arXiv preprints from January 1, 2026 through July 21, 2026 — 08:45:36 EST
We study a family of non-local isoperimetric energies $E_{γ,\varepsilon}$ on the round sphere $M = S^n$, where the non-local interaction kernel $K_\varepsilon$ is the fundamental solution of the Helmholtz operator $1 - \varepsilon^2 Δ$. To analyse these energies, we introduce a Riemannian autocorrelation function $c_Ω$ associated to a...
We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral projections. In addition, we give some applications to Sturm-Liouville operators.
This paper presents a geometric framework for analyzing output-feedback and input-feedforward passivization of linear time-invariant systems. We reveal that a system is passivizable with a given passivity index when the Nyquist plot for SISO systems or the Rayleigh quotient of the transfer function for MIMO systems lies within a...
We consider a discontinuous Galerkin method for the numerical solution of boundary value problems in two-dimensional domains with curved boundaries. A key challenge in this setting is the potential loss of convergence order due to approximating the physical domain by a polygonal mesh. Unless boundary conditions can be accurately...
We show that the logarithmic derivation module of (the cone of) the deformation A of a Weyl arrangement associated with a root system of simply laced type has projective dimension one if the deforming parameter ranges from -j to j+2. In addition, we give an explicit minimal free resolution when the root system is of type A3 and B2....
We prove the following Wiener-Wintner Theorem along the sequence of prime times, the first extension of the Wiener-Wintner Theorem to arithmetic sequences: for every probability space, $(X, ν),$ equipped with a measure-preserving transformation, $T : X \to X,$ and every $f \in L^p(X), 1 < p \leq \infty$, there exists a set of full...
These notes refer to a minicourse I gave at the occasion of the conference meeting ``Applications of Noncommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time'' to be held from 7 April to 11 April 2025 at the Centre International de Rencontres Mathématiques in Luminy. They consist in a review of a long standing...
Umbral theory, formulated in its modern version by S. Roman and G.~C. Rota, has been reconsidered in more recent times by G. Dattoli and collaborators with the aim of devising a working computational tool in the framework of special function theory. Concepts like umbral image and umbral vacuum have been introduced as pivotal elements...
The finite element method is an indispensable tool in engineering, but its computational complexity prevents applications for control or at system-level. Model order reduction bridges this gap, creating highly efficient yet accurate surrogate models. Reducing nonlinear setups additionally requires hyperreduction. Compatibility with...
We determine an infinite family of linear identities for the number $A_4(n)$ of partition pairs of $n$ with $4$-cores by employing elementary $q$-series techniques and certain $3$-dissection formulas. We then discover an infinite family of congruences for $A_4(n)$ as a consequence of these linear identities.
In the context of geometric Impulsive Mechanics of systems with a finite number of degrees of freedom, we model the roughness of a unilateral constraint ${\mathcal S\/}$ by introducing a suitable instantaneous kinetic constraint ${\mathcal B\/}\subset {\mathcal S\/}$. A constitutive characterization of ${\mathcal B\/}$ based only on...
We present a general approach to establish algebraic functional equations for big Galois representations over multiple $\mathbb{Z}_p$-extensions. Our result is formulated in both Selmer group and Selmer complex settings, and encompasses a broad range of Iwasawa-theoretic scenarios. In particular, our result applies to the triple...
In this paper, we prove the positivity of the double mixed discriminant associated with a positive linear map between spaces of third-order complex matrices, thereby settling the three-dimensional case of Finski's open problem. As an application, we obtain the weak positivity of the third Chern form for Griffiths positive vector...
Axioms for the generalization of root systems were defined and classified (irreducible) by V. Serganova, which precisely correspond to the root systems of basic classical Lie Superalgebras. Here, we present a unified method for constructing simple Lie Superalgebras from the abstract root system, with the choice of base having the...
This paper showcases the effectiveness of the quasiconvexity property in addressing the optimal regularity of the temporal derivative and establishes conditions for its continuity in nonlocal time-dependent obstacle problems.
Let $z_1,\dots,z_n$ be complex numbers with $|z_j|\le ρ$, where $ρ>1$. Cassels proved that, under an additional restriction on $ρ$, the inequality \[ \prod_{j\ne k}\bigl|1-\overline{z_j}z_k\bigr| \le \left(\frac{ρ^{2n}-1}{ρ^2-1}\right)^{\!n} \] holds. In a subsequent note, Alexander conjectured that this inequality is in fact valid...
The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard $\mathcal{O}(h^{-2})$ conditioning of second-order operators, the non-symmetry and non-local boundary coupling render them resistant to standard Algebraic...
This paper addresses the study of algebraic versions of Farkas lemma and strong duality results in the very broad setting of infinite-dimensional conic linear programming in dual pairs of vector spaces. To this end, purely algebraic properties of perturbed optimal value functions of both primal and dual problems and their...
For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov regularization (respectively, Landweber iterations) to set up a new search space on which the...
We define a real-valued distance metric $wd$ on the space $\mathcal{C}$ of short combinatorial games in canonical form. We demonstrate the existence of Cauchy sequences informed by sidling sequences, find limit points, and investigate the closure $\overline{\mathcal{C}}$, which is shown to partition the set of loopy games in a...
We show that any positive, continuous, and bounded function can be realised as the diffusion coefficient of an evolution equation associated with a gradient interacting particle system. The proof relies on the construction of an appropriate model and on the entropy method.
Let $p$ be an odd prime and let $F_i$ be the $i$th $(a,b)$-Fibonacci number with initial values $F_0=a$ and $F_1=b$. For a simple connected graph $G=(V,E)$, define a bijective function $f:V(G)\to \{0,1,\ldots,|V|-1\}$. If the induced function $f_p^*:E(G)\to \{0,1\}$, defined by $f_p^*(uv)=\frac{1+([F_{f(u)}+F_{f(v)}]/p)}{2}$ whenever...
Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this task since their complexity is a function of the desired fraction of the spectrum. In addition,...
Let $I(F,n)$ denote the maximum number of induced copies of a graph $F$ in an $n$-vertex graph. The inducibility of $F$, defined as $i(F)=\lim_{n\to \infty} I(F,n)/\binom{n}{v(F)}$, is a central problem in extremal graph theory. In this work, we investigate the inducibility of Turán graphs $F$. This topic has been extensively studied...
Adding the time as a component of a stochastic process before computing its signature terminal value ensures injectivity and supports universal approximation results, but it induces linear dependence among the components of the signature terminal value. For any natural number $N$, the terminal values of the signature components...