Institute of Mathematics and Informatics

AI Readiness Index in the Public Administration, Bulgaria 2026

The second national study, “Artificial Intelligence Readiness Index,” tracks changes in attitudes, knowledge, and practices regarding the use of AI in the Bulgarian public administration between 2025 and 2026. The data was collected from 5,475 employees at the central, regional,...

Viscosity Supersolution Barriers to a Non-local Free Boundary Problem

We study a parabolic obstacle partial integro-differential equation with a dynamically moving bilateral free boundary. This type of problem arises in the mathematical modeling of speculative asset bubbles with L\'evy jump processes. We investigate the existence of viscosity super...

A Generalization of a Classical Geometric Extremum Problem

Let ∂ C be the boundary of a compact convex body C in Rn, n≥2, and O be an interior point of C. Every straight line l containing O cuts from C a segment [AB] with end-points on ∂ C. It is shown that if [AB] is the shortest such segment, then ∂ C is smooth at the points A and B (i...

Asymptotic stability and cut-off phenomenon for the underdamped Langevin dynamics

In this article, we provide a detailed analysis of the long-time behavior of the underdamped Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise dynamical system converges to its unique attractor. We also observed that this condition is shar...

Convergence Analysis of a Numerical Algorithm for Spatial Segregation of Two Population Densities

Over the last few decades, the numerical approximation of spatial segregation equations for reaction-diffusion systems with $m$ population densities has gained significant interest. These problems are governed by a minimization problem subject to a closed but non-convex set. In t...

Mathematical model for non-monotone dose response to the PD-L1 blockade in vitro

Abstract Testing of new small molecules for oncotherapy often requires discrimination between the actual, target-specific bioactivity and non-specific toxicity. We present a mathematical model for T-cell reactivation under the action of therapeutic compounds targeting the PD-1/PD...

On the semigroups of fence-decreasing and fence-preserving transformations on a finite fence

Abstract For a natural number n , a fence [ n ] = {1 ≺ 2 ≻ 3 ≺ 4 ≻ 5 ≺⋯ n } is a partial ordered set. A partial transformation α is called fence-decreasing if xα ⪯ x for all x in the domain of α , and fence-preserving if x ≺ y implies xα ⪯ yα for all x and y in the domain of α ....

A note on multivariate diam-mean equicontinuity and frequent stability

Abstract Let <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> be a topological dynamical...

Taylor Recurrences and Coulomb-Corrected Asymptotics for the Schrödinger–Newton Ground State

We study the positive, radial ground-state profile of the stationary Schrödinger–Newton system in the fixed-energy normalization μ=1 with V(∞)=0. Using regularity and radial symmetry of solutions, we derive convergent even Taylor expansions for the wave function and Newtonian pot...