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991.
Mehmet Cenkci 《Discrete Mathematics》2009,309(6):1498-1510
We define the generalized potential polynomials associated to an independent variable, and prove an explicit formula involving the generalized potential polynomials and the exponential Bell polynomials. We use this formula to describe closed type formulas for the higher order Bernoulli, Eulerian, Euler, Genocchi, Apostol-Bernoulli, Apostol-Euler polynomials and the polynomials involving the Stirling numbers of the second kind. As further applications, we derive several known identities involving the Bernoulli numbers and polynomials and Euler polynomials, and new relations for the higher order tangent numbers, the higher order Bernoulli numbers of the second kind, the numbers , the higher order Bernoulli numbers and polynomials and the higher order Euler polynomials and their coefficients. 相似文献
992.
Cristina Balderrama Piotr Graczyk Wilfredo Urbina 《Journal de Mathématiques Pures et Appliquées》2009,92(4):375-395
We study operator semigroups associated with a family of generalized orthogonal polynomials with Hermitian matrix entries. For this we consider a Markov generator sequence, and therefore a Markov semigroup, for the family of orthogonal polynomials on related to the generalized polynomials. We give an expression of the infinitesimal generator of this semigroup and under the hypothesis of diffusion we prove that this semigroup is also Markov. We also give expressions for the kernel of this semigroup in terms of the one-dimensional kernels and obtain some classical formulas for the generalized orthogonal polynomials from the correspondent formulas for orthogonal polynomials on . 相似文献
993.
Let D be an X-outer S-derivation of a prime ring R, where S is an automorphism of R. The following is proved among other things: The degree of the minimal semi-invariant polynomial of the Ore extension R[X;S,D] is ν if charR=0, and is pkν for some k0 if charR=p2, where ν is the least integer ν1 such that SνDS−ν−D is X-inner. A similar result holds for cv-polynomials. These are done by introducing the new notion of k-basic polynomials for each integer k0, which enable us to analyze semi-invariant polynomials inductively. 相似文献
994.
R. M. Green 《Journal of Algebraic Combinatorics》2009,30(2):165-171
Let W be a Coxeter group of type
. We show that the leading coefficient, μ(x,w), of the Kazhdan–Lusztig polynomial P
x,w
is always equal to 0 or 1 if x is fully commutative (and w is arbitrary). 相似文献
995.
Let be a family of polynomials such that , i=1,…,r. We say that the family P has the PSZ property if for any set with there exist infinitely many such that E contains a polynomial progression of the form {a,a+p1(n),…,a+pr(n)}. We prove that a polynomial family P={p1,…,pr} has the PSZ property if and only if the polynomials p1,…,pr are jointly intersective, meaning that for any there exists such that the integers p1(n),…,pr(n) are all divisible by k. To obtain this result we give a new ergodic proof of the polynomial Szemerédi theorem, based on the fact that the key to the phenomenon of polynomial multiple recurrence lies with the dynamical systems defined by translations on nilmanifolds. We also obtain, as a corollary, the following generalization of the polynomial van der Waerden theorem: If are jointly intersective integral polynomials, then for any finite partition of , there exist i{1,…,k} and a,nEi such that {a,a+p1(n),…,a+pr(n)}Ei. 相似文献
996.
G. López Lagomasino A. Martínez-Finkelshtein I. Pérez Izquierdo 《Journal of Mathematical Analysis and Applications》2008,340(1):521-535
We obtain the strong asymptotics for the sequence of monic polynomials minimizing the norm
997.
Qian Lu 《Journal of Mathematical Analysis and Applications》2008,340(1):394-400
We consider the normality criterion for a families F meromorphic in the unit disc Δ, and show that if there exist functions a(z) holomorphic in Δ, a(z)≠1, for each z∈Δ, such that there not only exists a positive number ε0 such that |an(a(z)−1)−1|?ε0 for arbitrary sequence of integers an(n∈N) and for any z∈Δ, but also exists a positive number B>0 such that for every f(z)∈F, B|f′(z)|?|f(z)| whenever f(z)f″(z)−a(z)(f′2(z))=0 in Δ. Then is normal in Δ. 相似文献
998.
François Guéritaud 《Geometriae Dedicata》2008,134(1):203-216
This note defines a family of Laurent polynomials indexed in which generalize the Markoff numbers and relate to the character variety of the one-cusped torus. We describe which monomials
appear in each polynomial and prove all the coefficients are positive integers. We also conjecture a generalization of that
positivity result.
相似文献
999.
An application of the “generalized Zernike or disc polynomials”, recently introduced in the literature, is shown, resorting to the Lie algebra based investigation of the dynamics of quantum systems driven by two-mode interaction Hamiltonians. Further properties of the associated “disc functions” are deduced. Also, a generalization of the disc polynomials towards the Hahn polynomials is suggested. 相似文献
1000.
On some diophantine results related to Euler polynomials 总被引:1,自引:1,他引:0
Csaba Rakaczki 《Periodica Mathematica Hungarica》2008,57(1):61-71
In this paper we prove that there is at most one complex number b for which the shifted Euler polynomial E
n
(x) + b has at most two zeros of odd multiplicity.
Supported in part, by Grants T48791 and F68872 form HNFSR, and by the Hungarian Academy of Sciences. 相似文献