Abstract
We give a characterization of the ratio of two Dirichelt series convergent in a right half-plane under an analytic condition, which is applicable to a uniqueness problem for Dirichlet series admitting analytic continuation in the complex plane as meromorphic functions of finite order; uniqueness theorems are given in terms of a-points of the functions.
We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).
AbstractLet c be a nonzero constant and n a positive integer, let f be a transcendental meromorphic function of finite order, and let R be a nonconstant rational function. Under some conditions, we study the relationships between the exponent of convergence of zero points of $f-R$
f
−
R
, its shift $f(z+nc)$
f
(
z
+
n
c
)
and the differences $\Delta _{c}^{n} f$
Δ
c
n
f
.
We established new sharp estimates outside exceptional sets for of the logarithmic derivatives $\frac{d^ {k} \log f(z)}{dz^k}$ and its generalization $\frac{f^{(k)}(z)}{f^{(j)}(z)}$, where $f$ is a meromorphic function $f$ in the upper half-plane, $k>j\ge0$ are integers. These estimates improve known estimates due to the second author in the class of meromorphic functions of finite order.Examples show that size of exceptional sets are best possible in some sense.
We present a generalization of concept of bounded $l$-index for meromorphic
functions of finite order. Using known results for entire functions of bounded $l$-index
we obtain similar propositions for meromorphic functions.
There are presented analogs of Hayman's theorem and logarithmic criterion for this class.
The propositions are widely used to investigate $l$-index boundedness of entire solutions of differential equations.
Taking this into account we raise a general problem of generalization of some results from theory of entire functions of bounded $l$-index by
meromorphic functions of finite order and their applications to meromorphic solutions of differential equations.
There are deduced sufficient conditions providing $l$-index boundedness of meromoprhic solutions of finite order
for the Riccati differential equation. Also we proved that the Weierstrass $\wp$-function has bounded $l$-index with
$l(z)=|z|.$
Abstract
We consider spline functions over simplicial meshes in $\mathbb {R}^{n}$
ℝ
n
. We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are infinitely smooth. Such splines can have extra orders of smoothness at a vertex, a property known as supersmoothness, which plays a role in the construction of multivariate splines and in the finite element method. In this paper, we characterize supersmoothness in terms of the degeneracy of spaces of polynomial splines over the cell of simplices sharing the vertex, and use it to determine the maximal order of supersmoothness of various cell configurations.
AbstractIn this paper, we prove the analogous result of Fang [1] for transcendentalE-valued meromorphic functions of finite order, which generalizes and improves the result of Wu [6].
AbstractThe characterization of a separable polynomial over an indecomposable commutative ring (with no idempotents but 0 and 1) in terms of the discriminant proved by G. J. Janusz is generalized to a skew polynomial ring R [ X, ρ] over a not necessarily commutative ring R where ρ is an automorphism of R with a finite order. 1980 Mathematics subject classification (Amer. Math. Soc.): 16 A 05.
On Properties of Differences Polynomials about Meromorphic Functions
