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":"Analysis of Subdifferentials of Marginal and Performance Functions","authors":"Duong Thi Viet An,&nbsp;Jean-Paul Penot","doi":"10.1007/s00245-025-10251-9","DOIUrl":"10.1007/s00245-025-10251-9","url":null,"abstract":"<div><p>We study generalized derivatives of value functions for optimization problems depending on a parameter <i>w</i>. Interpretations of the results obtained with these substitutes to derivatives are known to be important. We endeavour to answer the question: can one obtain these results without knowing the nature of these substitutes and their constructions? Is there a means to obtain them in a unified way?</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761693","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":"Dynamics analysis and predefined-time sliding mode synchronization of multi-scroll systems based on a single memristor model","authors":"Shaohui Yan,&nbsp;Xinyu Wu,&nbsp;Jiawei Jiang","doi":"10.1016/j.chaos.2025.116337","DOIUrl":"10.1016/j.chaos.2025.116337","url":null,"abstract":"<div><div>To overcome the limitations of conventional designs for memristive multi-scroll chaotic systems, this paper introduces a novel memristor that relies solely on a single memristor function and a single state variable function to generate both odd and even numbers of double-scroll attractors. This design not only simplifies the memristor structure but also offers a new approach to constructing multi-scroll chaotic systems. The proposed memristor is integrate into a modified Sprott-C system to develop the one-dimensional memristive multi-scroll Sprott-C systems (1D-MMSCS), two-dimensional memristive multi-scroll Sprott-C systems (2D-MMSCS), and the three-dimensional memristive multi-scroll Sprott-C systems (3D-MMSCS). The complex dynamics of these memristive multi-scroll systems are analyzed using equilibrium points, Poincaré maps, bifurcation diagrams, and Lyapunov exponents. Interestingly, the constructed MMSCS exhibits extreme multi-stability, indicating its high sensitivity to initial conditions and enhanced unpredictability. To verify the practical feasibility of the system, it is developed a digital hardware platform based on a Field-Programmable Gate Array (FPGA) and successfully implemented both the 1D-MMSCS and 2D-MMSCS. Finally, leveraging Lyapunov stability theory and predefined-time stability theory, a novel predefined-time sliding mode control scheme (PTSMS) is proposed. This scheme is applied to achieve synchronization in the more complex 3D-MMSCS. Simulation results confirm that the proposed method ensures rapid synchronization and exhibits strong robustness against internal uncertainties and external disturbances.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116337"},"PeriodicalIF":5.3,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759619","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":"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":"The Impact of T-cell Exhaustion Dynamics on Tumour-Immune Interactions and Tumour Growth.","authors":"Nicholas Lai, Alexis Farman, Helen M Byrne","doi":"10.1007/s11538-025-01433-1","DOIUrl":"https://doi.org/10.1007/s11538-025-01433-1","url":null,"abstract":"<p><p>Tumours evade immune surveillance through a number of different immunosuppressive mechanisms. One such mechanism causes cytotoxic T-cells, a major driving force of the immune system, to differentiate to a state of 'exhaustion', rendering them less effective at killing tumour cells. We present a structured mathematical model that focuses on T-cell exhaustion and its effect on tumour growth. We compartmentalise cytotoxic T-cells into discrete subgroups based on their exhaustion level, which affects their ability to kill tumour cells. We show that the model reduces to a simpler system of ordinary differential equations (ODEs) that describes the time evolution of the total number of T-cells, their mean exhaustion level and the total number of tumour cells. Numerical simulations of the model equations reveal how the exhaustion distribution of T-cells changes over time and how it influences the tumour's growth dynamics. Complementary bifurcation analysis shows how altering key parameters significantly reduces the tumour burden, highlighting exhaustion as a promising target for immunotherapy. Finally, we derive a continuum approximation of the discrete ODE model, which admits analytical solutions that provide complementary insight into T-cell exhaustion dynamics and their effect on tumour growth.</p>","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 5","pages":"61"},"PeriodicalIF":2.0,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143762953","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}