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A Fractional-Order Model of the Cardiac Function
Improving the mathematical model of the cardiovascular system is an important aspect of the control and design of ventricular assist devices. In this...
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Singular Value Decomposition for the X-Ray Transforms on the Reduced Heisenberg Group, and a Two-Radius Theorem
We give an explicit Singular Value Decomposition of the sub-Riemannian X-ray transform on the Heisenberg group with compact center. By studying the...
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On estimation and prediction in spatial functional linear regression model
We consider a spatial functional linear regression, where a scalar response is related to a square-integrable spatial functional process. We use a...
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Extension of Tensor-Product Generalized and Dense-Norm Summation-by-Parts Operators to Curvilinear Coordinates
Methodologies are presented that enable the construction of provably linearly stable and conservative high-order discretizations of partial...
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Hamilton-Jacobi Equations and Mathematical Morphology in Pseudo-Riemannian Manifolds
Partial differential equations (PDEs) are very suitable in nonlinear data modeling and analysis. Hamilton-Jacobi (HJ) equations constitute a...
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An Explicit Exponential Integrator Based on Faber Polynomials and its Application to Seismic Wave Modeling
Exponential integrators have been applied successfully in several physics-related differential equations. However, their application in hyperbolic...
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Influence of Fractional Order Parameter on the Dynamics of Different Vibrating Systems
The aim of this work is to investigate the fractional differential equations associated to different vibration phenomena. More specifically, we will...
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Positive Solutions for the Fractional p-Laplacian via Mixed Topological and Variational Methods
We study a nonlinear, nonlocal Dirichlet problem driven by the degenerate fractional p-Laplacian via a combination of topological methods (degree...
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Semigroups and Their Generators
This chapter is a prelude. It contains a brief account of some basic notions and facts from the theory of strongly continuous semigroups of operators...
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Analytic Langlands correspondence for \(PGL_2\) on \({\mathbb {P}}^1\) with parabolic structures over local fields
We continue to develop the analytic Langlands program for curves over local fields initiated in our earlier papers, following a suggestion of...
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A Generalization of Boyd’s Interpolation Theorem
Boyd’s interpolation theorem for quasilinear operators is generalized in this paper, which gives a generalization for both the Marcinkiewicz...
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Evolutionary Optimisation of a Flexible-Launcher Simple Adaptive Control System
Attitude control of conventional launchers is relatively easy and straightforward and gives an adequate performance when applied to the nominal...
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Deep-HyROMnet: A Deep Learning-Based Operator Approximation for Hyper-Reduction of Nonlinear Parametrized PDEs
To speed-up the solution of parametrized differential problems, reduced order models (ROMs) have been developed over the years, including...
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Introduction to Eigenvalue Problems
This chapter provides an overview of the literature concerning explicit eigenvalue bounds achieved through numerical methods. It outlines the rapid...
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Robust Preconditioning of Mixed-Dimensional PDEs on 3d-1d Domains Coupled with Lagrange Multipliers
In the context of micro-circulation, the coexistence of two distinct length scales—the vascular radius and the tissue/organ scale—with a substantial...
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Moduli Space of Vector Bundles
In this chapter, we recall Mumford’s construction of a moduli space of semistable holomorphic vector bundles over Riemann surfaces by using geometric...
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Application of CCC–Schoenberg operators on image resampling
Image resampling is a widely used tool in image processing. The upsampling increases the number of pixels and introduces new information to the image...
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Fully Well-Balanced Methods for Shallow Water Linearized Moment Model with Friction
In this work, we are interested in the numerical study of hyperbolic shallow water moments equations with smooth bottom topographies and friction...
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On a novel gradient flow structure for the aggregation equation
The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow...