数学最新文献

{"title":"A remark on the formulation given in “A note on the lifted Miller-Tucker-Zemlin subtour elimination constraints for routing problems with time windows”","authors":"İmdat Kara,&nbsp;Gözde Önder Uzun","doi":"10.1016/j.disopt.2025.100888","DOIUrl":"10.1016/j.disopt.2025.100888","url":null,"abstract":"<div><div>In this paper, we show that, the formulation given in a recent paper [1] for the travelling salesman problem with time windows (TSPTW), may not find the optimal solution and then we recommend to add a new constraint to the model.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"56 ","pages":"Article 100888"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748273","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":"Feller generators with singular drifts in the critical range","authors":"D. Kinzebulatov ,&nbsp;Yu.A. Semënov","doi":"10.1016/j.jde.2025.113262","DOIUrl":"10.1016/j.jde.2025.113262","url":null,"abstract":"<div><div>We consider diffusion operator <span><math><mo>−</mo><mi>Δ</mi><mo>+</mo><mi>b</mi><mo>⋅</mo><mi>∇</mi></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, with drift <em>b</em> in a large class of locally unbounded vector fields that can have critical-order singularities. Covering the entire range of admissible magnitudes of singularities of <em>b</em>, we construct a strongly continuous Feller semigroup on the space of continuous functions vanishing at infinity, thus completing a number of results on well-posedness of SDEs with singular drifts. Our approach uses De Giorgi's method ran in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> for <em>p</em> sufficiently large, hence the gain in the assumptions on singular drift.</div><div>For the critical borderline value of the magnitude of singularities of <em>b</em>, we construct a strongly continuous semigroup in a “critical” Orlicz space on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> whose topology is stronger than the topology of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> for any <span><math><mn>2</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span> but is slightly weaker than that of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"433 ","pages":"Article 113262"},"PeriodicalIF":2.4,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747349","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":"Octonionic wavelet transform and uncertainly principle","authors":"Guangbin Ren,&nbsp;Xin Zhao","doi":"10.1016/j.amc.2025.129449","DOIUrl":"10.1016/j.amc.2025.129449","url":null,"abstract":"<div><div>This article centers around the octonion wavelet transform, exploring its transformation function <span><math><msup><mrow><mi>ψ</mi></mrow><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>S</mi></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo></math></span> derived from the admissible octonionic mother wavelet <em>ψ</em>, incorporating translation, rotation, and dilation components. We establish the inverse transform and the Plancherel formula, unveiling the inner product relationship of transformed functions. The Uncertainty Principle for the octonion wavelet transform reveals inherent bounds in wavelet analysis within the octonionic framework. However, it is essential to note that these discoveries are specific to the alternative properties of octonions and cannot be extended to general Cayley-Dickson algebras, where the sedenion wavelet transform lacks the isometry property observed in the octonionic setting.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129449"},"PeriodicalIF":3.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747354","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":"Univariate interpolation for a class of L-splines with adjoint natural end conditions","authors":"Aurelian Bejancu,&nbsp;Mohamed Dekhil","doi":"10.1016/j.amc.2025.129417","DOIUrl":"10.1016/j.amc.2025.129417","url":null,"abstract":"<div><div>For <span><math><mn>0</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mi>β</mi></math></span>, let <span><math><mi>L</mi><mo>=</mo><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, the Euler operator of the quadratic functional<span><span><span><math><munder><mo>∫</mo><mrow><mi>R</mi></mrow></munder><mrow><mo>{</mo><mo>|</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>(</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>|</mo><mi>D</mi><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>|</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>}</mo></mrow><mi>d</mi><mi>t</mi><mo>,</mo></math></span></span></span> where <em>D</em> is the first derivative operator. Given arbitrary values to be interpolated at a finite knot-set, we prove the existence of a unique <em>L</em>-spline interpolant from the natural space of functions <em>f</em>, for which the functional is finite. The natural <em>L</em>-spline interpolant satisfies adjoint differential conditions outside and at the end points of the interval spanned by the knot-set, and it is in fact the unique minimizer of the functional, subject to the interpolation conditions. This extends the approach by Bejancu (2011) for <span><math><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>=</mo><mi>β</mi></math></span>, corresponding to Sobolev spline (or Matérn kernel) interpolation. For <span><math><mn>0</mn><mo>=</mo><mi>α</mi><mo>&lt;</mo><mi>β</mi></math></span>, which is the special case of tension splines, our natural <em>L</em>-spline interpolant with adjoint end conditions can be identified as an “<span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>s</mi></mrow></msup></math></span>-spline interpolant in <span><math><mi>R</mi></math></span>” (for <span><math><mi>m</mi><mo>=</mo><mi>l</mi><mo>=</mo><mn>1</mn></math></span>, <span><math><mi>s</mi><mo>=</mo><mn>0</mn></math></span>), previously studied by Le Méhauté and Bouhamidi (1992) via reproducing kernel theory. Our <em>L</em>-spline error analysis, confirmed by numerical tests, is improving on previous convergence results for such tension splines.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129417"},"PeriodicalIF":3.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747273","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":"Graph convolutional network for structural equivalent key nodes identification in complex networks","authors":"Asmita Patel,&nbsp;Buddha Singh","doi":"10.1016/j.chaos.2025.116376","DOIUrl":"10.1016/j.chaos.2025.116376","url":null,"abstract":"<div><div>Identifying key influential nodes in complex networks is crucial for applications such as social network analysis, epidemiology, and recommendation systems. This paper proposes SE_GCN (Structural Equivalence with Graph Convolutional Network), a method that combines structural equivalence with Graph Convolutional Networks (GCNs) to identify key nodes in complex networks. SE_GCN leverages structural similarities among nodes at various hop distances to construct a comprehensive feature matrix, which is directly used for node embedding. GCNs are employed to process this feature matrix, learning effective representations of nodes within the network. The fully connected layer of SE_GCN computes the embedded score of each node, and a sigmoid function predicts the influential probabilities of nodes. The performance of SE_GCN is evaluated by comparing it with the Susceptible-Infected-Recovered (SIR) epidemiological model, Kendall's tau correlation, and Jaccard similarity. The proposed method is assessed using baseline methods in terms of infection rate, seed set size, correlation coefficient, and similarity index across several synthetic and real-world networks. The results demonstrate that SE_GCN outperforms existing methods, highlighting its effectiveness and robustness in identifying influential nodes.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116376"},"PeriodicalIF":5.3,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746964","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":"General Minimum Lower-order Confounding Split-plot Designs with Important Subplot Factors","authors":"Tao Sun,&nbsp;Sheng-li Zhao","doi":"10.1007/s10255-024-1027-5","DOIUrl":"10.1007/s10255-024-1027-5","url":null,"abstract":"<div><p>In this paper, we consider the regular <i>s</i>-level fractional factorial split-plot (FFSP) designs when the subplot (SP) factors are more important. The idea of general minimum lower-order confounding criterion is applied to such designs, and the general minimum lower-order confounding criterion of type SP (SP-GMC) is proposed. Using a finite projective geometric formulation, we derive explicit formulae connecting the key terms for the criterion with the complementary set. These results are applied to choose optimal FFSP designs under the SP-GMC criterion. Some two- and three-level SP-GMC FFSP designs are constructed.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"441 - 455"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749124","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":"Blow up, Growth and Decay of Solutions for Class of a Coupled Nonlinear Viscoelastic Kirchhoff Equations with Variable Exponents and Fractional Boundary Conditions","authors":"Abdelbaki Choucha,&nbsp;Salah Boulaaras,&nbsp;Djamel Ouchenane,&nbsp;Rashid Jan","doi":"10.1007/s10255-024-1150-3","DOIUrl":"10.1007/s10255-024-1150-3","url":null,"abstract":"<div><p>We examine a quasilinear system of viscoelastic equations in this study that have fractional boundary conditions, dispersion, source, and variable-exponents. We discovered that the solution of the system is global and constrained under the right assumptions about the relaxation functions and initial conditions. After that, it is demonstrated that the blow-up has negative initial energy. Subsequently, the growth of solutions is demonstrated with positive initial energy, and the general decay result in the absence of the source term is achieved by using an integral inequality due to Komornik.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"344 - 374"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749128","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":"Low-rank exponential integrators for stiff differential Riccati equations","authors":"Hao Chen,&nbsp;Alfio Borzì","doi":"10.1007/s10444-025-10228-w","DOIUrl":"10.1007/s10444-025-10228-w","url":null,"abstract":"<div><p>Exponential integrators are an efficient alternative to implicit schemes for the time integration of stiff system of differential equations. In this paper, low-rank exponential integrators of orders one and two for stiff differential Riccati equations are proposed and investigated. The error estimates of the proposed schemes are established. The proposed approach allows to overcome the main difficulties that lay in the interplay of time integration and low-rank approximation in the numerical schemes, which is uncommon in standard discretization of differential equations. Results of numerical experiments demonstrate the validity of the convergence analysis and show the performance of the proposed low-rank approximations with different settings.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"51 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749225","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":"Inverse Scattering Transform and Multi-soliton Solutions for the Sextic Nonlinear Schrödinger Equation","authors":"Xin Wu,&nbsp;Shou-fu Tian,&nbsp;Jin-Jie Yang","doi":"10.1007/s10255-025-0004-y","DOIUrl":"10.1007/s10255-025-0004-y","url":null,"abstract":"<div><p>In this work, we consider the inverse scattering transform and multi-soliton solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectral problem are derived directly, and the scattering data with <i>t</i> = 0 are obtained accordingly to analyze the symmetry and other related properties of the Jost functions. Then we make use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basis of that, the multi-soliton solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could enrich the nonlinear phenomena of the sextic nonlinear Schrödinger equation.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"536 - 555"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749085","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":"Ramsey and Gallai-Ramsey Numbers of Cycles and Books","authors":"Mei-qin Wei,&nbsp;Ya-ping Mao,&nbsp;Ingo Schiermeyer,&nbsp;Zhao Wang","doi":"10.1007/s10255-025-0009-6","DOIUrl":"10.1007/s10255-025-0009-6","url":null,"abstract":"<div><p>Given two non-empty graphs <i>G, H</i> and a positive integer <i>k</i>, the Gallai-Ramsey number gr_<i>k</i>(<i>G</i>: <i>H</i>) is defined as the minimum integer <i>N</i> such that for all <i>n</i> ≥ <i>N</i>, every exact <i>k</i>-edge-coloring of <i>K</i>_<i>n</i> contains either a rainbow copy of <i>G</i> or a monochromatic copy of <i>H</i>. Denote gr_<i>k</i>′(<i>G</i>: <i>H</i>) as the minimum integer <i>N</i> such that for all <i>n</i> ≥ <i>N</i>, every edge-coloring of <i>K</i>_<i>n</i> using at most <i>k</i> colors contains either a rainbow copy of <i>G</i> or a monochromatic copy of <i>H</i>. In this paper, we get some exact values or bounds for gr_<i>k</i>(<i>P</i>₅: <i>H</i>) and gr_<i>k</i>′(<i>P</i>₅: <i>H</i>), where <i>H</i> is a cycle or a book graph. In addition, our results support a conjecture of Li, Besse, Magnant, Wang and Watts in 2020.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"425 - 440"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749086","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}