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101.
A. Pérez-González J. M. Vilar-Fernández W. González-Manteiga 《Annals of the Institute of Statistical Mathematics》2009,61(1):85-109
The main objective of this work is the nonparametric estimation of the regression function with correlated errors when observations
are missing in the response variable. Two nonparametric estimators of the regression function are proposed. The asymptotic
properties of these estimators are studied; expresions for the bias and the variance are obtained and the joint asymptotic
normality is established. A simulation study is also included. 相似文献
102.
A. I. Aptekarev V. G. Lysov D. N. Tulyakov 《Theoretical and Mathematical Physics》2009,159(1):448-468
We consider ensembles of random Hermitian matrices with a distribution measure determined by a polynomial potential perturbed
by an external source. We find the genus-zero algebraic function describing the limit mean density of eigenvalues in the case
of an anharmonic potential and a diagonal external source with two symmetric eigenvalues. We discuss critical regimes where
the density support changes the connectivity or increases the genus of the algebraic function and consequently obtain local
universal asymptotic representations for the density at interior and boundary points of its support (in the generic cases).
The investigation technique is based on an analysis of the asymptotic properties of multiple orthogonal polynomials, equilibrium
problems for vector potentials with interaction matrices and external fields, and the matrix Riemann-Hilbert boundary value
problem.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 1, pp. 34–57, April, 2009. 相似文献
103.
Using a fixed point relation of the square-root type and the basic fourth-order method, improved methods of fifth and sixth order for the simultaneous determination of simple zeros of a polynomial are obtained. An increase in convergence is achieved without additional numerical operations, which points to high computational efficiency of the accelerated methods. The main aim of this work is the convergence analysis of improved simultaneous methods given under computationally verifiable initial conditions in the spirit of Smale’s point estimation theory. 相似文献
104.
从例外集的角度研究了亚纯函数微分多项式fkQ[f]+P[f]的零点分布,证明了:对于满足δ(∞,f)1-α>0的超越亚纯函数f(z),微分多项式fkQ[f]+P[f]在不含极点的可数个圆盘并集之外有无穷多个零点,其中k>1+ΓP+γP+α1(-1+αΓQ+ΓP-γP),ΓQ是Q[f]的权,ΓP,γP是P[f]的权和次数.本文推广了Hayman,Anderson,Langley等人的结论. 相似文献
105.
In this paper we generalize the notion of cyclic code and construct codes as ideals in finite quotients of non-commutative
polynomial rings, so called skew polynomial rings of automorphism type. We propose a method to construct block codes of prescribed
rank and a method to construct block codes of prescribed distance. Since there is no unique factorization in skew polynomial
rings, there are much more ideals and therefore much more codes than in the commutative case. In particular we obtain a [40,
23, 10]4 code by imposing a distance and a [42,14,21]8 code by imposing a rank, which both improve by one the minimum distance of the previously best known linear codes of equal
length and dimension over those fields. There is a strong connection with linear difference operators and with linearized
polynomials (or q-polynomials) reviewed in the first section.
相似文献
106.
The Zhang–Zhang polynomial (i.e., Clar covering polynomial) of hexagonal systems is introduced by H. Zhang and F. Zhang, which
can be used to calculate many important invariants such as the Clar number, the number of Kekulé structures and the first
Herndon number, etc. In this paper, we give out an explicit recurrence expression for the Zhang–Zhang polynomials of the cyclo-polyphenacenes,
and determine their Clar numbers, numbers of Kekulé structures and their first Herndon numbers. 相似文献
107.
The amoeba of a complex curve in the 2‐dimensional complex torus is its image under the projection onto the real parts of the logarithmic coordinates. A toric cycle in the complement to a curve is a fiber of this projection over a point in the complement to the amoeba of the curve. We consider amoebas of complex algebraic curves defined by so‐called Harnack polynomials. We prove that toric cycles are homologically independent in the complement to a such curve. 相似文献
108.
Hamed Taghavian 《Mathematical Methods in the Applied Sciences》2019,42(7):2169-2189
This paper presents an analytical method towards Laplace transform inversion of composite functions with the aid of Bell polynomial series. The presented results are used to derive the exact solution of fractional distributed order relaxation processes as well as time‐domain impulse response of fractional distributed order operators in new series forms. Evaluation of the obtained series expansions through computer simulations is also given. The results are then used to present novel series expansions for some special functions, including the one‐parameter Mittag‐Leffler function. It is shown that truncating these series expansions when combined with using potential partition polynomials provides efficient approximations for these functions. At the end, the results are shown to be also useful in studying asymptotical behavior of partial Bell polynomials. Numerical simulations as well as analytical examples are provided to verify the results of this paper. 相似文献
109.
We study polynomial-type solutions of the q-Heun equation, which is related with quasi-exact solvability. The condition that the q-Heun equation has a non-zero polynomial-type solution is described by the roots of the spectral polynomial, whose variable is the accessory parameter E. We obtain sufficient conditions that the roots of the spectral polynomial are all real and distinct. We consider the ultradiscrete limit to clarify the roots of the spectral polynomial and the zeros of the polynomial-type solution of the q-Heun equation. 相似文献
110.
HICKERNELL Fred J 《中国科学A辑(英文版)》2009,52(11):2309-2320
This article considers universal optimality of digital nets and lattice designs in a regression model. Based on the equivalence theorem for matrix means and majorization theory,the necessary and sufficient conditions for lattice designs being φp-and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions,and are... 相似文献