Related papers: Second main theorems with weighted counting functi…
In this paper, we establish a new second main theorem for meromorphic functions on a non-Archimedean field and small functions with counting functions truncated to level $1.$ As an application, we show that two meromorphic functions on a…
In this article, we prove that there are at most two meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 2)$ sharing $2n+2$ hyperplanes in general position regardless of multiplicity, where all zeros with…
Chapter 1 deals with the problem of the existence of an upper/lower envelope from a convex cone or, more generally, a convex set for functions on the projective limit of vector lattices with values in the completion of the Kantorovich space…
In this paper, we will show that if two meromorphic mappings $f$ and $g$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ have the same inverse images for $(2n+2)$ moving hyperplanes $\{a_i\}_{i=1}^{2n+2}$ with multiplicities counted to level…
Nevanlinna showed that two non-constant meromorphic functions on $\mathbb C$ must be linked by a M\"{o}bius transformation if they have the same inverse images counted with multiplicities for four distinct values. After that this results is…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
Since the great work on holomorphic curves into algebraic varieties intersecting hypersurfaces in general position established by Ru in 2009, recently there has been some developments on the second main theorem into algebraic varieties…
We proved a truncated second main theorem of level one with explicit exceptional sets for analytic maps into $\mathbb P^2$ intersecting the coordinate lines with sufficiently high multiplicities. As applications, we studied some cases of…
We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…
We apply an idea of Levin to obtain a non-truncated second main theorem for non-Archimedean analytic maps approximating algebraic hypersurfaces in subgeneral position. In some cases, for example when all the hypersurfaces are non-linear and…
In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem…
Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $|\,|$. We establish a Second Main Theorem type estimate for analytic map $f\colon…
In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…
Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be…
In this paper, we give some results on the number of meromorphic mappings of C^m into P^n under a condition on the inverse images of hyperplanes in P^n. At the same time, we give an answer for an open question by H.Fujimoto.
The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further,…
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on $\mathbb{R}^n$. Rearrangements are maps that are monotonic (up to sets of measure zero) and…
Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…
A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…
The purpose of this paper is to prove the First and Second Fundamental Theorems of invariant theory for the complex special linear supergroup and discuss the superalgebra of invariants, via the super Plucker relations.