Related papers: Nonlinear Kernel Partition Regularity: Necessary a…

In this short note we prove a lemma about the dimension of certain algebraic sets of matrices. This result is needed in our paper arXiv:1201.1672. The result presented here has also applications in other situations and so it should appear…

We continue the investigation into the computational status of the existence of moduli of regularity (and their use for rates of convergence) in the sense of Kohlenbach, Lopez and Nicolae (2019), carried out w.r.t. classical reverse…

We define the notion of componentwise regularity and study some of its basic properties. We prove an analogue, when working with weight orders, of Buchberger's criterion to compute Gr\"obner bases; the proof of our criterion relies on a…

Given the matrix equation ${\bf A X} + {\bf X B} + f({\bf X }) {\bf C} ={\bf D}$ in the unknown $n\times m$ matrix ${\bf X }$, we analyze existence and uniqueness conditions, together with computational solution strategies for $f \,:…

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matriz is superregular if all of its minors that are not trivially zero are nonzero. Given a a times b, a larger than or equal to b,…

Earlier, normalization conditions for the columns of the PCM (Polarized Continuum Model) were determined and a method of enlarged surface meshes was developed. We developed similar methods for the COSMO (COnductor like Screening MOdel).…

Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…

An RGD system $\mathcal{D}$ is called \emph{linear w.r.t. a root basis $\mathcal{B}$} if the commutation relations between the root groups of $\mathcal{D}$ are `linear' in a certain sense. Moreover, $\mathcal{D}$ is called…

A famous result in arithmetic Ramsey theory says that for many linear homogeneous equations $E$ there is a threshold value $R_k(E)$ (the Rado number of $E$) such that for any $k$-coloring of the integers in the interval $[1,n]$, with $n \ge…

For any positive integers $a$ and $b$, we enumerate all colored partitions made by noncrossing diagonals of a convex polygon into polygons whose number of sides is congruent to $b$ modulo $a$. For the number of such partitions made by a…

In recent work, Amdeberhan and Merca considered the integer partition function $a(n)$ which counts the number of integer partitions of weight $n$ wherein even parts come in only one color (i.e., they are monochromatic), while the odd parts…

Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is…

Let $P$ be a set of $n$ green and $n - k$ red points in $\mathbb{C}^2$. A line determined by $i$ green and $j$ red points such that $i + j \ge 2$ and $|i - j| \le r$ is called \emph{r-equichromatic}. We establish lower bounds for…

We prove a $C^{1,\alpha}$ interior regularity theorem for fully nonlinear uniformly elliptic integro-differential equations without assuming any regularity of the kernel. We then give some applications to linear theory and higher regularity…

We define a linear homogeneous equation to be strongly r-regular if, when a finite number of inequalities is added to the equation, the system of the equation and inequalities is still r-regular. In this paper, we show that, if a linear…

We consider some coloring issues related to the famous Erd\H {o}s Discrepancy Problem. A set of the form $A_{s,k}=\{s,2s,\dots,ks\}$, with $s,k\in \mathbb{N}$, is called a \emph{homogeneous arithmetic progression}. We prove that for every…

Let $n\in \mathbb{N}$, $R$ be a binary relation on $[n]$, and $C_1(i,j),\ldots,C_n(i,j) \in \mathbb{Z}$, for $i,j \in [n]$. We define the exponential system of equations $\mathcal{E}(R,(C_k(i,j)_{i,j,k})$ to be the system \[…

Identifying structural parameters in linear simultaneous-equation models is a longstanding challenge. Recent work exploits information in higher-order moments of non-Gaussian data. In this literature, the structural errors are typically…

A vertex colouring is called a \emph{parity vertex colouring} if every path in $G$ contains an odd number of occurrences of some colour. Let $\chi_{p}(G)$ be the minimal number of colours in a parity vertex colouring of $G$. We show that…

Handelman (J. Operator Theory, 1981) proved that if the spectral radius of a matrix $A$ is a simple root of the characteristic polynomial and is strictly greater than the modulus of any other root, then $A$ is conjugate to a matrix $Z$ some…