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Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…

Numerical Analysis · Mathematics 2020-07-20 Nirupama Bhattacharya , Gabriel A. Silva

The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…

Functional Analysis · Mathematics 2024-09-16 Meng Ning , Li-Ping Wu , Qing-yue Zhang , Bei Liu

We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…

Analysis of PDEs · Mathematics 2020-05-05 Emilia Blåsten , Hongyu Liu

The main result states that every convex set-valued function defined on a real interval with compact values in a locally convex space, admits an affine selection. In the case if the target space is a real line and the values are closed real…

Functional Analysis · Mathematics 2008-07-28 Szymon Wasowicz

The attractors of iterated function systems are usually obtained as the Hausdorff limit of any non-empty compact subset under iteration. In this note we show that an iterated function system on a boundedly compact metric space has compact,…

Dynamical Systems · Mathematics 2025-10-31 Şahin Koçak

In this paper, we obtain coupled fixed point theorem for (\psi, \phi)-contractions under some generalized conditions on the real valued functions \psi and \phi defined on (0,\infinity). Also, we present a generalized version of coupled…

Functional Analysis · Mathematics 2026-02-05 Athul P , D. Ramesh Kumar

In this paper we will show how to constructed an Skew-Field with trace-preserving endomorphisms of the affine plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in…

General Mathematics · Mathematics 2022-08-23 Orgest Zaka

We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of…

Algebraic Topology · Mathematics 2016-04-01 Peter Bubenik , Vin de Silva , Jonathan Scott

The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…

Dynamical Systems · Mathematics 2025-09-09 N. Pant

A characterization of valuations on the space of convex Lipschitz functions whose domain is a polytope in $\mathbb{R}^n$ is obtained. It is shown that every upper semicontinuous, equi-affine and dually epi-translation invariant valuation…

Metric Geometry · Mathematics 2025-12-10 Fernanda M. Baêta

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…

Analysis of PDEs · Mathematics 2015-05-11 Sascha Trostorff

In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine…

Functional Analysis · Mathematics 2020-10-06 Firdous A. Shah , Waseem Z. Lone

We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…

Dynamical Systems · Mathematics 2013-09-02 Michael Barnsley , Brendan Harding

To solve the issue of segmenting rich texture images, a novel detection methods based on the affine invariable principle is proposed. Considering the similarity between the texture areas, we first take the affine transform to get numerous…

Image and Video Processing · Electrical Eng. & Systems 2017-12-27 Jianwei Zhang , Xu Chen , Xuezhong Xiao

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…

Number Theory · Mathematics 2024-01-01 Ruikai Chen , Sihem Mesnager

We define fractal continuations and the fast basin of the IFS and investigate which properties they inherit from the attractor. Some illustrated examples are provided.

Dynamical Systems · Mathematics 2013-08-21 Michael Fielding Barnsley , Krzysztof Lesniak

This paper introduces advances in the geometry of the transforms for cross ratio of four points in a line in the Desargues affine plane. The results given here have a clean, based Desargues affine plan axiomatic's and definitions of…

General Mathematics · Mathematics 2025-04-11 Orgest Zaka , James F. Peters

The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…

Differential Geometry · Mathematics 2024-09-26 Ali Alshawabkeh , Georgios Tzounas , Angel Molina-Garcia , Federico Milano

As an application of Brouwer's fixed-point theorem we prove that a continuously differentiable convex function with gradient of constant norm is an affine mapping. It is a first-order characterization of affine mappings among continuously…

Classical Analysis and ODEs · Mathematics 2025-11-10 Csaba Vincze

All optical systems, which involve the collimation of a reflected, transmitted or scattered wave subsequent to tight focusing, are subject to two kinds of deviations. One is the wavefront curvature due to inaccurate focal placement of the…

Optics · Physics 2024-06-10 Nitish Kumar , Anirban Debnath , Nirmal K. Viswanathan