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Existence of periodic solutions for a scalar differential equation modelling optical conveyor belts 光学传送带建模标量微分方程周期解的存在性
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-15 DOI: arxiv-2407.10843
Luis Carretero, José Valero
{"title":"Existence of periodic solutions for a scalar differential equation modelling optical conveyor belts","authors":"Luis Carretero, José Valero","doi":"arxiv-2407.10843","DOIUrl":"https://doi.org/arxiv-2407.10843","url":null,"abstract":"We study a one-dimensional ordinary differential equation modelling optical\u0000conveyor belts, showing in particular cases of physical interest that periodic\u0000solutions exist. Moreover, under rather general assumptions it is proved that\u0000the set of periodic solutions is bounded.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal cubature rules and Koornwinder polynomials 最小立方规则和 Koornwinder 多项式
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-13 DOI: arxiv-2407.09903
Yuan Xu
{"title":"Minimal cubature rules and Koornwinder polynomials","authors":"Yuan Xu","doi":"arxiv-2407.09903","DOIUrl":"https://doi.org/arxiv-2407.09903","url":null,"abstract":"In his classical paper [5], Koornwinder studied a family of orthogonal\u0000polynomials of two variables, derived from symmetric polynomials. This family\u0000possesses a rare property that orthogonal polynomials of degree $n$ have\u0000$n(n+1)/2$ real common zeros, which leads to important examples in the theory\u0000of minimal cubature rules. This paper aims to give an account of the minimal\u0000cubature rules of two variables and examples originating from Koornwinder\u0000polynomials, and we will also provide further examples.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-potential systems with relativistic operators and maximal monotone boundary conditions 具有相对论算子和最大单调边界条件的非势系统
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-12 DOI: arxiv-2407.09425
Petru Jebelean, Calin Serban
{"title":"Non-potential systems with relativistic operators and maximal monotone boundary conditions","authors":"Petru Jebelean, Calin Serban","doi":"arxiv-2407.09425","DOIUrl":"https://doi.org/arxiv-2407.09425","url":null,"abstract":"We are concerned with solvability of a non-potential system involving two\u0000relativistic operators, subject to boundary conditions expressed in terms of\u0000maximal monotone operators. The approach makes use of a fixed point formulation\u0000and relies on a priori estimates and convergent to zero matrices.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The natural extension to PDEs of Lie's reduction of order algorithm for ODEs 李氏减阶算法对 ODE 的自然扩展
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-12 DOI: arxiv-2407.09063
George W. Bluman, Rafael de la Rosa
{"title":"The natural extension to PDEs of Lie's reduction of order algorithm for ODEs","authors":"George W. Bluman, Rafael de la Rosa","doi":"arxiv-2407.09063","DOIUrl":"https://doi.org/arxiv-2407.09063","url":null,"abstract":"In this paper, we further consider the symmetry-based method for seeking\u0000nonlocally related systems for partial differential equations. In particular,\u0000we show that the symmetry-based method for partial differential equations is\u0000the natural extension of Lie's reduction of order algorithm for ordinary\u0000differential equations by looking at this algorithm from a different point of\u0000view. Many examples exhibit various situations that can arise.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"88 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A restriction estimate for a hyperbolic paraboloid in $mathbb{R}^5$ 双曲抛物面在 $mathbb{R}^5$ 中的限制估计值
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-11 DOI: arxiv-2407.08549
Zhuoran Li
{"title":"A restriction estimate for a hyperbolic paraboloid in $mathbb{R}^5$","authors":"Zhuoran Li","doi":"arxiv-2407.08549","DOIUrl":"https://doi.org/arxiv-2407.08549","url":null,"abstract":"In this paper, we prove a restriction estimate for a hyperbolic paraboloid in\u0000$mathbb{R}^5$ by the polynomial partitioning method.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141615069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Landesman-Lazer conditions for systems involving twist and positively homogeneous Hamiltonian systems 涉及扭转和正均质哈密顿系统的兰德斯曼-拉泽尔条件
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-11 DOI: arxiv-2407.08389
Natnael Gezahegn Mamo, Wahid Ullah
{"title":"Landesman-Lazer conditions for systems involving twist and positively homogeneous Hamiltonian systems","authors":"Natnael Gezahegn Mamo, Wahid Ullah","doi":"arxiv-2407.08389","DOIUrl":"https://doi.org/arxiv-2407.08389","url":null,"abstract":"We present multiplicity results for the periodic and Neumann-type boundary\u0000value problems associated with coupled Hamiltonian systems. For the periodic\u0000problem, we couple a system having twist condition with another one whose\u0000nonlinearity lies between the gradients of two positive and positively\u00002-homogeneous Hamiltonain functions. Concerning the Neumann-type problem, we\u0000treat the same system without any twist assumption. We examine the cases of\u0000nonresonance, simple resonance, and double resonance by imposing some kind of\u0000Landesman--Lazer conditions.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141613717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Different Demonstration for Integral Identity Across Distinct Time Scales 不同时间尺度上整体同一性的不同证明
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-11 DOI: arxiv-2407.08144
Patrick Oliveira
{"title":"A Different Demonstration for Integral Identity Across Distinct Time Scales","authors":"Patrick Oliveira","doi":"arxiv-2407.08144","DOIUrl":"https://doi.org/arxiv-2407.08144","url":null,"abstract":"In the theory of time scales, given $mathbb{T}$ a time scale with at least\u0000two distinct elements, an integration theory is developed using ideas already\u0000well known as Riemann sums. Another, more daring, approach is to treat an\u0000integration theory on this scale from the point of view of the Lebesgue\u0000integral, which generalizes the previous perspective. A great tool obtained\u0000when studying the integral of a scale $mathbb{T}$ as a Lebesgue integral is\u0000the possibility of converting the ``$Delta$-integral of $mathbb{T}$'' to a\u0000classical integral of $mathbb{R}$. In this way, we are able to migrate from a\u0000calculation that is sometimes not so intuitive to a more friendly calculation.\u0000A question that arises, then, is whether the same result can be obtained just\u0000using the ideas of integration via Riemann sums, without the need to develop\u0000the Lebesgue integral for $mathbb{T}$. And, in this article, we answer this\u0000question affirmatively: In fact, for integrable functions an analogous result\u0000is valid by converting a $Delta$-integral over $mathbb{T}$ to a riemannian\u0000integral of $mathbb{R}$.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141613739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a planar Pierce--Yung operator 关于平面皮尔斯--杨算子
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-10 DOI: arxiv-2407.07563
David Beltran, Shaoming Guo, Jonathan Hickman
{"title":"On a planar Pierce--Yung operator","authors":"David Beltran, Shaoming Guo, Jonathan Hickman","doi":"arxiv-2407.07563","DOIUrl":"https://doi.org/arxiv-2407.07563","url":null,"abstract":"We show that the operator begin{equation*} mathcal{C} f(x,y) := sup_{vin mathbb{R}} Big|mathrm{p.v.}\u0000int_{mathbb{R}} f(x-t, y-t^2) e^{i v t^3} frac{mathrm{d} t}{t} Big|\u0000end{equation*} is bounded on $L^p(mathbb{R}^2)$ for every $1 < p < infty$.\u0000This gives an affirmative answer to a question of Pierce and Yung.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141585776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability Analysis of Cantilever-like Structures with Applications to Soft Robotic Arms 悬臂结构的稳定性分析及其在软机械臂中的应用
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-10 DOI: arxiv-2407.07601
Siva Prasad Chakri Dhanakoti
{"title":"Stability Analysis of Cantilever-like Structures with Applications to Soft Robotic Arms","authors":"Siva Prasad Chakri Dhanakoti","doi":"arxiv-2407.07601","DOIUrl":"https://doi.org/arxiv-2407.07601","url":null,"abstract":"The application of variational structure for analyzing problems in the\u0000physical sciences is widespread. Cantilever-like problems, where one end is\u0000subjected to a fixed value and the other end is free, have been less studied,\u0000especially in terms of their stability despite their abundance. In this\u0000article, we develop the stability conditions for these problems by examining\u0000the second variation of the energy functional using the generalized Jacobi\u0000condition, which includes computing conjugate points. These conjugate points\u0000are determined by solving a set of initial value problems from the resulting\u0000linearized equilibrium equations. We apply these conditions to investigate the\u0000nonlinear stability of intrinsically curved elastic cantilevers subject to a\u0000tip load. Kirchhoff rod theory is employed to model the elastic rod\u0000deformations. The role of intrinsic curvature in inducing complex nonlinear\u0000phenomena, such as snap-back instability, is particularly emphasized. This\u0000snap-back instability is demonstrated using various examples, highlighting its\u0000dependence on various system parameters. The presented examples illustrate the\u0000potential applications in the design of flexible soft robotic arms and\u0000mechanisms.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141585777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relation between asymptotic $L_p$-convergence and some classical modes of convergence 渐近$L_p$收敛与某些经典收敛模式之间的关系
arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-09 DOI: arxiv-2407.06830
Nuno J. Alves, Giorgi G. Oniani
{"title":"Relation between asymptotic $L_p$-convergence and some classical modes of convergence","authors":"Nuno J. Alves, Giorgi G. Oniani","doi":"arxiv-2407.06830","DOIUrl":"https://doi.org/arxiv-2407.06830","url":null,"abstract":"Asymptotic $L_p$-convergence, which resembles convergence in $L_p$, was\u0000introduced in cite{alves2024mode}, motivated by a question in diffusive\u0000relaxation. The main purpose of this note is to compare asymptotic\u0000$L_p$-convergence with convergence in measure and in weak $L_p$ spaces. One of\u0000the results obtained provides a characterization of convergence in measure on\u0000finite measure spaces in terms of asymptotic $L_p$-convergence.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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