Research
Research
Research
Research
336+ open-access research outputs.
We study log-concavity properties of real sequences $(a_n)_{n \ge 0}$ satisfying a $d$-th order linear recurrence whose coefficients are linear functions of $n$; the so-called P-recursive (or holonomi…
We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional…
We study Wakimoto-type free field constructions for superelliptic affine Lie algebras associated with coordinate rings $A=\mathbb{C}[t^{\pm1},u \mid u^m = p(t)]$, focusing on $\mathfrak{sl}_2$. We con…
In this article, we complete the study of the equivalences between the properties of $h$--dichotomy, $h$--noncriticality and $h$--expansiveness of a linear nonautonomous ODE system which had been init…
We prove that for any bounded convex domain $\Omega \subset \mathbb{R}^n$, the function \begin{equation*} \psi_\Omega(\xi) = \int_{\mathbb{R}^n\setminus\Omega} \frac{\mathrm{d}x}{|x-\xi|^{2n}}, \quad …
We study Schr\"odinger operators on the real line whose potentials are generated by the Fibonacci substitution sequence and a rule that replaces symbols by compactly supported potential pieces. We con…
In 2014, Juul, Kurlberg, Madhu and Tucker asked the following: given $K$ a number field and $f$ a rational function with coefficients in $K$, if $f_\mathfrak{p}$ denotes the reduction of $f$ modulo a …
Stanley's theorem establishes that for any finite graph $G$, the number $h_G(s)$ of magic labelings with magic sum $s$ can be expressed as a sum of two polynomials in $s$. However, determining the pre…
An urn scheme is a probabilistic model in which balls are placed into urns sequentially and independently of each other. All balls share the same probability distribution for hitting the urns. In the …
Let $a$, $b$, and $n$ be three integers such that $1\leq a \leq b < n$, $a \equiv b$ (mod $2$), and $na$ is even. A parity $[a,b]$-factor of $G$ is a spanning subgraph $H$ such that for each vertex $v…
The recent discovery of a family of aperiodic monotiles, which includes David Smith's famous Hat, has shaken the field of plane tessellations. Music composers have already utilised the visual represen…
In this paper, we generalize the notion of connections, which was introduced by Alain Connes in noncommutative differential geometry, to the differential graded (DG) homological algebra setting. Then,…
We investigate spectral lower bounds on the chromatic number $\chi$ of Hamming graph powers $H(n, q)^p$, Johnson graph powers $J(n, k)^p$, and Kneser graph powers $K(n, k)^p$ providing the first compu…
Consider a Markov chain $(X_i)_{i\ge0}$ with invariant measure $\mu$ that admits the representation $X_{i+1}=\Phi(X_i,U_i)$, where $(U_i)_{i\ge0}$ are i.i.d. random variables and $\Phi$ is a measurabl…
Russell's paradox is the most easily understandable way to illustrate the inconsistency of na\"ive set theory. This note proposes a direct encoding of Russell's paradox with type-in-type universe, sig…
We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\,, \] where a nonneg…
This article presents and formalizes an elementary multiplication method discovered independently by a 10-year-old student, Anthony Lima Dias. The method reorganizes digit interactions in base-10 mult…
We introduce the notion of directed scheme of ideals to characterize peculiar ideals on the reals, which comes from a formalization of the framework of Yorioka ideals for strong measure zero sets. We …
Historically, proofs of $\mathrm{BPI}$ in models without choice have relied on a contradiction framework that was introduced by Halpern. We introduce the filter extension property for permutation mode…
Although the theory of self-affine tiles and the theory of Rauzy fractals are quite different from each other, they have some common features. Both, self-affine tiles and Rauzy fractals have tiling pr…
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