*Correspondence: [email protected] 4School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou, 510006, People’s Republic of China Full list of author information is available at the end of the article Abstract In the note, we study the normality of families of meromorphic functions. We consider whether a family of meromorphic functions F is normal in D if, for a no...

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

in this paper, we defined two classes $s_{p}^{ast }(n,lambda ,a,b)$ and $ k_{p}(n,lambda ,a,b)$ of meromorphic $p-$valent functions associated with a new linear operator. we obtained convolution properties for functions in these classes.

In this paper, we introduce a new class of integrable systems, naturally associated to Hurwitz spaces (spaces of meromorphic functions over Riemann surfaces). The critical values of the meromorphic functions play the role of "times". Our systems give a natural generalization of the Ernst equation; in genus zero, they realize the scheme of deformation of integrable systems proposed by Burtsev, M...

In this paper subordination and inclusion relations are studied for some subclasses of multivalent meromorphic functions in the punctured unit disc having a pole of order p at the origin. The subclasses under investigation are defined through combinations and iterations of a meromorphic analogue of the Cho–Kwon–Srivastava operator for normalized analytic functions. Specially, emphasis is given ...

The paper deals with a novel method of control system design which applies meromorphic transfer functions as models for retarded linear time delay systems. After introducing an auxiliary state model a finite-spectrum observer is designed to close a stabilizing state feedback. The observer finite spectrum is the key to implement a state feedback stabilization scheme and to apply the affine param...

We study vanishing cycles of meromorphic functions. This gives a new and unitary point of view, extending the study of the topology of holomorphic germs – as initiated by Milnor in the sixties – and of the global topology of polynomial functions, which has been advanced more recently. We define singularities along the poles with respect to a certain (weak) stratification and prove local and glo...

Let Ī be a linearly semi-negative number. It is well known that P is smoothly hypercharacteristic. We show that φ ( 1 Ô , θ(γ) ·R ) ≥ ∫ ΨS,V ( T̃ , 1 ) dM ∧ cos−1 ( Γ̄ )

Extending the work of [7] on groups definable in compact complex manifolds and of [1] on strongly minimal groups definable in nonstandard compact complex manifolds, we classify all groups definable in nonstandard compact complex manifolds showing that if G is such a group then there are a linear algebraic group L, a definably compact group T , and definable exact sequence 1→ L → G → T → 1.

In this article, we obtain two results on $n$ the power of a meromorphic function and its shift operator sharing small together with value which improve complement some earlier results. particular, more or less have improved extended Qi-Yang [Meromorphic functions that share values their shifts $n$-th order differences, Analysis Math., 46(4)2020, 843-865] by dispelling superfluous conclusions i...