Related papers: Revisiting $\mathfrak b$ and $\mathfrak d$ through…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
Motivated by problems where jumps across lower dimensional subsets and sharp transitions across interfaces are of interest, this paper studies the properties of fractional bounded variation ($BV$)-type spaces. Two different natural…
We find the complete set of fundamental invariants for systems of ordinary differential equations of order $\ge 4$ under the group of point transformations generalizing similar results for contact invariants of a single ODE and point…
Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…
We introduce horizontal and vertical motivic invariants of birational maps between rational dominant maps and study their basic properties. As a first application, we show that the (usual) motivic invariants vanish for birational…
Integrodifference equations are versatile models in theoretical ecology for the spatial dispersal of species evolving in non-overlapping generations. The dynamics of these infinite-dimensional discrete dynamical systems is often illustrated…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
We introduce a universe of regular datatypes with variable binding information, for which we define generic formation and elimination (i.e. induction /recursion) operators. We then define a generic alpha-equivalence relation over the types…
Motivated by the Asymptotic Equipartition Property and its recently discovered role in the cutoff phenomenon, we initiate the systematic study of varentropy on discrete groups. Our main result is an approximate tensorization inequality…
We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic $D$-modules with dominated characteristic cycles.
We use tools of mathematical logic to analyse the notion of a path on an complex algebraic variety, and are led to formulate a "rigidity" property of fundamental groups specific to algebraic varieties, as well as to define a bona fide…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
Fekete, Jord\'an and Kaszanitzky [4] characterised the graphs which can be realised as 2-dimensional, infinitesimally rigid, bar-joint frameworks in which two given vertices are coincident. We formulate a conjecture which would extend their…
We extend some of the measures of association defined by Lazarsfeld and Martin, obtaining useful invariants to compare the birational geometry of two varieties having different dimensions. We explore such invariants providing examples and…
We consider combinatorial aspects of $\lambda$-terms in the model based on de Bruijn indices where each building constructor is of size one. Surprisingly, the counting sequence for $\lambda$-terms corresponds also to two families of binary…
We construct invariant polynomials on truncated multicurrent algebras, which are Lie algebras of the form $\mathfrak{g} \otimes_\mathbb{F} \mathbb{F}[t_1,\dotsc,t_\ell]/I$, where $\mathfrak{g}$ is a finite-dimensional Lie algebra over a…
The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…
We interpret the orthogonality relation of Kostka polynomials arising from complex reflection groups (c.f. [Shoji, Invent. Math. 74 (1983), J. Algebra 245 (2001)] and [Lusztig, Adv. Math. 61 (1986)]) in terms of homological algebra. This…
We commence the study of domination in the incidence graphs of combinatorial designs. Let $D$ be a combinatorial design and denote by $\gamma(D)$ the domination number of the incidence (Levy) graph of $D$. We obtain a number of results…
Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension, where the order statistics are taken componentwise.