共查询到20条相似文献,搜索用时 15 毫秒
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Gi-Sang Cheon 《Discrete Applied Mathematics》2007,155(18):2573-2584
We develop polynomials in z∈C for which some generalized harmonic numbers are special cases at z=0. By using the Riordan array method, we explore interesting relationships between these polynomials, the generalized Stirling polynomials, the Bernoulli polynomials, the Cauchy polynomials and the Nörlund polynomials. 相似文献
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Permutation polynomials have been an interesting subject of study for a long time and have applications in many areas of mathematics
and engineering. However, only a small number of specific classes of permutation polynomials are known so far. In this paper,
six classes of linearized permutation polynomials and six classes of nonlinearized permutation polynomials over are presented. These polynomials have simple shapes, and they are related to planar functions.
This work was supported by Australian Research Council (Grant No. DP0558773), National Natural Science Foundation of China
(Grant No. 10571180) and the Research Grants Council of the Hong Kong Special Administrative Region of China (Grant No. 612405) 相似文献
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We employ the basic properties for the Hasse-Teichmüller derivatives to give simple proofs of known explicit formulae for Bernoulli numbers (of higher order) and then obtain some parallel results for their counterparts in positive characteristic. 相似文献
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E. S. Salnikova 《Journal of Mathematical Sciences》2012,182(4):539-551
Estimates for approximations to logarithms of rational numbers by rational numbers and quadratic irrationalities are established. 相似文献
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In this note p(D) = Dm+ b1Dm 1+···+ bmis a polynomial Dirac operator in R~n, where D =nj=1ej xjis a standard Dirac operator in Rn, bjare the complex constant coefficients. In this note we discuss all decompositions of p(D) according to its coefficients bj,and obtain the corresponding explicit Cauchy integral formulae of f which are the solution of p(D)f = 0. 相似文献
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Mats Andersson 《Mathematische Zeitschrift》2011,267(3-4):835-850
We compute a quite explicit Koppelman formula for dd c on projective space, and obtain Green currents for closed (p, p)-currents. 相似文献
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For the dual pair considered, the Cauchy Harish-Chandra Integral, as a distribution on the Lie algebra, is the limit of the
holomorphic extension of the reciprocal of the determinant. We compute that limit explicitly in terms of the Harish-Chandra
orbital integrals.
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David Arcoya Lucio Boccardo Tommaso Leonori 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(6):1741-1757
In this paper we deal with solutions of problems of the type $$\left\{\begin{array}{ll}-{\rm div} \Big(\frac{a(x)Du}{(1+|u|)^2} \Big)+u = \frac{b(x)|Du|^2}{(1+|u|)^3} +f \quad &{\rm in} \, \Omega,\\ u=0 &{\rm on} \partial \, \Omega, \end{array} \right.$$ where ${0 < \alpha \leq a(x) \leq \beta, |b(x)| \leq \gamma, \gamma > 0, f \in L^2 (\Omega)}$ and Ω is a bounded subset of ${\mathbb{R}^N}$ with N ≥ 3. We prove the existence of at least one solution for such a problem in the space ${W_{0}^{1, 1}(\Omega) \cap L^{2}(\Omega)}$ if the size of the lower order term satisfies a smallness condition when compared with the principal part of the operator. This kind of problems naturally appears when one looks for positive minima of a functional whose model is: $$J (v) = \frac{\alpha}{2} \int_{\Omega}\frac{|D v|^2}{(1 + |v|)^{2}} + \frac{12}{\int_{\Omega}|v|^2} - \int_{\Omega}f\,v , \quad f \in L^2(\Omega),$$ where in this case a(x) ≡ b(x) = α > 0. 相似文献
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The main goal of this paper is centred around the study of the behavior of the Cauchy type integral and its corresponding
singular version, both over nonsmooth domains in Euclidean space. This approach is based on a recently developed quaternionic
Cauchy integrals theory [1, 5, 7] within the three-dimensional setting. The present work involves the extension of fundamental
results of the already cited references showing that the Clifford singular integral operator has a proper invariant subspace
of generalized H?lder continuous functions defined in a surface of the (m+1)-dimensional Euclidean space. 相似文献
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It is well known that continuous bilinear forms on C(K) × C(K) are 2-dominated. This paper shows that generalizations of this result are not to be expected. The main result asserts that for every
-space E(1 p ), every n 2, every r > 0 and every Banach space F , there exists an n-homogeneous polynomial P : E F such that P is not of type [r], hence P is neither r-dominated nor r-semi-integral (if n = 2 and p = , F is supposed to contain an isomorphic copy of some
, 1q < ).Received: 24 November 2003 相似文献
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Marcelo Muniz 《Designs, Codes and Cryptography》2006,41(2):147-152
Isometric embeddings of $\mathbb{Z}_{p^n+1}$ into the Hamming space ( $\mathbb{F}_{p}^{p^n},w$ ) have played a fundamental role in recent constructions of non-linear codes. The codes thus obtained are very good codes, but their rate is limited by the rate of the first-order generalized Reed–Muller code—hence, when n is not very small, these embeddings lead to the construction of low-rate codes. A natural question is whether there are embeddings with higher rates than the known ones. In this paper, we provide a partial answer to this question by establishing a lower bound on the order of a symmetry of ( $\mathbb{F}_{p}^{N},w$ ). 相似文献