A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional rationality (or meromorphicity) conditions for vertex operators. The vertex operator map for a meromorphic open-string vertex algebra satisfies rationality and associativity but in general does not s...

Let K be a non archimedean algebraically closed field of characteristic π, complete for its ultrametric absolute value. In a recent paper by Escassut and Yang ([6]) polynomial decompositions P (f) = Q(g) for meromorphic functions f , g on K (resp. in a disk d(0, r−) ⊂ K) have been considered, and for a class of polynomials P , Q, estimates for the Nevanlinna function T (ρ, f) have been derived....

and Applied Analysis 3 Let n r, f or n r, ∞̂ denote the number of poles of f z in |z| ≤ r and let n r, a, f denote the number of a-points of f z in |z| ≤ r, counting with multiplicities. Define the volume function associated with E-valued meromorphic function f z by V ( r, ∞̂, f V r, f 1 2π ∫ Cr log ∣∣ ∣ ∣ r ξ ∣∣ ∣ ∣Δ log ∥ ∥f ξ ∥ ∥dx ∧ dy, ξ x iy, V ( r, a, f ) 1 2π ∫ Cr log ∣ ∣ ∣ ∣ r ξ ∣ ∣ ∣ ∣Δ...

In this paper we study the problem of meromorphic function sharing one small function with its derivative and improve the results of K.-W. Yu and I. Lahiri and answer the open questions posed by K.-W. Yu.

We describe conditions under which a multiply connected wandering domain of a transcendental meromorphic function with a finite number of poles must be a Baker wandering domain, and we discuss the possible eventual connectivity of Fatou components of transcendental meromorphic functions. We also show that if f is meromorphic, U is a bounded component of F (f) and V is the component of F (f) suc...

We shall prove theorems on nonexistence of certain types of vector fields on a compact manifold with a positive definite Riemannian metric whose Ricci curvature is either everywhere positive or everywhere negative. Actually we shall have some relaxations of the requirements both as to curvature and as to compactness. We shall deal with real spaces with a customary metric and with complex analyt...

On the face of it, part (i) is a particular case of part (ii), and the latter part of (iii), but actually all three parts are algebraically equivalent by the following elementary argument. For given periods, we introduce the closed Riemann surface V2 of genus p = l on which our meromorphic functions are suitably defined, and we take it as known that on such or any other closed Riemann surface o...

Let f be a meromorphic, transcendental function in the finite plane having a finite number of a-points. The well-known theorem of Iversen [i, p. 224] asserts that in this case there exists a curve F going out to such that f(z) -~ a as z ~ ~, z ~ F. Such a curve is called an asymptotic curve. We henceforth make use of the standard notation from the theory of meromorphic functions [1] without spe...

‎in this paper‎, ‎we give some necessary conditions for a complex‎ ‎difference equation of malmquist type‎ $$‎sum^n_{j=1}f(z+c_j)=frac{p(f(z))}{q(f(z))}‎,$$ ‎where $n(in{mathbb{n}})geq{2}$‎, ‎and $p(f(z))$ and $q(f(z))$ are‎ ‎relatively prime polynomials in $f(z)$ with small functions as‎ ‎coefficients‎, ‎admitting a meromorphic function of finite order‎. ‎moreover‎, ‎the properties of finite o...