数学最新文献

{"title":"Phase-field computation for 3D shell reconstruction with an energy-stable and uniquely solvable BDF2 method","authors":"Dongting Cai,&nbsp;Boyi Fu,&nbsp;Renjun Gao,&nbsp;Xiangjie Kong,&nbsp;Junxiang Yang","doi":"10.1016/j.camwa.2025.03.022","DOIUrl":"10.1016/j.camwa.2025.03.022","url":null,"abstract":"<div><div>Three-dimensional (3D) reconstruction from points cloud is an important technique in computer vision and manufacturing industry. The 3D volume consists of a set of voxels which preserves the characteristics of scattered points. In this paper, a 3D shell (narrow volume) reconstruction algorithm based on the Allen–Cahn (AC) phase field model is proposed, aiming to efficiently and accurately generate 3D reconstruction models from point cloud data. The algorithm uses a linearized backward differentiation formula (BDF2) for time advancement and adopts the finite difference method to perform spatial discretization, unconditional energy stability and second-order time accuracy can be achieved. The present method is not only suitable for 3D reconstruction of unordered data but also has the effect of adaptive denoising and surface smoothing. In addition, theoretical derivation proves the fully discrete energy stability. In numerical experiments, the complex geometric models, such as Asian dragon, owl, and turtle, will be reconstructed to validate the energy stability. The temporal accuracy is validated by the numerical reconstructions of a Costa surface and an Amremo statue. Later, we reconstruct the Stanford dragon, teapot, and Thai statue to further investigate the capability of the proposed method. Finally, we implement a comparison study using a 3D happy Buddha. The numerical results show that the algorithm still has good numerical stability and reconstruction accuracy at large time steps, and can significantly preserve the detailed structure of the model. This research provides an innovative solution and theoretical support for scientific computing and engineering applications in the field of 3D reconstruction.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 1-23"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738385","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 fast implicit difference scheme with nonuniform discretized grids for the time-fractional Black–Scholes model","authors":"Qi Xin ,&nbsp;Xian-Ming Gu ,&nbsp;Li-Bin Liu","doi":"10.1016/j.amc.2025.129441","DOIUrl":"10.1016/j.amc.2025.129441","url":null,"abstract":"<div><div>The solution of the time-fractional Black–Scholes (TFBS) equation often exhibits a weak singularity at initial time and possible non-physical oscillations in the computed solution due to the degeneracy of the BS differential operator. To address this issue, we combine a modified graded mesh and a piecewise uniform mesh for temporal and spatial discretizations, respectively. Then we use the fast approximation (rather than the direct approximation) of the <em>L</em>1 scheme for the Caputo derivative to establish an implicit difference method for the TFBS model. Our analysis shows the stability and convergence of the proposed scheme, as well as the <em>α</em>-nonrobust error bounds. Finally, numerical results are presented to show the effectiveness of the proposed method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129441"},"PeriodicalIF":3.5,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738706","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":"Improved black widow optimization algorithm for multi-objective hybrid flow shop batch-scheduling problem","authors":"Xiyang Liu, Fangjun Luan","doi":"10.1007/s10878-025-01270-x","DOIUrl":"https://doi.org/10.1007/s10878-025-01270-x","url":null,"abstract":"<p>Sustainable scheduling is getting more and more attention with economic globalization and sustainable manufacturing. However, fewer studies on the batch scheduling problem consider energy consumption. This paper conducts an investigation into the multi-objective hybrid flow shop batch-scheduling problem with the objectives of minimizing both the makespan and electrical energy consumption. The study aims to select the optimal scheduling solution for the problem by considering batch splitting for all products. In this paper, we propose an improved black widow optimization (IBWO) algorithm to study the problem, which incorporates procreation, cannibalism, and mutation behaviors to maintain the population’s diversity and stability. To achieve our objectives, we use the dynamic entropy weight topsis method to select individual spiders. Finally, we use the nature theorem construction method, which relies on the property theorem, to solve the Pareto solution set and derive the optimization scheme for the hybrid flow shop batch scheduling problem. We verify the effectiveness of the proposed IBWO on instances of varying sizes. When we keep all other factors and cases constant, we compare the IBWO to the NSGA2 algorithm and find that it converges faster for both goals and has lower goals than the NSGA2.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"34 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143745304","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":"Decoupled algorithms and analyses for an advection-reaction-diffusion model with stocking and harvesting","authors":"Mayesha Sharmim Tisha ,&nbsp;Md. Kamrujjaman ,&nbsp;Muhammad Mohebujjaman ,&nbsp;Taufiquar Khan","doi":"10.1016/j.camwa.2025.03.024","DOIUrl":"10.1016/j.camwa.2025.03.024","url":null,"abstract":"<div><div>We propose a time-dependent Advection Reaction Diffusion (ARD) <em>N</em>-species competition model to investigate the Stocking and Harvesting (SH) effect on population dynamics. For ongoing analysis, we explore the outcomes of a single species and competition between two competing species in a heterogeneous environment under no-flux boundary conditions, meaning no individual can cross the boundaries. We establish results concerning the existence, uniqueness, and positivity of the solutions. As a continuation, we propose, analyze, and test two novel fully discrete decoupled linearized algorithms for a nonlinearly coupled ARD <em>N</em>-species competition model with SH effort. The time-stepping algorithms are first and second order accurate in time and optimally accurate in space. Stability and optimal convergence theorems of the decoupled schemes are proved rigorously. We verify the predicted convergence rates of our analysis and the efficacy of the algorithms using numerical experiments and synthetic data for analytical test problems. We also study the effect of harvesting or stocking and diffusion parameters on the evolution of species population density numerically and observe the coexistence scenario subject to optimal stocking or harvesting.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 24-47"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738386","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":"Extinction and persistence of a stochastic HBV model","authors":"Xiangkui Zhao,&nbsp;Ting Li","doi":"10.1016/j.chaos.2025.116339","DOIUrl":"10.1016/j.chaos.2025.116339","url":null,"abstract":"<div><div>We propose a stochastic model of the Hepatitis B Virus (HBV) and investigate viral extinction, persistence, and average residence time. To predict whether HBV will persist in the long term, we construct a crucial stochastic threshold. The establishment of this threshold faces some challenges due to the coexistence of predation and competition mechanisms in the model. To overcome this challenge, we integrate the interactions between infected hepatocytes and free virions into a unified equation, defining the crucial stochastic threshold. Our study shows that increased noise stabilizes the model when it approaches the infection-free equilibrium, but causes instability when the model approaches the infected equilibrium. This finding provides important theoretical basis for predicting HBV transmission and formulating intervention strategies. In addition, we provide detailed numerical simulations to support our conclusions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116339"},"PeriodicalIF":5.3,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738967","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":"A semi-implicit second-order temporal scheme for solving the pressure head-based form of Richards' and advection-dispersion equations","authors":"Nour-Eddine Toutlini ,&nbsp;Abdelaziz Beljadid ,&nbsp;Azzeddine Soulaïmani","doi":"10.1016/j.camwa.2025.03.011","DOIUrl":"10.1016/j.camwa.2025.03.011","url":null,"abstract":"<div><div>In this study, a semi-implicit finite element method is proposed to solve the coupled system of infiltration and solute transport in porous media. The Richards equation is used to describe unsaturated flow, while the advection-dispersion equation (ADE) is used for modeling solute transport. The proposed approach is applied to linearize the system in time, avoiding iterative processes. A free parameter is introduced to ensure the stability of the scheme. Numerical tests are conducted to analyze the accuracy of the proposed method in comparison with three second-order iterative schemes. The proposed scheme based on the optimal free parameter is accurate and efficient since it offers a considerable gain in computational time compared to the other methods. For reliability and effectiveness evaluation of the developed semi-implicit scheme, four showcase scenarios are used. The first two numerical tests focus on modeling water flow in heterogeneous medium and transient flow in variably saturated zones. The last numerical tests are carried out to simulate the salt and nitrate transport through unsaturated porous media. The simulation results are compared with reference solutions and laboratory data, and demonstrate the effectiveness of the proposed scheme in simulating infiltration and solute transport in porous media.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 106-131"},"PeriodicalIF":2.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739687","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":"Simple tunable generator of neuron-like activity","authors":"Lev V. Takaishvili ,&nbsp;Vladimir I. Ponomarenko ,&nbsp;Ilya V. Sysoev","doi":"10.1016/j.chaos.2025.116316","DOIUrl":"10.1016/j.chaos.2025.116316","url":null,"abstract":"<div><div>This study aims to develop a new electronic realization of a neuron. We based our work on a previously constructed circuit and modified it to reduce the number of elements. All modeling was done using ngSPICE circuit simulator. For the new developed circuit current–voltage characteristics were constructed, then dependence of signal amplitude on resistance of potentiometer was measured. In this way, we found that oscillations arose as a result of Andronov–Hopf bifurcation like in the FitzHugh–Nagumo neuron. Various implementations of nonlinearity were considered and the dependence of the shape of the generated signal on the asymmetry of the nonlinear element was investigated. It is shown that with increasing asymmetry this signal becomes more similar to nonlinear spikes, and with decreasing asymmetry it approaches the signal of a strongly nonlinear van der Pol oscillator. The oscillation frequency is mainly determined by the resonant frequency of the circuit and weakly depends on asymmetry: the period slightly decreases with increasing asymmetry. As a result, we developed a new simplified electronic neuron of FitzHugh–Nagumo type simple for hardware realization and modification.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116316"},"PeriodicalIF":5.3,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734979","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":"M-shape, lump, homoclinic breather and other soliton interaction of the Landau-Ginzburg-Higgs model in nonlinear fiber optics","authors":"Abdullah ,&nbsp;Ghaus ur Rahman ,&nbsp;J.F. Gómez-Aguilar","doi":"10.1016/j.chaos.2025.116335","DOIUrl":"10.1016/j.chaos.2025.116335","url":null,"abstract":"<div><div>This study investigates the intricate dynamics of different types of solitons and their interactions within the framework of the Landau-Ginzburg-Higgs model as applied to nonlinear fiber optics. Employing the Hirota bilinear transformation technique, we derive a range of analytical soliton solutions, and demonstrating their rich and diverse behaviors. The proposed methodology provides a more comprehensive framework for analyzing transport processes by expanding these equations. M-shaped rational wave solutions with one kink, M-shaped rational waves with two kinks having bright and dark effects, periodic cross-kink with bright and dark waves, lump mixed-type waves, homoclinic breathers, and breather waves are among the various types of solitons. These many waveforms make it clear, soliton movement within optical fiber is extremely essential. They also offer valuable information that could influence soliton-based signal processing, optical communication systems, drug research, and other scientific fields. This extension of methodology aids in understanding the intricacy of soliton transport and identifying the intricate mechanisms. Additionally, by selecting various constant values, we create 3D and related contour plots to be aware of the physical interpretations of these solutions. Therefore, we get superior physical behaviors from these solutions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116335"},"PeriodicalIF":5.3,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734980","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":"High-rate discretely-modulated continuous-variable quantum key distribution using quantum machine learning","authors":"Qin Liao ,&nbsp;Zhuoying Fei ,&nbsp;Jieyu Liu ,&nbsp;Anqi Huang ,&nbsp;Lei Huang ,&nbsp;Yijun Wang","doi":"10.1016/j.chaos.2025.116331","DOIUrl":"10.1016/j.chaos.2025.116331","url":null,"abstract":"<div><div>Continuous-variable quantum key distribution (CVQKD) is one of the promising ways to ensure information security. In this paper, we propose a high-rate scheme for discretely-modulated (DM) CVQKD using quantum machine learning technologies, which divides the whole CVQKD system into three parts, i.e., the initialization part that is used for training and estimating quantum classifier, the prediction part that is used for generating highly correlated raw keys, and the data postprocessing part that generates the final secret key string shared by Alice and Bob. To this end, a low-complexity quantum <span><math><mi>k</mi></math></span>-nearest neighbor (Q<span><math><mi>k</mi></math></span>NN) classifier is designed for predicting the lossy discretely-modulated coherent states (DMCSs) at Bob’s side. The performance of the proposed Q<span><math><mi>k</mi></math></span>NN-based CVQKD especially in terms of machine learning metrics and complexity is analyzed, and its theoretical security is proved by using semi-definite program (SDP) method. Numerical simulation shows that the secret key rate of our proposed scheme is explicitly superior to that of the existing DM CVQKD protocols, and it can be further enhanced with the increase of modulation variance.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116331"},"PeriodicalIF":5.3,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738353","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":"Edge isoperimetric method: At least 2/3 of h-extra edge-connectivity of a kind of cube-based graphs concentrates on 2n−1","authors":"Mingzu Zhang ,&nbsp;Hongxi Liu ,&nbsp;Chia-Wei Lee ,&nbsp;Weihua Yang","doi":"10.1016/j.dam.2025.03.019","DOIUrl":"10.1016/j.dam.2025.03.019","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The edge isopermetric problem on hypercube &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&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;, proposed by Harper in 1964, is to find a vertex subset with cardinality &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&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;, such that the edge cut separating any vertex subset with cardinality &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; from its complement has minimum size. Since Harper, Lindsey, Bernstein and Hart solved the edge isoperimetric problem of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&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; by lexicographic order, the edge isoperimetric problem is intimately tied to many-to-many disjoint paths problem. The maximum cardinality of edge disjoint paths connecting any two disjoint connected subgraphs of order &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; in a connected graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; can be defined by the minimum modified edge-cut, called the &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-extra edge-connectivity of &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. It is the cardinality of the minimum set of edges in a connected graph &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, if such a set exists, whose deletion disconnects &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and leaves every remaining component with at least &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; vertices. The &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;-enhanced hypercubes &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are constructed by adding a matching between some pair copies of &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; dimensional subcubes &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&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;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&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;. The distribution of the values of the &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-extra edge-connectivity on a recursive graph is uneven and presents a concentration phenomenon. In this paper, we start with analysing the fractal properties of the optimal solution of the edge isoperimetric problem of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. And it is shown that although the members of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are not isomorphic to each other according to different &lt;span&gt;&lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&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;, when &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; approaches infinity, the &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-extra edge-connectivity of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;-enhanced hypercubes presents a concentration phenome","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"370 ","pages":"Pages 167-174"},"PeriodicalIF":1.0,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734923","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}