数学最新文献

{"title":"CIR bridge for modeling of fish migration on sub-hourly scale","authors":"Hidekazu Yoshioka","doi":"10.1016/j.chaos.2025.116874","DOIUrl":"10.1016/j.chaos.2025.116874","url":null,"abstract":"<div><div>Bridges, which are stochastic processes with pinned initial and terminal conditions, have recently been applied to various problems. We show that a bridge based on the Cox–Ingersoll–Ross process, called a CIR bridge in this paper, reasonably models the intraday number of migrating fish at an observation point in a river. The studied fish migrates between sunrise and sunset each day, which are considered the initial and terminal times, respectively. The CIR bridge is well-defined as a unique pathwise continuous solution to a stochastic differential equation with unbounded drift and diffusion coefficients and potentially represents the on–off intermittency of the fish count data. Our bridge is theoretically novel in that it admits closed-form time-dependent averages and variances, with which the model parameters can be identified efficiently, and is computable by a recently-developed one-step numerical method. The CIR bridge is applied to the sub-hourly migration data of the diadromous fish <em>Plecoglossus altivelis altivelis</em> in the Nagara River, Japan, from February to June.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116874"},"PeriodicalIF":5.3,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713715","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":"Formulae and transformations for simplicial tensorial finite elements via polytopal templates","authors":"Adam Sky ,&nbsp;Michael Neunteufel ,&nbsp;Jack S. Hale ,&nbsp;Andreas Zilian","doi":"10.1016/j.camwa.2025.07.028","DOIUrl":"10.1016/j.camwa.2025.07.028","url":null,"abstract":"<div><div>We introduce a unified method for constructing the basis functions of a wide variety of partially continuous tensor-valued finite elements on simplices using polytopal templates. These finite element spaces are essential for achieving well-posed discretisations of mixed formulations of partial differential equations that involve tensor-valued functions, such as the Hellinger–Reissner formulation of linear elasticity. In our proposed polytopal template method, the basis functions are constructed from template tensors associated with the geometric polytopes (vertices, edges, faces etc.) of the reference simplex and any scalar-valued <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-conforming finite element space. From this starting point we can construct the Regge, Hellan–Herrmann–Johnson, Pechstein–Schöberl, Hu–Zhang, Hu–Ma–Sun and Gopalakrishnan–Lederer–Schöberl elements. Because the Hu–Zhang element and the Hu–Ma–Sun element cannot be mapped from the reference simplex to a physical simplex via standard double Piola mappings, we also demonstrate that the polytopal template tensors can be used to define a consistent mapping from a reference simplex even to a non-affine simplex in the physical mesh. Finally, we discuss the implications of element regularity with two numerical examples for the Reissner–Mindlin plate problem.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 322-348"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713999","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":"About the infinite windy firebreak location problem","authors":"Marc Demange ,&nbsp;Alessia Di Fonso ,&nbsp;Gabriele Di Stefano ,&nbsp;Pierpaolo Vittorini","doi":"10.1016/j.dam.2025.07.028","DOIUrl":"10.1016/j.dam.2025.07.028","url":null,"abstract":"<div><div>The severity of wildfires can be mitigated using preventive measures like the construction of firebreaks, which are strips of land from which the vegetation is completely removed. In this paper, we model the problem of wildfire containment as an optimization problem on infinite graphs called <span>Infinite Windy Firebreak Location</span>. A land of unknown size is modeled as an infinite undirected graph in which the vertices correspond to areas subject to fire and edges represent fire propagation from one area to another. A firebreak construction is modeled as removing the edge between two vertices. The number of firebreaks that can be installed depends on budget constraints. We assume that a fire ignites in a subset of vertices and propagates to the neighbors. The goal is to select a subset of edges to remove in order to contain the fire and avoid burning an infinite part of the graph. We prove that <span>Infinite Windy Firebreak Location</span> is coNP-complete in restricted cases, and we address some polynomial cases. We show that <span>Infinite Windy Firebreak Location</span> polynomially reduces to <span>Min Cut</span> for certain classes of graphs like infinite grid graphs and polyomino-grids.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 280-293"},"PeriodicalIF":1.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714080","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":"Existence and Orbital Stability of Standing-Wave Solutions of the Nonlinear Logarithmic Schrödinger Equation On a Tadpole Graph","authors":"Jaime Angulo Pava,&nbsp;Andrés Gerardo Pérez Yépez","doi":"10.1111/sapm.70085","DOIUrl":"https://doi.org/10.1111/sapm.70085","url":null,"abstract":"<p>This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS-log) on a tadpole graph, namely, a graph consisting of a circle with a half-line attached at a single vertex. By considering Neumann–Kirchhoff boundary conditions at the junction, we show the existence and the orbital stability of standing wave solutions with a profile determined by a positive single-lobe state. Via a splitting-eigenvalue method, we identify the Morse index and the nullity index of a specific linearized operator around a positive single-lobe state. To our knowledge, the results contained in this paper are the first to study the (NLS-log) on tadpole graphs. In particular, our approach has the prospect of being extended to study stability properties of other bound states for the (NLS-log) on a tadpole graph or other non-compact metric graph such as a looping-edge graphs.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermocapillary ultrathin self-rewetting film flows down a rotating fibre","authors":"Souradip Chattopadhyay","doi":"10.1016/j.physd.2025.134843","DOIUrl":"10.1016/j.physd.2025.134843","url":null,"abstract":"<div><div>This study investigates the influence of thermocapillarity on the dynamics and nonlinear stability of an ultrathin self-rewetting film flowing down a uniformly heated rotating vertical fibre. To capture the combined effects of intermolecular forces (van der Waals attraction) and centrifugal forces (due to rotation), a thin-film evolution equation is derived, assuming the film thickness is much smaller than the fibre radius. Linear stability analysis shows that the van der Waals attraction and rotation always enhance instability, whether acting alone or together. The impact of thermocapillarity in the presence of both van der Waals attraction and rotation on absolute/convective instability is also discussed. When <span><math><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>&lt;</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, where <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup></math></span> is the interfacial temperature and <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is the temperature at which surface tension is minimum, absolute instability occurs at a lower Marangoni number compared to the case where van der Waals attraction and rotation are absent. When <span><math><mrow><msup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>&gt;</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, the convective instability region expands with a higher Marangoni number, even when van der Waals attraction and rotation are present. A weakly nonlinear analysis using the method of multiple scales is conducted to study the bifurcation behavior of the nonlinear evolution equation. The results indicate the existence of both subcritical and supercritical regimes and demonstrate how thermocapillarity, combined with rotation and van der Waals forces, influences the shift of the bifurcation point. Finally, numerical simulations of the nonlinear evolution equation are performed for various flow parameters. These results explain how rotation, thermal effects, and intermolecular forces influence the flow dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134843"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724586","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":"A note on obtaining bipartite radio graceful graphs of arbitrarily large radio numbers with radio graceful complements","authors":"Ushnish Sarkar","doi":"10.1016/j.dam.2025.07.012","DOIUrl":"10.1016/j.dam.2025.07.012","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Motivated by the frequency assignment problem (FAP), a radio coloring of a graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is an assignment &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of non-negative integers to the vertices of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; satisfying the condition &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mtext&gt;diameter of&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the distance between any two vertices &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of the graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The span of a radio coloring of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is the difference of the maximum and minimum non-negative integers used as colors. The minimum span of a radio coloring of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is referred as the radio number of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Any radio coloring with the minimum span is referred as an optimal radio coloring of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. If an optimal radio coloring of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is a bijection from &lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, then the graph is referred as radio graceful. In this article, using a recursive construction, we have shown that for each positive integer &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, there exists a bipartite graph &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; vertices such that both &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and its complement &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; are radio graceful graphs. In the process, we show that each such &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; contain a Hamiltonian path.&lt;/div&gt;&lt;div&gt;Note that our construction obtains radio graceful graphs of arbitrarily large radio numbers without going for big cliques. This has an interesting similarity with the motivation behind the Mycielski’s construction which ensures the exis","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"377 ","pages":"Pages 350-355"},"PeriodicalIF":1.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144712954","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":"Numerical analysis of a discontinuous Galerkin method for time-fractional Navier-Stokes-Fokker-Planck equations with weakly singular solutions","authors":"Dong Liu ,&nbsp;Weihua Deng","doi":"10.1016/j.camwa.2025.07.031","DOIUrl":"10.1016/j.camwa.2025.07.031","url":null,"abstract":"<div><div>In this paper, a class of time-fractional Navier-Stokes-Fokker-Planck equations (TF-NSFPEs) describing position of particles with anomalous diffusion in viscous incompressible fluids are proposed. We develop the symmetric interior penalty discontinuous Galerkin (IPDG) method for TF-NSFPEs. The <em>L</em>1 method in the time on graded mesh is used for the reason that the solution of the time fractional Fokker-Planck equation (TFFPE) usually has a weak singularity near the initial time. The stability and the optimal error estimates of the IPDG semi-discrete scheme are proved by using the discrete fractional Grönwall inequality. Further, based on these results, the fully discrete optimal error estimates are obtained. Finally, some numerical experiments are performed to justify the effectiveness of the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 280-295"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713797","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":"Some novel minimax results for perfect matchings of polyomino graphs","authors":"Chunhu Sun ,&nbsp;Heping Zhang","doi":"10.1016/j.dam.2025.07.030","DOIUrl":"10.1016/j.dam.2025.07.030","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a graph with a perfect matching <span><math><mi>M</mi></math></span>. The forcing number of <span><math><mi>M</mi></math></span> in <span><math><mi>G</mi></math></span>, denoted by <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span>, is the minimal size of an edge subset of <span><math><mi>M</mi></math></span> that are contained in no other perfect matchings of <span><math><mi>G</mi></math></span>, and the anti-forcing number of <span><math><mi>M</mi></math></span> in <span><math><mi>G</mi></math></span>, denoted by <span><math><mrow><mi>a</mi><mi>f</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span>, is the minimal size of an edge subset of <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> whose deletion results in a subgraph with a unique perfect matching <span><math><mi>M</mi></math></span>. For a polyomino graph <span><math><mi>P</mi></math></span>, Zhou and Zhang (2016) established a minimax result: For every perfect matching <span><math><mi>M</mi></math></span> of <span><math><mi>P</mi></math></span> with the maximum forcing number or minus one, <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> is equal to the maximum number of disjoint <span><math><mi>M</mi></math></span>-alternating squares in <span><math><mi>P</mi></math></span>. In this paper, we show that for every perfect matching <span><math><mi>M</mi></math></span> of a polyomino graph <span><math><mi>P</mi></math></span> which contains no 3 × 3 chessboard as a nice subgraph, <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> is equal to the maximum number of disjoint <span><math><mi>M</mi></math></span>-alternating squares in <span><math><mi>P</mi></math></span>. Further we show that for every perfect matching <span><math><mi>M</mi></math></span> of <span><math><mi>P</mi></math></span>, <span><math><mrow><mi>a</mi><mi>f</mi><mrow><mo>(</mo><mi>P</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> always equals the number of <span><math><mi>M</mi></math></span>-alternating squares of <span><math><mi>P</mi></math></span> if and only if <span><math><mi>P</mi></math></span> has no 1 × 3 chessboard as a nice subgraph.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 270-279"},"PeriodicalIF":1.0,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714079","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":"Robust parameter estimation for rational ordinary differential equations","authors":"Oren Bassik ,&nbsp;Yosef Berman ,&nbsp;Soo Go ,&nbsp;Hoon Hong ,&nbsp;Ilia Ilmer ,&nbsp;Alexey Ovchinnikov ,&nbsp;Chris Rackauckas ,&nbsp;Pedro Soto ,&nbsp;Chee Yap","doi":"10.1016/j.amc.2025.129638","DOIUrl":"10.1016/j.amc.2025.129638","url":null,"abstract":"<div><div>We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a loop, the corresponding outputs are computed by solving the ODE numerically, followed by computing the error from the given time series data. If the error is small, the loop terminates and the parameter values are returned. Otherwise, heuristics/theories are used to possibly improve the guess and continue the loop. These approaches tend to be non-robust in the sense that their accuracy often depends on the search interval and the true parameter values; furthermore, they cannot handle cases where the parameters are only locally identifiable.</div><div>In this paper, we propose a new approach, which does not suffer from the above non-robustness. In particular, it does not require making good initial guesses for the parameter values or specifying search intervals. Instead, it uses differential algebra, rational function interpolation of the data, and multivariate polynomial system solving. We also compare the performance of the resulting software with several other estimation software packages.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"509 ","pages":"Article 129638"},"PeriodicalIF":3.5,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714428","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":"The Riemann solutions of the Chaplygin Euler equations with discontinuity terms: The disappearance and generation of a delta shock wave","authors":"Zhijian Wei,&nbsp;Lihui Guo","doi":"10.1016/j.cnsns.2025.109170","DOIUrl":"10.1016/j.cnsns.2025.109170","url":null,"abstract":"<div><div>In this paper, the Riemann problems for Euler equations with the Chaplygin gas under two different discontinuity source terms are considered in detail. Four kinds of Riemann solutions are constructed in fully explicit forms by the contact discontinuity or the delta shock wave. Different from previous studies with continuous source terms, some interesting nonlinear phenomena are found. For instance, the delta shock wave disappears completely and splits into two contact discontinuities in finite time.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109170"},"PeriodicalIF":3.8,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723772","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}