Related papers: Two meromorphic mappings sharing 2n + 2 hyperplane…

This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give the existence of unique range sets for meromorphic functions that are zero sets of polynomials that do not…

We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N=2 superfield…

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…

A function $f$ of a graph is called a complete graph invariant if the isomorphism of graphs $G$ and $H$ is equivalent to the equality $f(G)=f(H)$. If, in addition, $f(G)$ is a graph isomorphic to $G$, then $f$ is called a canonical form for…

Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…

Multiplication by the pseudoscalar $\mathbf{I}$ has been traditionally used in geometric algebra to perform non-metric operations such as calculating coordinates and the regressive product. In algebras with degenerate metrics, such as…

Let f : (M,p)\to (M',p') be a formal (holomorphic) nondegenerate map, i.e. with formal holomorphic Jacobian J_f not identically vanishing, between two germs of real analytic generic submanifolds in \C^n, p'=f(p). Assuming the target…

We prove that for every complete multipartite graph $F$ there exist very dense graphs $G_n$ on $n$ vertices, namely with as many as ${n\choose 2}-cn$ edges for all $n$, for some constant $c=c(F)$, such that $G_n$ can be decomposed into…

There are operations that transform a map M (an embedding of a graph on a surface) into another map in the same surface, modifying its structure and consequently its set of flags F(M). For instance, by truncating all the vertices of a map…

This paper confirms a conjecture of Amdeberhan and Moll that the power of 2 dividing the number of plane partitions in an n-cube is greater than the power of 2 dividing the number of totally symmetric plane partitions in the same cube when…

The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a…

We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…

We prove the existence of "half-plane differentials" with prescribed local data on any Riemann surface. These are meromorphic quadratic differentials with higher-order poles which have an associated singular flat metric isometric to a…

We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting…

We say that two arithmetic functions f and g form a Mobius pair if f(n) = \sum_{d \mid n} g(d) for all natural numbers n. In that case, g can be expressed in terms of f by the familiar Mobius inversion formula of elementary number theory.…

It is proved that for any positive number $\lambda$, $1<\lambda<2$; there exists a meromorphic function $f$ with logarithmic order $\lambda$= $\displaystyle\limsup_{r\to+\infty}\frac{\log T(r,f)}{\log\log r}$ such that $f$ has no Julia…

The paper develops an equidistribution theory of meromorphic mappings from a complete K\"ahler manifold with non-negative Ricci curvature into a complex projective manifold intersecting normal crossing divisors. When the domain manifolds…

Let $F: C^n \rightarrow C^m$ be a polynomial map with $degF=d \geq 2$. We prove that $F$ is invertible if $m = n$ and $\sum^{d-1}_{i=1} JF(\alpha_i)$ is invertible for all $i$, which is trivially the case for invertible quadratic maps. More…

Let $f: R^{m+1}\to R^{m+2^r}$, where $2^{r-1}\leq m+1 <2^r$, be a continuous map. Improving a recent result of Frick and Harrison, we show that there are $4$ points $x_0,\, x_1,\, y_0,\, y_1$ in $R^m$, which are distinct if…

We consider {\em monotone} embeddings of a finite metric space into low dimensional normed space. That is, embeddings that respect the order among the distances in the original space. Our main interest is in embeddings into Euclidean…