Research
Research
Research
Research
141+ open-access research outputs.
We develop a method for the rigorous estimation of Hausdorff dimensions of limit sets produced by continued fraction iterated function systems. Our method is based on the approximation of a Perron-Fro…
Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations re…
We present, in detail and with a modern rigor, the two title proofs. The Weak Jordan Theorem (WJT) states that the complement of any topological circuit in the plane is disconnected.…
In this article, we examine the well-posedness and asymptotic behavior of the energy associated with the wave equation that incorporates a Kelvin-Voigt nonlocal damping structure given by $-||\nabla u…
This paper presents a geometrically explicit formulation for Cosserat rods that unifies configuration-space and strain-based representations within a single modeling framework. The proposed method use…
Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries…
This study presents a hybrid reduced-order modeling (ROM) framework for turbulent incompressible flows on collocated finite volume grids. The methodology employs the "discretize-then-project" consiste…
Geometric and Topological Deep Learning are rapidly growing research areas that enhance machine learning through the use of geometric and topological structures. Within this framework, Group Equivaria…
Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Tawa Pukllay (TP), where arithmetic operations do not require mental calculations: no carries…
Multi-Agent Reinforcement Learning (MARL) has emerged as a powerfulparadigm for cooperative decision-making in connected autonomous vehicles(CAVs); however, existing approaches often fail to guarantee…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require ex…
Clinician scheduling remains a persistent challenge due to limited clinical resources and fluctuating demands. This complexity is especially acute in large academic anesthesiology departments as physi…
The central path revolutionized the study of optimization in the 1980s and 1990s due to its favorable convergence properties, and as such, it has been investigated analytically, algorithmically, and c…
The rapid development of artificial intelligence (AI), marked by breakthroughs like 'AlphaEvolve' and 'Gemini Deep Think', is beginning to offer powerful new tools that have the potential to significa…
We study two special families of cubic hypersurfaces with vanishing Hessian in $\mathbb{P}^N$, obtaining rational parametrizations and computing their degree in $\mathbb{P}(S_3)$. For $N \leq 6$, thes…
This paper establishes a Feynman-Kac formula to represent the solution to general time inhomogeneous stochastic parabolic partial differential equations driven by multiplicative fractional Gaussian no…
2023 year marks the hundredth birth anniversary of prominent Russian mathematician and thinker Igor Rostislavovich Shafarevich (1923-2017). The article presents a selection of quotations from various …
This paper introduces a numerical method to enclose the global minimum of a nonlinear function subject to simple bounds on the variables. Using interval analysis, coupled with the computational power …
This paper develops a methodological framework for addressing a novel and application-oriented inverse nodal problem in Sturm-Liouville operators, having significant applications in seismic wave analy…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattic…
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