arXiv preprints from January 1, 2026 through July 21, 2026 — 08:20:27 EST
We introduce a new two-parameter fractional time operator with Volterra structure, denoted by ${}^{W}D_{t}^{α,β}$, defined through the Laplace symbol \[ Φ_{α,β}(s) = \frac{s^α}{\bigl(1+(1-α)s^{α-1}\bigr)^β}, \qquad 0<α<1, \ β\ge0. \] The operator preserves the Caputo-type high-frequency behavior while allowing a controlled...
We exhibit new biorthogonal sequences generated by index integrals of the squares of the modified Bessel functions and gamma functions. The composition orthogonality, involving differential operators is employed. Generalized Wilson polynomials are introduced. Some properties are investigated.
We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally Hölder continuous solutions. Notably, our results accommodate data exhibiting singularities nearly as critical as the inverse square of the distance...
We prove an upper bound for the Morse index of min-max stationary integral varifolds realizing the $d$-dimensional $p$-width of a closed Riemannian manifold.
For a given second order elliptic operation $\mathcal{L}$ in a domain $Ω\subset{\mathbb{R}}^\mathbf{N}$, $\mathbf{N}\ $, and a compact set $\mathbf{K}\subsetΩ$, order $\mathbf{N}$-$2$-Ahlfors-David regular, we define the space $\mathcal{H}^{\mathbf{r}+ω}_{\mathcal{L}}(\mathbf{K})$ of continuous functions $f(x),\, x\in\mathbf{K}$,...
Using a modified curve shortening flow, we construct $λ$-Angenent curve, which was first constructed by the shooting method.
We study traces of Hecke operators on spaces of elliptic cusp forms and Drinfeld cusp forms and show that, modulo any prime power, these traces are periodic in the weight.
We consider the policy gradient adaptive control (PGAC) framework, which adaptively updates a control policy in real time, by performing data-based gradient descent steps on the linear quadratic regulator cost. This method has empirically shown to react to changing circumstances, such as model parameters, efficiently. To formalize...
Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not necessarily hold true in fractional calculus. In this work we will compare various methods presented...
Registration methods in bounded domains have received significant attention in the model reduction literature, as a valuable tool for nonlinear approximation. The aim of this work is to provide a concise yet complete overview of relevant results for registration methods in $n$-dimensional domains, from the perspective of parametric...
We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a majorization-minimization algorithm by using the difference-of-convexity (DC) reformuation for the rank-one...
In this paper, we study backward stochastic differential equations driven by G-Brownian motion where the generator has time-varying monotonicity with respect to y and Lipsitz property with respect to z. Through the Yosida approximation, we have proved the existence and uniqueness of the solutions to these equations.
A non-trivial topological group is called \emph{$d$-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting it trivially. This notion was introduced by Márquez and Tkachenko and has been intensively studied in the metrizable setting. In particular, they proved that...
Bojańczyk, Pilipczuk, and Grohe [LICS '18] proved that for graphs of bounded linear clique-width, clique-decompositions of bounded width can be produced by a CMSO transduction. We show that in the case of tournaments, a first-order transduction suffices. This implies that the logics CMSO and existential MSO are equivalent over bounded...
Lawler and Trujillo Ferreras constructed a well-known coupling between the Brownian loop soups on $\mathbb{R}^2$ and the (discrete-time) random walk loop soups on $\mathbb{Z}^2$ (one rescales the random walk loops by $1/N$, their time parametrizations by $1/(2N^2)$, and lets $N\to \infty$), which led to numerous applications. It...
For every flat surface, almost every flat surface in its $\mathsf{SL}(2,\mathbb{R})$ orbit has the following property: the sequence of its saddle connection lengths in non-decreasing order is uniformly distributed in the unit interval.
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional constant-coefficient elliptic equations with both divergence and non-divergence forms and all types of...
We develop a framework to study the K-stability of weighted Fano hypersurfaces based on a combination of birational and convex-geometric techniques. As an application, we prove that all quasi-smooth weighted Fano hypersurfaces of index 1 with at most two weights greater than 1 are K-stable. We also construct several examples of...
An AG-monoid is an AG-groupoid (a groupoid satisfying the identity called left invertive law $(xy)z=(zy)x$) and having a left identiy. In this paper we enumerate AG-monoids algebraically and then implement them in GAP to compute them computationally.
We introduce a new basis of the group algebra of the symmetric group, built using the left-to-right minima sets of permutations. We show that on this basis, the descent algebra acts by triangular operators, thus making it an analogue of a cellular basis. The proof involves Dynkin elements (nested commutators) of the free algebra and...
The structure of continuous Hopfield networks is revisited from a system-theoretic point of view. After adopting a novel electrical network interpretation involving nonlinear capacitors, it is shown that Hopfield networks admit a port-Hamiltonian formulation provided an extra passivity condition is satisfied. Subsequently it is shown...
Motivated by a connection to the infinite Ginibre point process, decoupled random walks were introduced in a recent article Alsmeyer, Iksanov and Kabluchko (2025). The decoupled random walk is a sequence of independent random variables, in which the $n$th variable has the same distribution as the position at time $n$ of a standard...
We study the homogeneous Landau equation with Maxwell molecules and prove that the entropy production is non-increasing provided the directional temperatures are well-distributed and the solution admits a moment of order $\ell$, for some $\ell$ arbitrarily close to $2$. It implies that for an initial condition with finite moment of...
We show a first rectification result for homotopy chain coalgebras over a field. On the one hand, we consider the $\infty$-category obtained by localizing differential graded coalgebras over an operad with respect to quasi-isomorphisms; on the other, we give a general definition of an $\infty$-category of coalgebras over an enriched...
In this article, we study $c$-spherical Ricci metrics, that is, Riemannian metrics whose Gaussian curvature $K$ satisfies \begin{equation*} (K - c)ΔK - |\nabla K|^2 - 4K(K - c)^2 = 0, \end{equation*} for some $c>0$. We explicitly construct a two-parameter family of such metrics with rotational symmetry and show that infinitely many...