Related papers: A note ON MONOGENEITY of pure number fields
Every generic linear functional $f$ on a convex polytope $P$ induces an orientation on the graph of $P$. From the resulting directed graph one can define a notion of $f$-arborescence and $f$-monotone path on $P$, as well as a natural graph…
Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems. We demonstrate the computational power of two methods--a symbolic one called the Comprehensive Gr\"obner basis and a…
In this study, we investigated a phenomenon that one intuitively would assume does not exist: self-citations on the paper basis. Actually, papers citing themselves do exist in the Web of Science (WoS) database. In total, we obtained 44,857…
Jacobson et al. [JKSH13] hypothesized that the local coherency of the generalized winding number function could be used to correctly determine consistent facet orientations in polygon meshes. We report on an approach to consistently…
The problem of estimating the multiplicity of the zero of a polynomial when restricted to the trajectory of a non-singular polynomial vector field, at one or several points, has been considered by authors in several different fields. The…
A general theorem on fibers of singular sets is presented.
Here we consider piecewise fractional linear maps with three branches. The paper presents a study of invariant measures with densities which can be written as infinite series. These series either have infinitely many poles or they sum up to…
We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced…
In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the…
Let $K = \mathbb{Q} (\alpha) $ be a pure number field generated by a root $\alpha$ of a monic irreducible polynomial $ F(x) = x^{2^u\cdot 3^v\cdot 5^t}-m$, with $ m \neq \pm 1 $ a square free rational integer, $u$, $v$ and $t$ three…
We obtain some asymptotic formulae (with power savings in their error terms) for the number of quadruples in the Cartesian product of an arbitrary set $A \subset \mathbf{R}$ and for the number of quintuplets in $A\times A$ for any subset…
Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also…
This is the first in a series of two papers that study monogenicity of number rings from a moduli-theoretic perspective. Given an extension of algebras $B/A$, when is $B$ generated by a single element $\theta \in B$ over $A$? In this paper,…
There is an increasing amount of literature concerning electronic properties of graphene close to the neutrality point. Many experiments continue using the two-probe geometry or invasive contacts or do not control samples' macroscopic…
In this note we give a quantitative estimate on the number of singular points of multiplicity $Q$ of a $2$-dimensional $Q$-valued energy minimizing map, in terms of the value of its frequency function.
We study betweenness preserving mappings (we call them \emph{monotone}) defined on subsets of the plane. Once the domain is a convex set, such a mapping is either the restriction of a homography, or its image is contained in the union of a…
We prove that there exists, up to isomorphism, exactly one function field over the finite field of two elements of class number one and genus four. This result, together with the ones of MacRae, Madan, Leitzel, Queen and Stirpe, establishes…
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the…