数学最新文献_第6页

On proper hamiltonicity and proper (even) pancyclicity of arc-colored complete (balanced bipartite) digraphs

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.disc.2025.114507

Mengyu Duan , Zhiwei Guo , Binlong Li , Shenggui Zhang

引用次数: 0

Bour's theorem for helicoidal surfaces with singularities

IF 0.6 4区数学

Differential Geometry and its Applications Pub Date : 2025-04-03 DOI: 10.1016/j.difgeo.2025.102248

Yuki Hattori , Atsufumi Honda , Tatsuya Morimoto

引用次数: 0

Hypergraph p-Laplacian regularization on point clouds for data interpolation

IF 1.3 2区数学

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-04-03 DOI: 10.1016/j.na.2025.113807

Kehan Shi , Martin Burger

{"title":"Hypergraph p-Laplacian regularization on point clouds for data interpolation","authors":"Kehan Shi , Martin Burger","doi":"10.1016/j.na.2025.113807","DOIUrl":"10.1016/j.na.2025.113807","url":null,"abstract":"<div><div>As a generalization of graphs, hypergraphs are widely used to model higher-order relations in data. This paper explores the benefit of the hypergraph structure for the interpolation of point cloud data that contain no explicit structural information. We define the <span><math><msub><mrow><mi>ɛ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-ball hypergraph and the <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-nearest neighbor hypergraph on a point cloud and study the <span><math><mi>p</mi></math></span>-Laplacian regularization on the hypergraphs. We prove the variational consistency between the hypergraph <span><math><mi>p</mi></math></span>-Laplacian regularization and the continuum <span><math><mi>p</mi></math></span>-Laplacian regularization in a semisupervised setting when the number of points <span><math><mi>n</mi></math></span> goes to infinity while the number of labeled points remains fixed. A key improvement compared to the graph case is that the results rely on weaker assumptions on the upper bound of <span><math><msub><mrow><mi>ɛ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. To solve the convex but non-differentiable large-scale optimization problem, we utilize the stochastic primal–dual hybrid gradient algorithm. Numerical experiments on data interpolation verify that the hypergraph <span><math><mi>p</mi></math></span>-Laplacian regularization outperforms the graph <span><math><mi>p</mi></math></span>-Laplacian regularization in preventing the development of spikes at the labeled points.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"257 ","pages":"Article 113807"},"PeriodicalIF":1.3,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759750","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}

引用次数: 0

A new and efficient meshfree method to solve partial differential equations: Application to three-dimensional transient heat transfer problems

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-03 DOI: 10.1016/j.camwa.2025.03.034

Daud Ali Abdoh

{"title":"A new and efficient meshfree method to solve partial differential equations: Application to three-dimensional transient heat transfer problems","authors":"Daud Ali Abdoh","doi":"10.1016/j.camwa.2025.03.034","DOIUrl":"10.1016/j.camwa.2025.03.034","url":null,"abstract":"<div><div>The paper presents the average radial particle method (ARPM), a new mesh-free technique for solving partial differential equations (PDEs). Here, we use the ARPM to solve 3D transient heat transfer problems. ARPM numerically approximates spatial derivatives by discretizing the domain by particles such that each particle is only affected by its direct neighbors. One feature that makes ARPM different is using a representative neighboring particle whose average variable value, like temperature, is used to approximate first and second spatial derivatives. ARPM has several advantages over other numerical methods. It is highly efficient, with a time requirement of only 0.6 µs per particle per step. It makes conducting rapid simulations with half a million particles in one minute possible. It is also distinct from other methods because it does not suffer from boundary or surface effects. Besides, the ARPM application is straightforward and could be easily integrated into software packages. Additionally, ARPM has lower convergence requirements for both time and space. The method's effectiveness is validated through five problems with different configurations and boundary conditions, demonstrating its accuracy and efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 181-202"},"PeriodicalIF":2.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759533","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}

引用次数: 0

Distributions of parity differences and biases in partitions into distinct parts

IF 1 3区数学

European Journal of Combinatorics Pub Date : 2025-04-03 DOI: 10.1016/j.ejc.2025.104157

Siu Hang Man

引用次数: 0

MFPC-PIML: Physics-informed machine learning based on multiscale Fourier feature phase compensation

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-03 DOI: 10.1016/j.camwa.2025.03.026

Naixing Feng , Shuiqing Zeng , Xianpeng Wang , Jinfeng Zhu , Atef Z. Elsherbeni

{"title":"MFPC-PIML: Physics-informed machine learning based on multiscale Fourier feature phase compensation","authors":"Naixing Feng , Shuiqing Zeng , Xianpeng Wang , Jinfeng Zhu , Atef Z. Elsherbeni","doi":"10.1016/j.camwa.2025.03.026","DOIUrl":"10.1016/j.camwa.2025.03.026","url":null,"abstract":"<div><div>The paradigm of physics-driven forward electromagnetic computation holds significance for enhancing the accuracy of network approximations while reducing the dependence on large-scale datasets. However, challenges arise during the training process when dealing with objective functions characterized by high-frequency and multi-scale features. These challenges frequently occur as difficulties in effectively minimizing loss or encountering conflicts among competing objectives. To overcome these obstacles, we carried out analysis leveraging the Neural Tangent Kernel (NTK) as our theoretical framework for analysis. Through this, we propose a novel architectural solution: a Multi-scale Fourier Feature Phase Compensation (MFPC) technology, according to Gaussian kernel mapping. This architecture leverages a Gaussian kernel to enhance the spectral representation of coordinate data, expanding the frequency domain coverage of Fourier feature mapping. Additionally, by compensating for phase loss inherent in conventional Fourier mapping, our approach effectively mitigates training difficulties, accelerates convergence, and significantly improves the model's accuracy in capturing high-frequency components. Our research comprises a range of challenging examples, including the high-frequency Poisson equation and the isotropic layered medium scattering model. Through these examples, we demonstrate the proficiency of our proposed method in accurately solving high-frequency, multi-scale Partial Differential Equation (PDE) equations. This highlights its potential not only in forward modeling but also in solving evolution and inverse problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 166-180"},"PeriodicalIF":2.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759532","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}

引用次数: 0

Impact of network heterogeneity on neuronal synchronization

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-03 DOI: 10.1016/j.cnsns.2025.108810

Javier Used , Jesús M. Seoane , Irina Bashkirtseva , Lev Ryashko , Miguel A.F. Sanjuán

{"title":"Impact of network heterogeneity on neuronal synchronization","authors":"Javier Used , Jesús M. Seoane , Irina Bashkirtseva , Lev Ryashko , Miguel A.F. Sanjuán","doi":"10.1016/j.cnsns.2025.108810","DOIUrl":"10.1016/j.cnsns.2025.108810","url":null,"abstract":"<div><div>Synchronization dynamics is a phenomenon of great interest in many fields of science. One of the most important fields is neuron dynamics, as synchronization in certain regions of the brain is related to some of the most common mental illnesses. To study the impact of the network heterogeneity in the neuronal synchronization, we analyze a small-world network of non-identical Chialvo neurons that are electrically coupled. We introduce a mismatch in one of the model parameters to introduce the heterogeneity of the network. Our study examines the effects of this parameter mismatch, the noise intensity in the stochastic model, and the coupling strength between neurons on synchronization and firing frequency. We have identified critical values of noise intensity, parameter mismatch, and rewiring probability that facilitate effective synchronization within the network. Furthermore, we observe that the balance between excitatory and inhibitory connections plays a crucial role in achieving global synchronization. Our findings offer insights into the mechanisms driving synchronization dynamics in complex neuron networks.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"146 ","pages":"Article 108810"},"PeriodicalIF":3.4,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769340","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}

引用次数: 0

Some pseudo-spectrum equalities of 2 × 2 unbounded upper triangular operator matrices and applications

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-03 DOI: 10.1016/j.jmaa.2025.129556

Deyu Wu , Xinran Liu

引用次数: 0

A remark on the formulation given in “A note on the lifted Miller-Tucker-Zemlin subtour elimination constraints for routing problems with time windows”

IF 0.9 4区数学

Discrete Optimization Pub Date : 2025-04-02 DOI: 10.1016/j.disopt.2025.100888

İmdat Kara, Gözde Önder Uzun

引用次数: 0

Feller generators with singular drifts in the critical range

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2025-04-02 DOI: 10.1016/j.jde.2025.113262

D. Kinzebulatov , Yu.A. Semënov

{"title":"Feller generators with singular drifts in the critical range","authors":"D. Kinzebulatov , 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><</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}

引用次数: 0