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On the multifractal measures: proportionality and dimensions of Moran sets
The aim of this work is to discuss the proportionality of the multifractal measures. We will prove that the ratio of the multifractal measures is...
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FMM-Accelerated Solvers for the Laplace–Beltrami Problem on Complex Surfaces in Three Dimensions
The Laplace–Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface...
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Projection Theorems for Hewitt–Stromberg and Modified Intermediate Dimensions
The aim of this paper is to prove a Marstrand-type theorem to give the almost sure Hewitt–Stromberg and certain modified intermediate dimensions of...
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Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus
In this paper, we mainly make research on the approximation of continuous functions in the view of the fractal structure based on previous studies....
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Embedding Dimensions of Matrices Whose Entries are Indefinite Distances in the Pseudo-Euclidean Space
A finite set of the Euclidean space is called an s -distance set provided that the number of Euclidean distances in the set is s . Determining the...
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Gauge Theories in Low Dimensions: Reminiscences of Work with Sergio Albeverio
This is an expository account of the author’s works influenced by Sergio Albeverio. Much of it focuses on gauge theories in two and three dimensions.
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On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions
We consider the Dirichlet problem for a compressible two-fluid model in multi-dimensions. It consists of the continuity equations for each fluid and...
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Approximation of curve-based sleeve functions in high dimensions
Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation,...
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A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate
Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider...
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Nonconforming spectral element method: a friendly introduction in one dimension and a short review in higher dimensions
In this article we present the nonconforming spectral element method (NSEM) for linear second-order ordinary differential equations with boundary...
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Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions
In this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three...
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Discretized Fast–Slow Systems with Canards in Two Dimensions
We study the problem of preservation of maximal canards for time discretized fast–slow systems with canard fold points. In order to ensure such...
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Stability of Curvature-Dimension Condition for Negative Dimensions Under Concentration Topology
In this paper, we prove the stability of metric measure spaces satisfying the curvature-dimension condition for negative dimensions under the...