We are interested in the actions of an algebraic group G over the grassmannians of a finite dimensional K-vector space V (K algebraically closed) deduced from an action of G over V. We prove that the dimension of the orbit space of G(i,V) is smalle...
In this note we consider a quotient π: X-> X/G, with G a finite group and X a smooth projective scheme such that X/G is smooth. We compare the equivariant derived category D^G(X) and the derived category of the quotient D(X/G) by giving the image...
A new general eigenvalue formula for the eigenvalues of Casimir invariants, for the type-I quantum superalgebras, is applied to the construction of link polynomials associated with {\em any} finite dimensional unitary irrep for these algebras. This...
The construction of link polynomials associated with finite dimensional representations of ribbon quasi-Hopf algebras is discussed in terms of the formulation of an appropriate Markov trace. We then show that this Markov trace is invariant under tw...
Extensive-form games (EFGs) model finite sequential interactions between players. The amount of memory required to represent these games is the main bottleneck of algorithms for computing optimal strategies and the size of these strategies is often i...
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its worst case...
In this paper we give a conjecture for the average number of unramified $G$-extensions of a quadratic field for any finite group $G$. The Cohen-Lenstra heuristics are the specialization of our conjecture to the case that $G$ is abelian of odd order....
We show the analogue of Muhlherr's [Coxeter groups in Coxeter groups, Finite Geom. and Combinatorics, Cambridge Univ. Press (1993), 277-287] for Artin-Tits monoids, and for Artin-Tits groups of spherical type. That is, the submonoid (resp. subgroup...
This is an introduction (in German) to projective geometry by the late Heinz Lueneburg. Projective spaces are treated as lattices with particular properties, and finite geometries receive special attention. The final chapters deal with Segre and Gras...
We introduce and prove the $n$-dimensional Pizza Theorem: Let $\mathcal{H}$ be a hyperplane arrangement in $\mathbb{R}^{n}$. If $K$ is a measurable set of finite volume, the {pizza quantity} of $K$ is the alternating sum of the volumes of the regions...
We study the Mana and Magic for quantum states. They have a standard definition through the Clifford group, which is finite and thus classically computable. We introduce a modified Mana and Magic, which keep their main property of classical computabi...
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction of Post`s C...
Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many scholars co...
We continue our study of the perfect kernel of the space of transitive actions of Baumslag-Solitar groups by investigating high transitivity. We show that actions of finite phenotype are never highly transitive, except when the phenotype is 1, in whi...
Easily create a finite state machine and define legal state transitions. Listen to state entrances, departures, and transitions. (⭐ 65)
In this expository note, I present some of the key features of the lattice of torsion classes of a finite-dimensional algebra, focussing in particular on its complete semidistributivity and consequences thereof. This is intended to serve as an introd...
Let R be the skew group algebra of a finite group acting on the path algebra of a quiver. This article develops both theoretical and practical methods to do computations in the Morita reduced algebra associated to R. Reiten and Riedtmann proved that...
Scenario-aware dataflow (SADF) is a prominent tool for modeling and analysis of dynamic embedded dataflow applications. In SADF the application is represented as a finite collection of synchronous dataflow (SDF) graphs, each of which represents one p...
We study adequate subgroups of $GL_n$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to be adequate....
Let $\mathfrak{F}_n$ be the set of unitary cuspidal automorphic representations of $\mathrm{GL}_n$ over a number field $F$, and let $S\subseteq\mathfrak{F}_n$ be an arbitrary finite subset. Given $π_0\in\mathfrak{F}_{n_0}$, we establish large sieve...
In this paper we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming finite element method on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a new robust stabiliz...
For an irreducible character $χ$ of a finite group $G$, let $\mathrm{cod}(χ):=|G: \ker(χ)|/χ(1)$ denote the codegree of $χ$, and let $\mathrm{cod}(G)$ be the set of irreducible character codegrees of $G$. In this note, we prove that if $\ker(χ)...
We report the detection of sub-Saturn-mass planet MOA-2008-BLG-310Lb and argue that it is the strongest candidate yet for a bulge planet. Deviations from the single-lens fit are smoothed out by finite-source effects and so are not immediately appar...
Consider a finite simple digraph $D$ with vertex set $V(D)$. An Italian dominating function (IDF) on $D$ is a function $f:V(D)\rightarrow\{0,1,2\}$ satisfying every vertex $u$ with $f(u)=0$ has an in-neighbor $v$ with $f(v)=2$ or two in-neighbors $w$...
We analyze the extreme high-magnification microlensing event OGLE-2008-BLG-279, which peaked at a maximum magnification of A ~ 1600 on 30 May 2008. The peak of this event exhibits both finite-source effects and terrestrial parallax, from which we d...
Morphological analysis is the study of the formation and structure of words. It plays a crucial role in various tasks in Natural Language Processing (NLP) and Computational Linguistics (CL) such as machine translation and text and speech generation....
Cellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications, finite-dimensi...
In this paper we study urban segregation of two different communities A and B, poor and rich, distributed randomly on finite samples, to check cheap and expensive residences. For this purpose we avoid the complications of the Schelling model which...
Permutation tests are a popular choice for distinguishing distributions and testing independence, due to their exact, finite-sample control of false positives and their minimax optimality when paired with U-statistics. However, standard permutation t...
We give an elementary proof of the theorem which states that a finite unramified algebra over a discrete field is tracically étale. -- Nous donnons une démonstration élémentaire du théorème selon lequel toute algèbre nette sur un cors disc...
Let $(X, d)$ be an unbounded metric space and let $\tilde r=(r_n)_{n\in\mathbb N}$ be a sequence of positive real numbers tending to infinity. A pretangent space $Ω_{\infty, \tilde r}^{X}$ to $(X, d)$ at infinity is a limit of the rescaling sequence...
A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found....
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths), culminating...
We introduce an algorithm which, given probabilities $μ\leq_{\text{cx}} ν$ in convex order and defined on a separable Banach space $B$, constructs finitely-supported approximations $μ_n \to μ, ν_n\to ν$ which are in convex order $μ_n \leq_{\te...
We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where "one piece is big" is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer's proof of the Hindm...
The recently-discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. Phy. Rev. Lett. 121, 024502, 2018) has offered an explanation for the origin of elasto-inertial turbulence (EIT) which occurs at lower Weissenberg ($W...
Let $n\ge 1$ be an integer and $\mathbb{F}_q$ be a finite field of characteristic $p$ with $q$ elements. In this paper, it is proved that the Wenger graph $W_n(q)$ and linearized Wenger graph $L_m(q)$ are edge-girth-regular $(v,k,g,λ)$-graphs, and t...
Let $q=p^e$, where $p$ is a prime and $e\geq 1$ is an integer. For $m\geq 1$, let $P$ and $L$ be two copies of the $(m+1)$-dimensional vector spaces over the finite field $\mathbb{F}_q$. Consider the bipartite graph $W_m(q)$ with partite sets $P$ and...
In over 20 years of committed diversity and inclusion efforts, we’ve learned that diversity is not a finite goal; it is a journey that requires constant self-assessment and recommitment.
A flat plumbing basket is a surface consisting a disk and finitely many bands which are contained in distinct pages of the trivial open book decomposition of $\mathbf{S}^{3}$. In this paper, we construct a Legendrian link from a flat plumbing basket,...