数学最新文献

{"title":"Education","authors":"Hélène Frankowska","doi":"10.1137/24n976018","DOIUrl":"https://doi.org/10.1137/24n976018","url":null,"abstract":"SIAM Review, Volume 66, Issue 4, Page 749-749, November 2024. <br/> In this issue the Education section presents two contributions. The first paper, “Sandpiles and Dunes: Mathematical Models for Granular Matter,” by Piermarco Cannarsa and Stefano Finzi Vita, presents a review of mathematical models for formation of sand piles and dunes. In nature and everyday life various materials appear as conglomerates of particles, like, for instance, sand, gravel, fresh snow, rice, sugar, etc. On larger scales, granular material exhibits new and more complex phenomena which are still not fully understood. It is very different from that of a solid, liquid, or gas in the sense that it can show characteristics similar to one or the other depending on the energy of the system. Its modeling can help in understanding complex natural phenomena such as dune migration, erosion, landslides, and avalanches, and can contribute to the development of environmental protection programs. Such models are also important in various applications in agriculture, construction, energy production, as well as in the chemical, pharmaceutical, food, and metallurgical industries. Even if a sufficiently consolidated general model for the dynamics of granular materials is not available yet, significant progress has been made recently with the introduction of new theoretical models adapted to more specific situations. In this article, after a general description and some historical comments, the authors limit themselves to considering the problem of the growth of a pile of sand on a table under the action of a vertical source of small intensity, neglecting the effects of wind, which has an important role in dune formation. Still, even for such an apparently simpler case, many interesting phenomena do arise and are described in an easily accessible way. Accompanying pictures of real-life experiences make the reading truly enjoyable, and numerical illustrations bring even better intuition on the complexity of phenomena. The authors also indicate literature for further learning. This article is well organized, neatly written, and presents the subject highlighting some of the major aspects. This review of existing models can become a starting point for research projects in a Master's program of applied mathematics and partial differential equations. It could also be used by advanced mathematics students to learn differential models of granular material in an affordable way. The second paper, “Developing Workforce with Mathematical Modeling Skills,” is presented by Ariel Cintrón-Arias, Ryan Andrew Nivens, Anant Godbole and Calvin B. Purvis. Undergraduate mathematics degrees constitute a very small portion of all awarded degrees in the U.S., and this portion is stagnating, while the job growth between 2016 and 2026 for Statisticians and Mathematicians is expected to be substantial. So the need for growth in mathematical training becomes imperative. The authors discuss the nationwide production o","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":null,"pages":null},"PeriodicalIF":10.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Feynman's Inverse Problem","authors":"Adrian Kirkeby","doi":"10.1137/23m1611488","DOIUrl":"https://doi.org/10.1137/23m1611488","url":null,"abstract":"SIAM Review, Volume 66, Issue 4, Page 694-718, November 2024. <br/> We analyze an inverse problem for water waves posed by Richard Feynman in the BBC documentary Fun to Imagine. We show that the problem can be modeled as an inverse Cauchy problem for gravity-capillary waves, conduct a detailed analysis of the Cauchy problem, and give a uniqueness proof for the inverse problem. Somewhat surprisingly, this results in a positive answer to Feynman's question. In addition, we derive stability estimates for the inverse problem for both continuous and discrete measurements, propose a simple inversion method, and conduct numerical experiments to verify our results.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":null,"pages":null},"PeriodicalIF":10.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Oscillatory Networks: Insights from Piecewise-Linear Modeling","authors":"Stephen Coombes, Mustafa Şayli, Rüdiger Thul, Rachel Nicks, Mason A. Porter, Yi Ming Lai","doi":"10.1137/22m1534365","DOIUrl":"https://doi.org/10.1137/22m1534365","url":null,"abstract":"SIAM Review, Volume 66, Issue 4, Page 619-679, November 2024. <br/> There is enormous interest---both mathematically and in diverse applications---in understanding the dynamics of coupled-oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology, and more. It is common to describe the rich emergent behavior in these systems in terms of complex patterns of network activity that reflect both the connectivity and the nonlinear dynamics of the network components. Such behavior is often organized around phase-locked periodic states and their instabilities. However, the explicit calculation of periodic orbits in nonlinear systems (even in low dimensions) is notoriously hard, so network-level insights often require the numerical construction of some underlying periodic component. In this paper, we review powerful techniques for studying coupled-oscillator networks. We discuss phase reductions, phase--amplitude reductions, and the master stability function for smooth dynamical systems. We then focus, in particular, on the augmentation of these methods to analyze piecewise-linear systems, for which one can readily construct periodic orbits. This yields useful insights into network behavior, but the cost is that one needs to study nonsmooth dynamical systems. The study of nonsmooth systems is well developed when focusing on the interacting units (i.e., at the node level) of a system, and we give a detailed presentation of how to use saltation operators, which can treat the propagation of perturbations through switching manifolds, to understand dynamics and bifurcations at the network level. We illustrate this merger of tools and techniques from network science and nonsmooth dynamical systems with applications to neural systems, cardiac systems, networks of electromechanical oscillators, and cooperation in cattle herds.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":null,"pages":null},"PeriodicalIF":10.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gabor Phase Retrieval via Semidefinite Programming","authors":"Philippe Jaming, Martin Rathmair","doi":"10.1007/s10208-024-09683-6","DOIUrl":"https://doi.org/10.1007/s10208-024-09683-6","url":null,"abstract":"<p>We consider the problem of reconstructing a function <span>(fin L^2({mathbb R}))</span> given phase-less samples of its Gabor transform, which is defined by </p><span>$$begin{aligned} {mathcal {G}}f(x,y) :=2^{frac{1}{4}} int _{mathbb R}f(t) e^{-pi (t-x)^2} e^{-2pi i y t},text{ d }t,quad (x,y)in {mathbb R}^2. end{aligned}$$</span><p>More precisely, given sampling positions <span>(Omega subseteq {mathbb R}^2)</span> the task is to reconstruct <i>f</i> (up to global phase) from measurements <span>({|{mathcal {G}}f(omega )|: ,omega in Omega })</span>. This non-linear inverse problem is known to suffer from severe ill-posedness. As for any other phase retrieval problem, constructive recovery is a notoriously delicate affair due to the lack of convexity. One of the fundamental insights in this line of research is that the connectivity of the measurements is both necessary and sufficient for reconstruction of phase information to be theoretically possible. In this article we propose a reconstruction algorithm which is based on solving two convex problems and, as such, amenable to numerical analysis. We show, empirically as well as analytically, that the scheme accurately reconstructs from noisy data within the connected regime. Moreover, to emphasize the practicability of the algorithm we argue that both convex problems can actually be reformulated as semi-definite programs for which efficient solvers are readily available. The approach is based on ideas from complex analysis, Gabor frame theory as well as matrix completion. As a byproduct, we also obtain improved truncation error for Gabor expensions with Gaussian generators.</p>","PeriodicalId":55151,"journal":{"name":"Foundations of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142597481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On injective chromatic index of sparse graphs with maximum degree 5","authors":"Jian Lu, Zhen-Mu Hong, Zheng-Jiang Xia","doi":"10.1007/s10878-024-01234-7","DOIUrl":"https://doi.org/10.1007/s10878-024-01234-7","url":null,"abstract":"<p>A <i>k</i>-edge coloring <span>(varphi )</span> of a graph <i>G</i> is injective if <span>(varphi (e_1)ne varphi (e_3))</span> for any three consecutive edges <span>(e_1, e_2)</span> and <span>(e_3)</span> of a path or a triangle. The injective chromatic index <span>(chi _i'(G))</span> of <i>G</i> is the smallest <i>k</i> such that <i>G</i> admits an injective <i>k</i>-edge coloring. By discharging method, we demonstrate that any graph with maximum degree <span>(Delta le 5)</span> has <span>(chi _i'(G)le 12)</span> (resp. 13) if its maximum average degree is less than <span>(frac{20}{7})</span> (resp. 3), which improves the results of Zhu (2023).\u0000</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142597835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ROC Analysis for Classification and Prediction in Practice","authors":"Mauricio Tec","doi":"10.1080/01621459.2024.2423434","DOIUrl":"https://doi.org/10.1080/01621459.2024.2423434","url":null,"abstract":"Published in Journal of the American Statistical Association (Just accepted, 2024)","PeriodicalId":17227,"journal":{"name":"Journal of the American Statistical Association","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142589033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DL-integral and DQ-integral n-Cayley graphs","authors":"Lantao Zou,&nbsp;Yongjiang Wu,&nbsp;Lihua Feng","doi":"10.1016/j.amc.2024.129178","DOIUrl":"10.1016/j.amc.2024.129178","url":null,"abstract":"<div><div>In this paper, we derive a decomposition formula for spectra of the distance Laplacian matrix <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>L</mi></mrow></msup></math></span> and distance signless Laplacian matrix <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> of <em>n</em>-Cayley graphs by using group representation theory. Besides, we compute the <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>L</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span> spectra of the <em>n</em>-gonal <em>n</em>-cone graph and the <em>n</em>-sunlet graph. Finally, we present some examples of <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>L</mi></mrow></msup></math></span>-integral graphs and <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>Q</mi></mrow></msup></math></span>-integral graphs.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global bounded solution in an attraction repulsion Chemotaxis-Navier-Stokes system with Neumann and Dirichlet boundary conditions","authors":"Luli Xu,&nbsp;Chunlai Mu,&nbsp;Minghua Zhang,&nbsp;Jing Zhang","doi":"10.1016/j.nonrwa.2024.104247","DOIUrl":"10.1016/j.nonrwa.2024.104247","url":null,"abstract":"<div><div>This paper deals with an attraction–repulsion Chemotaxis-Navier–Stokes system with Dirichlet boundary for the attraction signal and Neumann boundary for the repulsion signal. Based on the work of Winkler (2020) and Wang et al. (2022), by using a series estimates, it is shown that in two dimension the classical solution of the system is globally bounded, under the condition of small initial values <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> in the explicit expressions for <span><math><msub><mrow><mo>‖</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></msub></math></span> and attraction–repulsion coefficients.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Traveling waves to a chemotaxis-growth model with Allee effect","authors":"Qi Qiao ,&nbsp;Xiang Zhang","doi":"10.1016/j.jde.2024.10.040","DOIUrl":"10.1016/j.jde.2024.10.040","url":null,"abstract":"<div><div>For a chemotaxis-growth model with Allee effect, whose chemotactic sensitivity and diffusion coefficient of the chemical substance are both small, we prove existence of the positive traveling waves with slow wave speeds and their unstability and asymptotic stability with shift depending on the choice of the parameters of the system.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lp-solutions of Multi-dimensional Oblique Reflected BSDEs and Optimal Switching Problem on Finite or Infinite Time Horizon","authors":"Xue-jun Shi,&nbsp;Qun Feng,&nbsp;Long Jiang","doi":"10.1007/s10255-024-1136-1","DOIUrl":"10.1007/s10255-024-1136-1","url":null,"abstract":"<div><p>In this paper, we study mulit-dimensional oblique reflected backward stochastic differential equations (RBSDEs) in a more general framework over finite or infinite time horizon, corresponding to the pricing problem for a type of real option. We prove that the equation can be solved uniquely in <i>L</i>^<i>p</i>(1 &lt; <i>p</i> ≤ 2)-space, when the generators are uniformly continuous but each component taking values independently. Furthermore, if the generator of this equation fulfills the infinite time version of Lipschitzian continuity, we can also conclude that the solution to the oblique RBSDE exists and is unique, despite the fact that the values of some generator components may affect one another.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}