros of partial sums of power series for a family of entire functions defined by exponential integrals. The zeros grow on the order of \(O(n)\) , and after rescaling, we explicitly calculate their limit curve. We find that the rate at which the zeros approach the curve depends on the order of the singularities/zeros of the integrand in the exponential integrals. As an application of our findings, we derive results concerning the zeros of partial sums of power series for Bessel functions of the first kind. 相似文献
6.
Summary In this paper, we continue our study of the location of the zeros and poles of general Padé approximants toe
z
. We state and prove here new results for the asymptotic location of the normalized zeros and poles for sequences of Padé approximants toe
z
, and for the asymptotic location of the normalized zeros for the associated Padé remainders toe
z
. In so doing, we obtain new results for nontrivial zeros of Whittaker functions, and also generalize earlier results of Szegö and Olver.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2688Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2729, and by the Energy Research and Development Administration (ERDA) under Grant EY-76-S-02-2075 相似文献
7.
Hinkkanen's problem (1984) is completely solved, i.e., it is shown that any meromorphic function f of one complex variable is determined by its zeros and poles and the zeros of f(j) for j=1,2,3,4. To cite this article: G. Frank et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
8.
Formica Maria Rosaria Vasil’ovich Kozachenko Yuriy Ostrovsky Eugeny Sirota Leonid 《Lithuanian Mathematical Journal》2020,60(3):330-358
We derive exponential bounds for the tail of the distribution of normalized sums of triangular arrays of random variables, not necessarily independent, under the law of ordinary logarithm.
Furthermore, we provide estimates for partial sums of triangular arrays of independent random variables belonging to suitable grand Lebesgue spaces and having heavy-tailed distributions.
相似文献9.
关于不同分布两两NQD列的Jamison型加权乘积和的强稳定性 总被引:5,自引:0,他引:5
本文讨论了不同分布两两NQD列的Jamison型加权乘积和的强稳定性及乘积和的Marcinkiewicz型强大数律,推广并改进了Etemadi[1]关于不同分布两两独立列部分和的工作及Matula[2],王岳宝等[3]关于同分布两两NQD列部分和的工作. 相似文献
10.
R. A. Lasuriya 《Ukrainian Mathematical Journal》2003,55(7):1099-1109
We investigate the behavior of deviations of rectangular partial Fourier sums on sets of
-differentiable functions of many variables. 相似文献
11.
本文通过积分检验, 刻画了不同分布的$\varphi$-混合序列后置和的极限结果,并由此导出了它们的Chover型重对数律,推广和改进了已有的结果. 相似文献
12.
Maosheng Xiong 《Designs, Codes and Cryptography》2014,72(3):511-528
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases in Ding et al. (IEEE Trans Inform Theory 57(12), 8000–8006, 2011); Ma et al. (IEEE Trans Inform Theory 57(1):397–402, 2011); Wang et al. (Trans Inf Theory 58(12):7253–7259, 2012); and Xiong (Finite Fields Appl 18(5):933–945, 2012). In this paper we use the method developed in Xiong (Finite Fields Appl 18(5):933–945, 2012) to solve one more special case. We make extensive use of standard tools in number theory such as characters of finite fields, the Gauss sums and the Jacobi sums. The problem of finding the weight distribution is transformed into a problem of evaluating certain character sums over finite fields, which turns out to be associated with counting the number of points on some elliptic curves over finite fields. We also treat the special case that the characteristic of the finite field is 2. 相似文献
13.
14.
In this paper, the complete convergence of weighted sums for ρ*-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for ρ*-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. (J. Theoret. Probab., 1995, 8(1): 49-76) from i.i.d. to ρ*-mixing setting but also obtain their necessities and relax their conditions. 相似文献
15.
In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent (NQD) random variables. The results obtained improve the corresponding theorems of Hu et al. (2013), and Qiu and Yang (2006) under some weaker conditions. 相似文献
16.
Saralees Nadarajah 《Journal of multivariate analysis》2008,99(5):1010-1012
The recent paper by Alshabani et al. [Partial size-and-shape distributions, J. Multivariate Anal. (2006), in press] derived the partial size-and-shape distributions motivated by a study in human movement analysis. The paper contained three main results (referred to as Results 1-3), each deriving an expression of the partial size-and-shape distribution. Two of the three results are expressed as infinite sums of terms involving special functions. Here, I would like to point that at least one of these results can be reduced to an explicit and manageable form. 相似文献
17.
Liudas Giraitis Piotr Kokoszka Remigijus Leipus Gilles Teyssière 《Statistical Inference for Stochastic Processes》2000,3(1-2):113-128
The paper is concerned with the estimation of the long memory parameter in a conditionally heteroskedastic model proposed by Giraitis et al. (1999b). We consider estimation methods based on the partial sums of the squared observations, which are similar in spirit to the classical R / S analysis, as well as spectral domain approximate maximum likelihood estimators. We review relevant theoretical results and present an empirical simulation study. 相似文献
18.
In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent (NSD, in short) random variables is established. By using the exponential inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors. 相似文献
19.
Albert Edrei 《Constructive Approximation》1985,1(1):359-396
The author considers $$f(z) = \exp (g(z)) = \sum\limits_{j = 0}^\infty {a_j z^j ,}$$ , whereg(z) is a real, entire, transcendental function admissible in the sense of W. K. Hayman [(1956): Reine Angew. Math.,196:67-95]. The aim of the paper is to study, asm→+∞, the distribution of the zeros of the partial sums $$s_m (z) = \sum\limits_{j = 0}^m {a_j z^j .}$$ The results are stated in terms of Hayman's auxiliary functions Ifr>0 is large enough, botha(r) andb(r) are positive,a(r) is strictly increasing, and $$a(r) \to + \infty ,b(r) \to + \infty (r \to + \infty ).$$ Define the sequence (R m ) (m>m 0) by the relationsa(R m )=m. From the following proposition, typical of those stated in the paper, it is easy to deduce accurate information regarding those zeros ofs m (z) that lie near the positive axis: Letζ be an auxiliary complex variable; then asm→+∞, and forR=R m , the functions $$\left\{ {1 + \zeta \left( {\frac{2}{{b(R)}}} \right)^{1/2} } \right\}^{ - m} \{ f(R)\} ^{ - 1} s_m \left( {R\left( {1 + \zeta \left( {\frac{2}{{b(R)}}} \right)^{1/2} } \right)} \right)$$ tend to $$\frac{1}{2}e^{\zeta ^2 } \left( {1 - \frac{2}{{\sqrt \pi }}\int_0^\zeta {e^{ - \sigma ^2 } d\sigma } } \right)$$ uniformly on every compact subset of theζ-plane. There are similar, equally precise, results covering those zeros ofs m (z) that lie near any rayte i?(0<t<+∞,?≠0). 相似文献
20.
We prove a functional central limit theorem for the partial sums of a class of time varying processes with long memory. To cite this article: A. Philippe et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献