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1.
On Homogeneous Differential Polynomials
of Meromorphic Functions 总被引:2,自引:0,他引:2
In this paper, we study one conjecture proposed by W. Bergweiler and show that any
transcendental meromorphic functions f(z) have the form exp(αz+β) if f(z)f″(z)–a(f′ (z))2≠0,
where
. Moreover, an analogous normality criterion is obtained.
Supported by National Natural Science Foundation and Science Technology Promotion Foundation of Fujian
Province (2003) 相似文献
2.
Peter P. Varju 《Constructive Approximation》2007,26(3):317-337
Let
be the boundary of a convex domain symmetric to the origin. The conjecture that any continuous even function can be uniformly
approximated by homogeneous polynomials of even degree on K is proven in the following cases: (a) if d = 2; (b) if K is twice
continuously differentiable and has positive curvature in every point; or (c) if K is the boundary of a convex polytope. 相似文献
3.
The aim of this note is to study a set of paravector valued homogeneous monogenic polynomials that can be used for a construction of sequences of generalized Appell polynomials in the context of Clifford analysis. Therefore, we admit a general form of the vector part of the first degree polynomial in the Appell sequence. This approach is different from the one presented in recent papers on this subject. We show that in the case of paravector valued polynomials of three real variables, there exist essentially two different types of such polynomials together with two other trivial types of polynomials. The proof indicates a way of obtaining analogous results in the case of polynomials of more than three variables. 相似文献
4.
We consider the algebras, with two generators a and b, generated by the quadratic relations ba = α2 + βab + γb2, where the coefficients α, β, and γ belong to an arbitrary field F of characteristic 0. We find conditions for such an algebra to be expressed as a skew polynomial algebra with generator b over the polynomial ring F [a]. These conditions are equivalent to the existence of the Poincaree-Birkhoff-Witt basis, i. e., basis of the form {am, bn}. Bibliography: 16 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 144–171. 相似文献
5.
6.
Remez-type inequalities provide upper bounds for the uniformnorms of polynomials p on given compact sets K, provided that|p(x)| 1 for every x K\E, where E is a subset of K of smallmeasure. In this paper we prove sharp Remez-type inequalitiesfor homogeneous polynomials on star-like surfaces in Rd. Inparticular, this covers the case of spherical polynomials (whend = 2 we deduce a result of Erdélyi for univariate trigonometricpolynomials). 相似文献
7.
Matthew Buck 《Results in Mathematics》2013,63(3-4):805-815
We substantially strengthen an unpublished result of Whitehead from his PhD thesis (Whitehead, A.: Differential equations and differential polynomials in the complex. PhD thesis, University of Nottingham, 2002) using a refinement of his techniques. 相似文献
8.
9.
Benyamini Yoav; Lassalle Silvia; Llavona Jose G. 《Bulletin London Mathematical Society》2006,38(3):459-469
The main result in this paper is a representation theorem forhomogeneous orthogonally additive polynomials on Banach lattices.The representation theorem is used to study the linear spanof the set of zeros of homogeneous real-valued orthogonallyadditive polynomials. It is shown that in certain lattices everyelement can be represented as the sum of two or three zerosor, at least, can be approximated by such sums. It is also indicatedhow these results can be used to study weak topologies inducedby orthogonally additive polynomials on Banach lattices. 2000Mathematics Subject Classification 46G25, 46B42, 47B38. 相似文献
10.
IfPis a continuousm-homogeneous polynomial on a real normed space andPis the associated symmetricm-linear form, the ratio P/P always lies between 1 andmm/m!. We show that, as in the complex case investigated by Sarantopoulos (1987,Proc. Amer. Math. Soc.99, 340–346), there areP's for which P/P=mm/m! and for whichPachieves norm if and only if the normed space contains an isometric copy of ℓm1. However, unlike the complex case, we find a plentiful supply of such polynomials providedm4. 相似文献
11.
M. Reimer 《Constructive Approximation》1997,13(3):357-362
Recently, H. Hakopian proved that the squares of a bivariate homogeneous polynomial and of its gradient have, in general,
the same set of maximum points on the sphere. A generalization of this result mentioned can be gained by a method O. D. Kellogg
used years ago in the estimate of some coefficient functionals.
Date received: July 31, 1995. Date revised: May 14, 1996. 相似文献
12.
We factor the virtual Poincaré polynomial of every homogeneous space G/H, where G is a complex connected linear algebraic group and H is an algebraic subgroup, as t2u (t2–1)r QG/H(t2) for a polynomial QG/H with nonnegative integer coefficients. Moreover, we show that QG/H(t2) divides the virtual Poincaré polynomial of every regular embedding of G/H, if H is connected. 相似文献
13.
Mathematical Notes - Regular multilinear operators and regular homogeneous polynomials acting between Banach lattices are automatically continuous, but the converse, in general, is not true. The... 相似文献
14.
G. Y. Li 《Journal of Optimization Theory and Applications》2011,150(1):194-203
The minimax theorem for a convex-concave bifunction is a fundamental theorem in optimization and convex analysis, and has
a lot of applications in economics. In the last two decades, a nonconvex extension of this minimax theorem has been well studied
under various generalized convexity assumptions. In this note, by exploiting the hidden convexity (joint range convexity)
of separable homogeneous polynomials, we establish a nonconvex minimax theorem involving separable homogeneous polynomials.
Our result complements the existing study of nonconvex minimax theorem by obtaining easily verifiable conditions for the nonconvex
minimax theorem to hold. 相似文献
15.
16.
Rogério Serôdio 《Advances in Applied Clifford Algebras》2007,17(2):245-258
We discuss the generalization of results on quaternionic polynomials to the octonionic polynomials. In contrast to the quaternions
the octonionic multiplication is non-associative. This fact although introducing some difficulties nevertheless leads to some
new results. For instance, the monic and non-monic polynomials do not have, in general, the same set of zeros.
Concerning the zeros, it is shown that in the monic and non-monic cases they are not the same, in general, but they belong
to the same set of conjugacy classes.
Despite these difficulties created by the non-associativity, we obtain equivalent results to the quaternionic case with respect
to the number of zeros and the procedure to compute them. 相似文献
17.
《Quaestiones Mathematicae》2013,36(3):347-353
We establish an estimate on the difference of orthonormal polynomials for a general class of exponential weights. 相似文献
18.
The domination polynomial of a graph G of order n is the polynomial ${D(G, x) = \sum_{i=\gamma(G)}^{n} d(G, i)x^i}$ where d(G, i) is the number of dominating sets of G of size i, and γ(G) is the domination number of G. We investigate here domination roots, the roots of domination polynomials. We provide an explicit family of graphs for which the domination roots are in the right half-plane. We also determine the limiting curves for domination roots of complete bipartite graphs. Finally, we prove that the closure of the roots is the entire complex plane. 相似文献
19.
Jaume GINE 《数学学报(英文版)》2006,22(6):1613-1620
The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we give new centers for s = 6, 7 a linear center perturbed by They are completely classified these results for s = 2, 3, 4, 5, 相似文献
20.
Let V be a vector space over a field k, P : V → k, d ≥?3. We show the existence of a function C(r, d) such that rank(P) ≤ C(r, d) for any field k, char(k) > d, a finite-dimensional k-vector space V and a polynomial P : V → k of degree d such that rank(?P/?t) ≤ r for all t ∈ V ??0. Our proof of this theorem is based on the application of results on Gowers norms for finite fields k. We don’t know a direct proof even in the case when k = ?. 相似文献