Research
Research
Research
Research
2,015+ open-access research outputs.
Christoph, Dragani\'{c}, Gir\~{a}o, Hurley, Michel, and M\"{u}yesser conjectured that, when $d\mid n$, the expected number of cycles in a uniformly random cycle-factor of a directed $d$-regular graph …
We study local regularity properties of solutions to stationary anisotropic magnetic Schr\"odinger equations in $\mathbb{R}^d$, $d \ge 2$, arising from singular magnetic potentials concentrated along …
In previous work, we extracted the intrinsic finite algebraic state data of a finite-node conifold degeneration in the form $A_\Sigma := (V_\Sigma,E_\Sigma,c_\Sigma)$, where $V_\Sigma$ is the finite n…
Let $k$ be a perfect field of characteristic $p>0$, and let $d$ be a positive integer not divisible by $p$. We define a non-empty Zariski open subset $U$ of the space of polynomials of degree $d$, and…
Let $\pi:X\to \Delta$ be a one-parameter degeneration whose central fiber $X_0$ is a complex threefold with finitely many ordinary double points $\Sigma=\{p_1,\dots,p_r\}\subset X_0$. Associated with …
We describe an implementation of the biset category of finite groups as a tower of standard categorical constructions, all of which are implemented in the software project CAP for algorithmic category…
We study second-order stochastic parabolic equations in a cylindrical domain with homogeneous Dirichlet boundary conditions. Under a natural compatibility condition on the gradient noise, we establish…
In this paper, we determine the reduced automorphism groups of hyperelliptic curves of a small genus in characteristic $2$, when they are of $2$-rank $0$. Such a curve is an Artin-Schreier curve defin…
Classical symbolic protocol verification under Dolev--Yao uses binary attacker knowledge (known/unknown). This abstraction misses cumulative side-channel settings, where repeated noisy observations pr…
We show that the category of (right-)preordered groups is a quasivariety of universal algebras by giving explicit axioms. We then look at lattices of effective equivalence relations, which turn out to…
We establish Schauder-type estimates for linear parabolic systems driven by variable-coefficient nonlocal pseudo-differential operators of order $s>0$. These estimates are formulated in critical time-…
Let $k$ be a complete valuation field. We formulate a free Banach $k$-vector space as a Banach $k$-vector space with an orthonormal Schauder basis, and an almost free Banach $k$-vector space as a non-…
Given a finitely generated $G$ and a subgraph $H \leq G$, the relative number of ends $e(G,H)$ is the number of ends of a Schreier graph $\mathrm{Sch}(G,H)$ and the number of coends $\tilde{e}(G,H)$ i…
We study one-parameter conifold degenerations whose central fiber has finitely many ordinary double points. Working within a deliberately minimal finite-node bulk/localized-sector formalism, we identi…
We study pathwise $p$-th variation of continuous paths on a compact interval along a fixed partition sequence. Although the class of continuous paths with finite $p$-th variation is generally not line…
We study a one parameter degeneration of Calabi Yau threefolds whose central fiber contains a single ordinary double point. Using the nearby and vanishing cycle formalism, we construct a canonical per…
We propose a structure-preserving discontinuous Galerkin scheme for the Cahn--Hilliard equations with degenerate mobility based on the Symmetric Weighted Interior Penalty formulation. By evaluating th…
We introduce a primitive computation problem in the free tridendriform algebra generated by one element which is a Hopf algebra based on Schroeder trees. We know a complex way to generate all of them.…
Given a finitely generated, torsion-free nilpotent group, we find the maximum possible (critical) regularity for its faithful actions by diffeomorphisms of the closed or half-open interval and of the …
Finitely generated modules over the polynomial ring in $n$ indeterminates are isomorphic to quotients of finite rank free modules. We introduce a theory of relative Gr\"obner bases for those quotien…
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