数学最新文献

{"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":"<div><div>Motivated by the frequency assignment problem (FAP), a radio coloring of a graph <span><math><mi>G</mi></math></span> is an assignment <span><math><mi>f</mi></math></span> of non-negative integers to the vertices of <span><math><mi>G</mi></math></span> satisfying the condition <span><math><mrow><mrow><mo>|</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>+</mo><mi>d</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow><mo>≥</mo><mtext>diameter of</mtext><mspace></mspace><mi>G</mi><mo>+</mo><mn>1</mn></mrow></math></span>, where <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> is the distance between any two vertices <span><math><mi>u</mi></math></span> and <span><math><mi>v</mi></math></span> of the graph <span><math><mi>G</mi></math></span>. The span of a radio coloring of <span><math><mi>G</mi></math></span> is the difference of the maximum and minimum non-negative integers used as colors. The minimum span of a radio coloring of <span><math><mi>G</mi></math></span> is referred as the radio number of <span><math><mi>G</mi></math></span>. Any radio coloring with the minimum span is referred as an optimal radio coloring of <span><math><mi>G</mi></math></span>. If an optimal radio coloring of <span><math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> is a bijection from <span><math><mi>V</mi></math></span> to <span><math><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mspace></mspace><mn>1</mn><mo>,</mo><mspace></mspace><mo>…</mo><mo>,</mo><mspace></mspace><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow><mo>−</mo><mn>1</mn><mo>}</mo></mrow></math></span>, then the graph is referred as radio graceful. In this article, using a recursive construction, we have shown that for each positive integer <span><math><mrow><mi>n</mi><mo>≥</mo><mn>9</mn></mrow></math></span>, there exists a bipartite graph <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> with <span><math><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math></span> vertices such that both <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and its complement <span><math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span> are radio graceful graphs. In the process, we show that each such <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and <span><math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span> contain a Hamiltonian path.</div><div>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":"A reduction of the “cycles plus K4's” problem","authors":"Aseem Dalal ,&nbsp;Jessica McDonald ,&nbsp;Songling Shan","doi":"10.1016/j.disc.2025.114696","DOIUrl":"10.1016/j.disc.2025.114696","url":null,"abstract":"<div><div>Let <em>H</em> be a 2-regular graph and let <em>G</em> be obtained from <em>H</em> by gluing in vertex-disjoint copies of <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>. The “cycles plus <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>'s” problem is to show that <em>G</em> is 4-colourable; this is a special case of the <em>Strong Colouring Conjecture</em>. In this paper we reduce the “cycles plus <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>'s” problem to a specific 3-colourability problem. In the 3-colourability problem, vertex-disjoint triangles are glued (in a limited way) onto a disjoint union of triangles and paths of length at most 12, and we ask for 3-colourability of the resulting graph.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114696"},"PeriodicalIF":0.7,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714244","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":"The distance spectral radius of k -uniform hypertrees with given number of vertices of maximum degree","authors":"Xiaoqi Liu, Haiying Shan, Chenghao Shen","doi":"10.1080/03081087.2025.2538148","DOIUrl":"https://doi.org/10.1080/03081087.2025.2538148","url":null,"abstract":"","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":"14 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144719629","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":"Corrigendum to “Stability of linear operators in locally convex cones” [Bull. Sci. Math. 191 (2024) 103380]","authors":"Iz-iddine EL-Fassi ,&nbsp;Abbas Najati","doi":"10.1016/j.bulsci.2025.103703","DOIUrl":"10.1016/j.bulsci.2025.103703","url":null,"abstract":"","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"204 ","pages":"Article 103703"},"PeriodicalIF":1.3,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713637","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":"The two-grid decoupled method for hybrid-dimensional fracture models based on the discontinuous Galerkin method","authors":"Shuangshuang Chen,&nbsp;Yuna Xu,&nbsp;Longchao Jin","doi":"10.1016/j.camwa.2025.07.029","DOIUrl":"10.1016/j.camwa.2025.07.029","url":null,"abstract":"<div><div>In this paper, we consider a kind of hybrid-dimensional fracture models, in which fractures are treated as <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-dimensional objects in a <em>n</em>-dimensional porous medium, and the interaction between fractures and surrounding domain is taken into account. For the model with one single fracture, the discontinuous Galerkin (DG) method is firstly proposed, and the optimal order error estimate in the discrete <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm for the pressure is derived. Moreover, a two-grid decoupled method is considered, which uses a coarse grid rough approximations of the interface variables to decouple the mixed domain problem on a fine grid, and the optimal error estimate is also analyzed. The proposed DG method and two-grid decoupled method are then extended to a model with complex intersecting fractures, as well as the corresponding theoretical analysis. Numerical examples with both one single fracture and intersecting fractures are all presented to verity the accuracy of the considered methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 296-321"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713795","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":"Interior C2 estimates for a class of sum Hessian equations","authors":"Changyu Ren,&nbsp;Ziyi Wang","doi":"10.1016/j.jde.2025.113631","DOIUrl":"10.1016/j.jde.2025.113631","url":null,"abstract":"<div><div>In this paper, we mainly study the interior <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> estimates for a class of sum Hessian equations. We establish the interior estimates and the Pogorelov type estimates for <span><math><mn>0</mn><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><mi>n</mi></math></span>. If <span><math><mi>k</mi><mo>=</mo><mi>n</mi></math></span>, we derive a weaker Pogorelov type estimates.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113631"},"PeriodicalIF":2.4,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713378","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":"A posteriori error estimates for the DD+L2 jumps method on the neutron diffusion equations","authors":"Patrick Ciarlet ,&nbsp;Minh Hieu Do ,&nbsp;Mario Gervais ,&nbsp;François Madiot","doi":"10.1016/j.camwa.2025.07.026","DOIUrl":"10.1016/j.camwa.2025.07.026","url":null,"abstract":"<div><div>We analyze <em>a posteriori</em> error estimates for the discretization of the neutron diffusion equations with a Domain Decomposition Method, the so-called DD+<span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> jumps method. We provide guaranteed and locally efficient estimators on a base block equation, the one-group neutron diffusion equation. Classically, one introduces a Lagrange multiplier to account for the jumps on the interface. This Lagrange multiplier is used for the reconstruction of the physical variables. Remarkably, no reconstruction of the Lagrange multiplier is needed to achieve the optimal <em>a posteriori</em> estimates.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 349-365"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713796","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}