Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (1,121)

Search Parameters:
Keywords = matching theory

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
23 pages, 888 KB  
Article
Quantifying Urban Ecosystem Services for Community-Level Planning: A Machine Learning Framework for Service Quality and Residents’ Perceptions in Wuhan, China
by Fan Zhang, Yuqing Dong, Qikai Zhang, Yifang Luo and Aihua Han
Urban Sci. 2025, 9(11), 449; https://doi.org/10.3390/urbansci9110449 (registering DOI) - 30 Oct 2025
Abstract
Urban ecosystem services (ESs) are increasingly recognized as critical determinants of residents’ quality of life and well-being. This study develops a data-driven demand–supply matching framework to integrate ES concepts into community-level planning and service performance evaluation. Based on 312 resident surveys across 10 [...] Read more.
Urban ecosystem services (ESs) are increasingly recognized as critical determinants of residents’ quality of life and well-being. This study develops a data-driven demand–supply matching framework to integrate ES concepts into community-level planning and service performance evaluation. Based on 312 resident surveys across 10 communities in Wuhan, China, we identify the key environmental attributes shaping perceived service quality. A random forest (RF) algorithm is employed to assess the relative importance of environmental features, while a multinomial logit (Mlogit) model quantifies their specific effects. The results highlight that community autonomy, neighborhood relations, environmental awareness, and infrastructure—such as broadband networks and security systems—play pivotal roles in improving service quality. Although provisioning and regulating ESs, such as safety and infrastructure, are relatively well established, cultural services that promote social cohesion and civic participation remain under-supported. These findings uncover the heterogeneity of residents’ environmental expectations and provide actionable insights for incorporating ES-oriented thinking into community planning and fiscal decision-making. By bridging ecological theory with operational urban governance, this study contributes a replicable approach for advancing more inclusive and sustainable community development. Full article
Show Figures

Figure 1

18 pages, 2257 KB  
Article
What Do We Focus on? Investigating Chinese Public Preferences for CSR Initiatives in Professional Sports Clubs
by Chenxu Wang, Jiatong Song and Zhiwen Wang
Sustainability 2025, 17(21), 9648; https://doi.org/10.3390/su17219648 (registering DOI) - 30 Oct 2025
Abstract
Purpose: This study examines the Chinese public’s preferences for corporate social responsibility (CSR) measures implemented by professional sports clubs, with a focus on identifying priority dimensions and heterogeneity across demographic groups. Approach: A choice-based conjoint analysis was conducted with 1043 residents [...] Read more.
Purpose: This study examines the Chinese public’s preferences for corporate social responsibility (CSR) measures implemented by professional sports clubs, with a focus on identifying priority dimensions and heterogeneity across demographic groups. Approach: A choice-based conjoint analysis was conducted with 1043 residents across 22 Chinese cities hosting professional basketball or football clubs. Participants evaluated hypothetical CSR scenarios comprising six dimensions and 20 attribute levels. Cluster analysis was employed to analyze preference heterogeneity. Findings: Labor rights protection emerged as the most influential CSR dimension, ac-counting for 28.64% of the total importance. Subsequent dimensions, including Product/Service Quality (19.51%), Fair Sportsmanship (17.01%), Sports Development (14.07%), Economic Impact (12.73%), and Community Engagement (8.05%), also exerted substantial influence. Cluster analysis revealed five distinct preference segments: Labor Rights Prioritizers (24.5%), Performance-Driven Advocates (20.6%), Ethics-Focused Supporters (24.8%), Community-Embedded Participants (16.0%), and Economy-Boost Enthusiasts (15.1%). Notably, negative CSR practices (e.g., wage delays, match-fixing) significantly diminished public support, while proactive measures (e.g., employee development, community programs) enhanced preferences. Innovation: This study makes three incremental contributions compared with existing literature. First, it integrates both positive and negative CSR practices into a unified framework, whereas most prior studies examine only positive practices. Second, it expands CSR research beyond fan groups to include the broader public, thus enriching stakeholder theory applications in sports. Third, it adds empirical insights from developing countries to the academic community, thereby contextualizing CSR preferences within China’s unique institutional and cultural environment. Full article
Show Figures

Figure 1

20 pages, 856 KB  
Article
Career Calling and Professional Match Among Chinese Graduates: The Roles of Career Loyalty and Industry Income
by Ting Zhang, Huan Zhang, Guan Ren, Hongxi Ge and Ziqiang Zhang
Behav. Sci. 2025, 15(11), 1472; https://doi.org/10.3390/bs15111472 - 29 Oct 2025
Abstract
This study investigates the role of career calling in shaping Chinese graduates’ professional match, with a focus on the mediating role of career loyalty and the moderating effect of industry income. Drawing on Conservation of Resources (COR) theory and person–environment (P–E) fit theory, [...] Read more.
This study investigates the role of career calling in shaping Chinese graduates’ professional match, with a focus on the mediating role of career loyalty and the moderating effect of industry income. Drawing on Conservation of Resources (COR) theory and person–environment (P–E) fit theory, we developed a three-wave, multi-source design with 2025 graduates across diverse industries. The results reveal that career calling significantly enhances professional match, and this relationship is fully mediated by career loyalty. Moreover, industry income strengthens the positive effect of calling, suggesting that external rewards amplify internal motivation in achieving sustainable career outcomes. Theoretically, the study extends calling research into the graduate labor market and integrates contextual economic factors into the COR and P–E fit frameworks. Practically, the findings highlight the importance of cultivating career calling through higher education, organizational practices, and policy initiatives to improve workforce alignment and long-term career sustainability. Full article
Show Figures

Figure 1

17 pages, 15672 KB  
Article
Optimizing Parameters of Marine Hydrodynamic Models Based on AFS Theory and PCA
by Yangxin Zhang, Jiangmei Zhang, Xinghua Feng, Haolin Liu, Guowei Yang, Tuantuan Liu, Yongzhuo Liu and Jiaze Li
Water 2025, 17(21), 3089; https://doi.org/10.3390/w17213089 - 28 Oct 2025
Abstract
The parameter optimization of marine hydrodynamic models currently relies predominantly on expert empirical knowledge, but the quantitative indicators and weighting mechanisms for rapid calibration remain unclear due to inherent model uncertainties and complexities. This study addresses these challenges through expert questionnaires that collect [...] Read more.
The parameter optimization of marine hydrodynamic models currently relies predominantly on expert empirical knowledge, but the quantitative indicators and weighting mechanisms for rapid calibration remain unclear due to inherent model uncertainties and complexities. This study addresses these challenges through expert questionnaires that collect fuzzy evaluations of calibration criteria, developing an integrated methodology combining the theory of axiomatic fuzzy set (AFS) with principal component analysis (PCA). Numerical case studies quantify calibration indicator weights and assess critical parameter impacts, revealing that bathymetry and roughness coefficients predominantly govern simulation accuracy. Elevated roughness conditions demonstrate two regimes: (1) at 1–2 × baseline roughness, strong positive correlations (with a coefficient of determination R2 increased by up to 0.568 compared to baseline) confirm effective model-data matching for tidal levels/currents; (2) beyond 2 × baseline roughness, progressive correlation decay accompanies increasing coefficients, indicating amplified simulation–measurement discrepancies. Notably, under reduced roughness conditions, high accuracy persists during spring/mid-tide phases but significantly diminishes during neap tides, demonstrating enhanced roughness sensitivity in low-tidal energy regimes. Full article
(This article belongs to the Section Oceans and Coastal Zones)
Show Figures

Figure 1

12 pages, 318 KB  
Article
Sharp Unified Smoothness Theory for Cavalieri Estimation via Fourier Decay
by Francisco-Javier Soto
Axioms 2025, 14(11), 786; https://doi.org/10.3390/axioms14110786 - 26 Oct 2025
Viewed by 101
Abstract
Cavalieri estimation is a widely used technique in stereology (applied geometric sampling) for approximating the volume of a solid by sampling cross-sectional areas along a fixed axis. Classical theory shows that, under systematic equidistant sampling (the well-known Cavalieri estimator), the variance decay depends [...] Read more.
Cavalieri estimation is a widely used technique in stereology (applied geometric sampling) for approximating the volume of a solid by sampling cross-sectional areas along a fixed axis. Classical theory shows that, under systematic equidistant sampling (the well-known Cavalieri estimator), the variance decay depends on the smoothness of the area function, which is essentially measured by the number of continuous derivatives. This paper focuses on the natural assumptions under which the theory holds. We first obtain sharp and explicit variance rates: when the Fourier decay is of order s>1/2, the variance of the Cavalieri estimator decays as t2s with a constant independent of t. Building on this, we show that the smoothness condition expressed in terms of the algebraic Fourier decay subsumes both integer- and fractional-order frameworks used to date. Finally, we establish a matching converse showing that, under general assumptions, no broader smoothness framework extends the theory; that is, any algebraic variance decay implies the corresponding Fourier decay. Full article
(This article belongs to the Special Issue Numerical Analysis, Approximation Theory and Related Topics)
Show Figures

Figure 1

23 pages, 9048 KB  
Article
A Systematic Approach to Disability Employment: An Evolutionary Game Framework Involving Government, Employers, and Persons with Disabilities
by Zhaofa Sun, Qiaoshi Hu and Junhua Guo
Systems 2025, 13(11), 948; https://doi.org/10.3390/systems13110948 - 24 Oct 2025
Viewed by 230
Abstract
Against the backdrop of inclusive development and modernization of employment governance, the limitations of traditional approaches to promoting employment for persons with disabilities—such as information asymmetries and inefficient resource allocation—have become increasingly salient. Building a systematic promotion framework for disability employment has therefore [...] Read more.
Against the backdrop of inclusive development and modernization of employment governance, the limitations of traditional approaches to promoting employment for persons with disabilities—such as information asymmetries and inefficient resource allocation—have become increasingly salient. Building a systematic promotion framework for disability employment has therefore emerged as a critical agenda for advancing modern social governance. Drawing on bounded rationality and information asymmetry theories, this study develops a tripartite evolutionary game model encompassing government, employers, and persons with disabilities. By incorporating key elements such as initial intentions, skill matching, and policy signal transmission, the model analyzes the strategic choices and dynamic interactions among stakeholders. We conduct numerical simulations using delay differential equations (DDEs), perform stability and sensitivity analyses in MATLAB R2024b, and triangulate findings with a practice-based case from Shanghai. The results indicate that persons with disabilities exhibit the highest policy responsiveness within the employment ecosystem and act as the core driver of convergence toward desirable equilibria through four mechanisms: skill-matching effects, policy signal diffusion, perceived institutional fairness, and system-level synergy gains. Although employer subsidies and penalties directly target firms, they exert the strongest psychological incentive effects on persons with disabilities, revealing a “misaligned incentives” feature in policy signaling. Systemic synergy gains activate market network effects, facilitating a pivotal shift from “policy transfusion” to “market self-sustenance.” Based on these findings, we propose a diversified policy toolkit, enhanced policy signaling mechanisms, and innovations in concentrated employment models to support the modernization of disability employment governance. Full article
Show Figures

Figure 1

17 pages, 6416 KB  
Article
Novel High-Contrast Photoacoustic Imaging Method for Cancer Cell Monitoring Based on Dual-Wavelength Confocal Metalenses
by Zixue Chen, Ruihao Zhang, Hongbin Zhang, Bingqiang Zhang, Lei Qin, Jiansen Du, Tao Zhao and Bin Wang
Photonics 2025, 12(11), 1053; https://doi.org/10.3390/photonics12111053 - 24 Oct 2025
Viewed by 208
Abstract
This study proposes a high-contrast photoacoustic (PA) imaging methodology based on a dual-wavelength confocal metalens, designed to monitor the dissemination of cancer cells and to inform subsequent cancer treatment strategies. The metalens is composed of two metasurfaces that perform filtering and focusing functions, [...] Read more.
This study proposes a high-contrast photoacoustic (PA) imaging methodology based on a dual-wavelength confocal metalens, designed to monitor the dissemination of cancer cells and to inform subsequent cancer treatment strategies. The metalens is composed of two metasurfaces that perform filtering and focusing functions, effectively reducing the cross-talk between the two wavelengths of light in space and achieving a confocal effect. Furthermore, to minimize process complexity, a uniform material system of silicon dioxide (SiO2) and titanium dioxide (TiO2) is employed across the different metasurfaces of the metalens. The designed metalens has a radius of 25 µm and an operational focal length of 98.5 µm. The results confirm that this dual-metasurface design achieves high focusing efficiency alongside precise focusing capability, with the deviations of the actual focal lengths for both beams from the design values being within 1.5 µm. Additionally, this study developed a skin tissue model and simulated multi-wavelength photoacoustic imaging of cancer cells within the human body by integrating theories of radiative transfer, photothermal conversion, and the wave equation. The results demonstrate that the enhancement trend of the reconstructed signal closely matches the original signal, confirming the model’s excellent fitting performance. The sound pressure values generated by cancer cells are significantly higher than those of normal cells, proving that this method can effectively distinguish cancerous tissue from healthy tissue. This research provides new theoretical support and methodological foundations for the clinical application of multi-wavelength photoacoustic imaging technology. Full article
(This article belongs to the Special Issue The Principle and Application of Photonic Metasurfaces)
Show Figures

Figure 1

27 pages, 2783 KB  
Article
Improved Robust Model Predictive Trajectory Tracking Control for Intelligent Vehicles Based on Multi-Cell Hyperbody Vertex Modeling and Double-Layer Optimization
by Xiaoyu Wang, Guowei Dou, Te Chen and Jiankang Lu
Sensors 2025, 25(21), 6537; https://doi.org/10.3390/s25216537 - 23 Oct 2025
Viewed by 310
Abstract
Aiming at the problem of model parameter perturbation in vehicle trajectory tracking control, an improved robust model predictive control (RMPC) method is proposed. Based on the two-degree-of-freedom vehicle model and Serret Frenet error model, a multi-cell hypercube vertex modeling is adopted to map [...] Read more.
Aiming at the problem of model parameter perturbation in vehicle trajectory tracking control, an improved robust model predictive control (RMPC) method is proposed. Based on the two-degree-of-freedom vehicle model and Serret Frenet error model, a multi-cell hypercube vertex modeling is adopted to map the disturbance range of parameters such as vehicle speed and lateral stiffness to a set of vertices, and dynamic linear combination is achieved through normalized weights. The algorithm design mainly focuses on the dual-layer optimization of the switching mechanism, decomposing the infinite time domain problem into finite time domain optimization and terminal constraints. At the same time, it dynamically updates the vertex parameters to match time-varying uncertainties and then combines Lyapunov theory to design a control invariant set. The results show that in complex road conditions and vehicle state transitions, RMPC can reduce the peak lateral deviation from 1.0 m to 0.2 m, converge the heading deviation to within 2 deg, and significantly reduce the mean and root mean square values of control errors compared to traditional MPC, under the influence of vehicle model parameter perturbations. RMPC has good robustness and real-time performance. Full article
Show Figures

Figure 1

10 pages, 1367 KB  
Article
Influence of the Etching Material Deposition Rate and Annealing Time on Nanohole Morphology Etched into InP/In0.52Al0.48As Layers via Local Droplet Epitaxy
by Dennis Deutsch and Dirk Reuter
Crystals 2025, 15(11), 913; https://doi.org/10.3390/cryst15110913 - 23 Oct 2025
Viewed by 161
Abstract
Local droplet etching and subsequent refilling enables the fabrication of highly symmetric quantum dots with low fine structure splitting, suitable for generating polarization entangled photons. While well established in GaAs/AlxGa1−xAs, this approach does not yield emission in the [...] Read more.
Local droplet etching and subsequent refilling enables the fabrication of highly symmetric quantum dots with low fine structure splitting, suitable for generating polarization entangled photons. While well established in GaAs/AlxGa1−xAs, this approach does not yield emission in the telecom bands required for low loss fiber-based quantum communication. To achieve emission at 1.55 μm, local droplet etching must be adapted to alternative material platforms such as InP. Here, we systematically investigate how the etching material deposition rate and etching time influence nanohole morphology in In0.52Al0.48As layers lattice-matched to InP. In the first experiment, InAl was deposited at fluxes of 0.2–4.0 Å s−1 at Tetch = 350 °C and 460 °C. Lower fluxes produced nanoholes with lower density and larger ring diameters, indicating fewer and larger initial droplets, consistent with scaling theory. The average nanohole diameter decreased monotonically with increasing flux, whereas the average depth showed no clear dependence on flux. In the second experiment, etching times of 30–600 s were tested for InAl, In, and Al droplets. Average nanohole diameters remained constant for Al across all etching times, but decreased for In and InAl with increasing etching time, suggesting sidewall redeposition during etching. For all droplet types, depths peaked at intermediate times and decreased for prolonged etching, consistent with material diffusion into the nanohole after droplet consumption. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
Show Figures

Figure 1

23 pages, 7037 KB  
Article
Are Sport Clubs Mediating Urban Expressive Crimes?—London as the Case Study
by Rui Wang, Yijing Li, Sandeep Broca, Zakir Patel and Inderpal Sahota
ISPRS Int. J. Geo-Inf. 2025, 14(11), 409; https://doi.org/10.3390/ijgi14110409 - 22 Oct 2025
Viewed by 268
Abstract
The study is referenced by interdisciplinary theories, i.e., routine activity, and social cohesion, to investigate the impacts of sport clubs and events on London’s expressive crimes at varied geographical scales, by utilizing Geographical-temporally weighted regression model. It has identified the spatial patterns of [...] Read more.
The study is referenced by interdisciplinary theories, i.e., routine activity, and social cohesion, to investigate the impacts of sport clubs and events on London’s expressive crimes at varied geographical scales, by utilizing Geographical-temporally weighted regression model. It has identified the spatial patterns of effects from sport clubs’ onto local expressive crimes among London wards, with several boroughs standing out for their being significantly affected. The case study in the home borough of the Hotspur Football Club has further been conducted, by proving the seasonal influences of sports clubs on reducing youth violence within school terms. It was also found disproportional increases in expressive crimes on Premier League match days, especially when receiving the results of draw. The data-driven evidence has generated insights on localized policies and strategies on developing tailored sports to support local young people’s development; pinpointing the optimisation of police forces resources on stop and search practices during sports events in hot spot stadiums. The methodology and workflow had also been proved with high replicability into other UK cities. Full article
Show Figures

Figure 1

23 pages, 4483 KB  
Article
D2T2 Analysis of a Loss of Main Feed Water Accident
by Silvia Tolo and John Andrews
Systems 2025, 13(10), 927; https://doi.org/10.3390/systems13100927 - 21 Oct 2025
Viewed by 131
Abstract
The availability of accurate models capturing the realistic behaviour of complex systems is critical for the safe operation and optimal management of nuclear installations. However, the dynamic nature of such systems and the resulting dense network of interdependencies existing among their parts are [...] Read more.
The availability of accurate models capturing the realistic behaviour of complex systems is critical for the safe operation and optimal management of nuclear installations. However, the dynamic nature of such systems and the resulting dense network of interdependencies existing among their parts are no match for current risk modelling techniques, which rely on oversimplifying premises. Dependencies are often simplified or ignored, with conservative assumptions introduced to compensate, leading to results of uncertain realism. Alternative methods address these limitations but often remain difficult to scale, interpret, or integrate into established Probabilistic Safety Assessment practice. The Dynamic and Dependent Tree Theory (D2T2) offers a bridging framework that preserves the familiar FT/ET structure while enabling dependencies to be represented directly at the basic-event, intermediate, or subsystem level through compact submodels. This paper applies D2T2 to a loss of main feed water accident in a boiling water reactor, capturing dependencies from maintenance strategies to subsystem interactions. Results show that D2T2 improves reliability predictions compared with conventional FT/ET, aligns closely with dynamic benchmarks, and remains computationally tractable. Beyond accuracy, the approach makes modelling assumptions explicit and transparent, promoting deeper system understanding while lowering barriers to adoption in safety-critical applications. Full article
(This article belongs to the Special Issue Advances in Reliability Engineering for Complex Systems)
Show Figures

Figure 1

29 pages, 2314 KB  
Article
Fermatean Fuzzy Two-Sided Matching Model Considering Regret Aversion and Matching Willingness
by Chuanyang Ruan and Sinong Lin
Mathematics 2025, 13(20), 3321; https://doi.org/10.3390/math13203321 - 17 Oct 2025
Viewed by 226
Abstract
Against the backdrop of incomplete evaluation information prevalent in real-world decision-making scenarios and the limited application of Fermatean fuzzy numbers (FFNs) in the domain of two-sided matching (TSM) models, this paper proposes a Fermatean fuzzy two-sided matching model that integrates the regret aversion [...] Read more.
Against the backdrop of incomplete evaluation information prevalent in real-world decision-making scenarios and the limited application of Fermatean fuzzy numbers (FFNs) in the domain of two-sided matching (TSM) models, this paper proposes a Fermatean fuzzy two-sided matching model that integrates the regret aversion psychological behavior of agents and their matching willingness. Firstly, the TSM problem characterized by incomplete Fermatean fuzzy preference is described. Based on the incomplete Fermatean fuzzy evaluation information provided by bilateral agents, satisfaction matrices are constructed, and a fairness-aware matching willingness matrix is quantified. Moreover, a multi-objective TSM optimization model is established to maximize the satisfaction of agents on both sides, and the optimal TSM scheme is obtained by solving the model. Finally, the feasibility, effectiveness, and innovation of the proposed approach are validated by an example analysis of TSM on a data trading platform. Full article
(This article belongs to the Special Issue Multi-Criteria Decision-Making and Operations Research)
Show Figures

Figure 1

24 pages, 7689 KB  
Article
Design and Evaluation of Shared Tennis Service Robots Based on AHP–FCE
by Xiaoxia Xu, Ping Meng, Miao Zhao, Yan Li, Yuannian Cai and Xinxing Tang
Appl. Sci. 2025, 15(20), 11147; https://doi.org/10.3390/app152011147 - 17 Oct 2025
Viewed by 155
Abstract
To address persistent challenges in tennis—such as inefficient ball retrieval, the high cost of serving equipment, and difficulties in scheduling matches—this study proposes the design of a shared tennis service robot aimed at improving user experience and validating design feasibility. Grounded in user [...] Read more.
To address persistent challenges in tennis—such as inefficient ball retrieval, the high cost of serving equipment, and difficulties in scheduling matches—this study proposes the design of a shared tennis service robot aimed at improving user experience and validating design feasibility. Grounded in user experience theory, user requirements were collected through questionnaires and structured interviews. The Analytic Hierarchy Process (AHP) was adopted to construct a hierarchical model of requirements. Weighted calculations were then applied to quantify and rank user needs. Design solutions were then derived based on these rankings. To evaluate the solutions, the Fuzzy Comprehensive Evaluation (FCE) method was utilized for multidimensional assessment. The results show that AHP identified three core requirements: intelligent ball retrieval, intelligent serving, and personalized serving parameter customization. Guided by these priorities, the proposed design integrates a shared rental model with multisensory interactive feedback. The final evaluation yielded an FCE score of 87.83, confirming the effectiveness of the solution. The combined AHP-FCE method provides a systematic framework for quantifying user needs and objectively evaluating design alternatives. It also offers a methodological foundation for the development of sports service robots. The shared tennis robot effectively reduces labor and operational costs while enhancing the overall user experience. Full article
Show Figures

Figure 1

19 pages, 398 KB  
Article
From Fibonacci Anyons to B-DNA and Microtubules via Elliptic Curves
by Michel Planat
Quantum Rep. 2025, 7(4), 49; https://doi.org/10.3390/quantum7040049 - 17 Oct 2025
Viewed by 263
Abstract
By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient G=Z52I, where 2I is the binary icosahedral group. The Gröbner basis decomposition of its [...] Read more.
By imposing finite order constraints on Fibonacci anyon braid relations, we construct the finite quotient G=Z52I, where 2I is the binary icosahedral group. The Gröbner basis decomposition of its SL(2,C) character variety yields elliptic curves whose L-function derivatives L(E,1) remarkably match fundamental biological structural ratios. Specifically, we demonstrate that the Birch–Swinnerton-Dyer conjecture’s central quantity: the derivative L(E,1) of the L-function at 1 encodes critical cellular geometries: the crystalline B-DNA pitch-to-diameter ratio (L(E,1)=1.730 matching 34Å/20Å=1.70), the B-DNA pitch to major groove width (L=1.58) and, additionally, the fundamental cytoskeletal scaling relationship where L(E,1)=3.57025/7, precisely matching the microtubule-to-actin diameter ratio. This pattern extends across the hierarchy Z52P with 2P{2O,2T,2I} (binary octahedral, tetrahedral, icosahedral groups), where character tables of 2O explain genetic code degeneracies while 2T yields microtubule ratios. The convergence of multiple independent mathematical pathways on identical biological values suggests that evolutionary optimization operates under deep arithmetic-geometric constraints encoded in elliptic curve L-functions. Our results position the BSD conjecture not merely as abstract number theory, but as encoding fundamental organizational principles governing cellular architecture. The correspondence reveals arithmetic geometry as the mathematical blueprint underlying major biological structural systems, with Gross–Zagier theory providing the theoretical framework connecting quantum topology to the helical geometries that are essential for life. Full article
12 pages, 368 KB  
Article
Formation of Multispheres and Myelin Based on Multiple Solutions of Membrane Shape Equation
by Tao Xu and Zhong-Can Ou-Yang
Membranes 2025, 15(10), 319; https://doi.org/10.3390/membranes15100319 - 16 Oct 2025
Viewed by 408
Abstract
In this work, we construct a multiple solutions theory based on a membrane shape equation. The membrane shape of a vesicle or a red blood cell is determined using the Zhongcan–Helfrich shape equation. These spherical solutions, which have an identical radius rs [...] Read more.
In this work, we construct a multiple solutions theory based on a membrane shape equation. The membrane shape of a vesicle or a red blood cell is determined using the Zhongcan–Helfrich shape equation. These spherical solutions, which have an identical radius rs but different center positions, can be described by the same equation: ϕρ/rs=0. A degeneracy for the spherical solutions exists, leading to multisphere solutions with the same radius. Therefore, there can be multiple solutions for the sphere equilibrium shape equation, and these need to satisfy a quadratic equation. The quadratic equation has a maximum of two roots. We also find that the multiple solutions should be in a line to undergo rotational symmetry. We use the quadratic equation to compute the sphere radius, together with a membrane surface constraint condition, to obtain the number of small spheres. We ensure matching with the energy constraint condition to determine the stability of the full solutions. The method is then extended into the myelin formation of red blood cells. Our numerical calculations show excellent agreement with the experimental results and enable the comprehensive investigation of cell fission and fusion phenomena. Additionally, we have predicted the existence of the bifurcation phenomenon in membrane growth and proposed a control strategy. Full article
(This article belongs to the Special Issue Composition and Biophysical Properties of Lipid Membranes)
Show Figures

Figure 1

Back to TopTop