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20 pages, 5994 KB

Open AccessArticle

Modeling the Evolution of Dynamic Triadic Closure Under Superlinear Growth and Node Aging in Citation Networks

by Li Liang, Hao Liu and Shi-Cai Gong

Entropy 2025, 27(9), 915; https://doi.org/10.3390/e27090915 - 29 Aug 2025

Viewed by 602

Citation networks are fundamental for analyzing the mechanisms and patterns of knowledge creation and dissemination. While most studies focus on pairwise attachment between papers, they often overlook compound relational structures, such as co-citation. Combining two key empirical features, superlinear node inflow and the [...] Read more.

Citation networks are fundamental for analyzing the mechanisms and patterns of knowledge creation and dissemination. While most studies focus on pairwise attachment between papers, they often overlook compound relational structures, such as co-citation. Combining two key empirical features, superlinear node inflow and the temporal decay of node influence, we propose the Triangular Evolutionary Model of Superlinear Growth and Aging (TEM-SGA). The fitting results demonstrate that the TEM-SGA reproduces key structural properties of real citation networks, including degree distributions, generalized degree distributions, and average clustering coefficients. Further structural analyses reveal that the impact of aging varies with structural scale and depends on the interplay between aging and growth, one manifestation of which is that, as growth accelerates, it increasingly offsets aging-related disruptions. This motivates a degenerate model, the Triangular Evolutionary Model of Superlinear Growth (TEM-SG), which excludes aging. A theoretical analysis shows that its degree and generalized degree distributions follow a power law. By modeling interactions among triadic closure, dynamic expansion, and aging, this study offers insights into citation network evolution and strengthens its theoretical foundation. Full article

(This article belongs to the Topic Computational Complex Networks)

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29 pages, 28606 KB

Open AccessArticle

The Speed of Shared Autonomous Vehicles Is Critical to Their Demand Potential

by Tilmann Schlenther and Kai Nagel

World Electr. Veh. J. 2025, 16(8), 447; https://doi.org/10.3390/wevj16080447 - 7 Aug 2025

Viewed by 742

Abstract

Under a 2021 amendment to German law, the KelRide project became the first public on-demand service operating electric autonomous vehicles (AVs) without fixed routes on public roads. This paper addresses two notable gaps in the literature by (1) conducting an ex post evaluation [...] Read more.

Under a 2021 amendment to German law, the KelRide project became the first public on-demand service operating electric autonomous vehicles (AVs) without fixed routes on public roads. This paper addresses two notable gaps in the literature by (1) conducting an ex post evaluation of demand predictions for a non-infrastructure (Mobility-on-Demand (MoD)) project and (2) using real-world data to analyze how demand responds to key Autonomous Mobility-on-Demand (AMoD) system parameters in a rural context. Earlier simulation-based demand forecasts are compared to observed booking data, and the recalibrated model is used to investigate the sensitivity of passenger numbers to vehicle speed, fleet size, service area, operating hours, and idle vehicle positioning. Results show that increasing vehicle speed leads to a superlinear rise in passenger numbers—especially at small fleet sizes—while demand saturates at large fleet sizes. A linear increase in demand is observed with expanding service areas, provided fleet size is sufficient. Extending operating hours from 9 a.m.–4 p.m. to full-day service increases demand by a factor of two to four. Passengers numbers also vary notably depending on the positioning of idle vehicles. Consistent with empirical findings, the analysis underscores that raising AV speed is essential for ensuring the long-term viability of autonomous mobility services. Full article

(This article belongs to the Special Issue Changes in Travel Behavior When Autonomous Vehicles Are Integrated into the Existing Transport System in Urban Cities)

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36 pages, 3106 KB

Open AccessArticle

Tamed Euler–Maruyama Method of Time-Changed McKean–Vlasov Neutral Stochastic Differential Equations with Super-Linear Growth

by Jun Zhang, Liping Xu and Zhi Li

Symmetry 2025, 17(8), 1178; https://doi.org/10.3390/sym17081178 - 23 Jul 2025

Viewed by 494

Abstract

This paper examines temporal symmetry breaking and structural duality in a class of time-changed McKean–Vlasov neutral stochastic differential equations. The system features super-linear drift coefficients satisfying a one-sided local Lipschitz condition and incorporates a fundamental duality: one drift component evolves under a random [...] Read more.

This paper examines temporal symmetry breaking and structural duality in a class of time-changed McKean–Vlasov neutral stochastic differential equations. The system features super-linear drift coefficients satisfying a one-sided local Lipschitz condition and incorporates a fundamental duality: one drift component evolves under a random time change

E_{t}

, while the other progresses in regular time t. Within the symmetric framework of mean-field interacting particle systems, where particles exhibit permutation invariance, we establish strong convergence of the tamed Euler–Maruyama method over finite time intervals. By replacing the one-sided local condition with a globally symmetric Lipschitz assumption, we derive an explicit convergence rate for the numerical scheme. Two numerical examples validate the theoretical results. Full article

(This article belongs to the Section Mathematics)

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15 pages, 632 KB

Open AccessArticle

Structured Stability of Hybrid Stochastic Differential Equations with Superlinear Coefficients and Infinite Memory

by Chunhui Mei and Mingxuan Shen

Symmetry 2025, 17(7), 1077; https://doi.org/10.3390/sym17071077 - 7 Jul 2025

Viewed by 329

Abstract

The stability of hybrid stochastic differential equations (SDEs in short) depends on multiple factors, such as the structures and parameters of subsystems, switching rules, delay, etc. Regarding stability analysis for hybrid stochastic systems incorporating subsystems with diverse structures, existing research results require the [...] Read more.

The stability of hybrid stochastic differential equations (SDEs in short) depends on multiple factors, such as the structures and parameters of subsystems, switching rules, delay, etc. Regarding stability analysis for hybrid stochastic systems incorporating subsystems with diverse structures, existing research results require the system to possess either Markovian properties or finite memory characteristics. However, the stability problem remains unresolved for hybrid stochastic differential equations with infinite memory (hybrid IMSDEs in short), as no systematic theoretical framework currently exists for such systems. To bridge this gap, this paper develops a rigorous stability analysis for a class of hybrid IMSDEs by introducing a suitably chosen phase space and leveraging the theory of fading memory spaces. We establish sufficient conditions for exponential stability, extending the existing results to systems with unbounded memory effects. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria. Full article

(This article belongs to the Section Mathematics)

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25 pages, 338 KB

Open AccessArticle

Characterization of the Convergence Rate of the Augmented Lagrange for the Nonlinear Semidefinite Optimization Problem

by Yule Zhang, Jia Wu, Jihong Zhang and Haoyang Liu

Mathematics 2025, 13(12), 1946; https://doi.org/10.3390/math13121946 - 11 Jun 2025

Viewed by 475

Abstract

The convergence rate of the augmented Lagrangian method (ALM) for solving the nonlinear semidefinite optimization problem is studied. Under the Jacobian uniqueness conditions, when a multiplier vector

(π, Y)

and the penalty parameter

σ

are chosen such that

σ

is [...] Read more.

The convergence rate of the augmented Lagrangian method (ALM) for solving the nonlinear semidefinite optimization problem is studied. Under the Jacobian uniqueness conditions, when a multiplier vector

(π, Y)

and the penalty parameter

σ

are chosen such that

σ

is larger than a threshold

σ^{*} > 0

and the ratio

∥ (π, Y) - (π^{*}, Y^{*}) ∥ / σ

is small enough, it is demonstrated that the convergence rate of the augmented Lagrange method is linear with respect to

∥ (π, Y) - (π^{*}, Y^{*}) ∥

and the ratio constant is proportional to

1 / σ

, where

(π^{*}, Y^{*})

is the multiplier corresponding to a local minimizer. Furthermore, by analyzing the second-order derivative of the perturbation function of the nonlinear semidefinite optimization problem, we characterize the rate constant of local linear convergence of the sequence of Lagrange multiplier vectors produced by the augmented Lagrange method. This characterization shows that the sequence of Lagrange multiplier vectors has a Q-linear convergence rate when the sequence of penalty parameters

{σ_{k}}

has an upper bound and the convergence rate is superlinear when

{σ_{k}}

is increasing to infinity. Full article

(This article belongs to the Section D: Statistics and Operational Research)

17 pages, 1090 KB

Open AccessArticle

A Chebyshev–Halley Method with Gradient Regularization and an Improved Convergence Rate

by Jianyu Xiao, Haibin Zhang and Huan Gao

Mathematics 2025, 13(8), 1319; https://doi.org/10.3390/math13081319 - 17 Apr 2025

Viewed by 587

Abstract

High-order methods are particularly crucial for achieving highly accurate solutions or satisfying high-order optimality conditions. However, most existing high-order methods require solving complex high-order Taylor polynomial models, which pose significant computational challenges. In this paper, we propose a Chebyshev–Halley method with gradient regularization, [...] Read more.

High-order methods are particularly crucial for achieving highly accurate solutions or satisfying high-order optimality conditions. However, most existing high-order methods require solving complex high-order Taylor polynomial models, which pose significant computational challenges. In this paper, we propose a Chebyshev–Halley method with gradient regularization, which retains the convergence advantages of high-order methods while effectively addressing computational challenges in polynomial model solving. The proposed method incorporates a quadratic regularization term with an adaptive parameter proportional to a certain power of the gradient norm, thereby ensuring a closed-form solution at each iteration. In theory, the method achieves a global convergence rate of

O (k^{- 3})

or even

O (k^{- 5})

, attaining the optimal rate of third-order methods without requiring additional acceleration techniques. Moreover, it maintains local superlinear convergence for strongly convex functions. Numerical experiments demonstrate that the proposed method compares favorably with similar methods in terms of efficiency and applicability. Full article

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15 pages, 2613 KB

Open AccessArticle

The Influence of Energy Levels and Defects on the Thermoluminescence of LiF: SiO₅ Phosphors Doped with Ce³⁺

by Habtamu F. Etefa, Xolani G. Mbuyise, Fikadu T. Geldasa, Genene T. Mola, Makaiko L. Chithambo and Francis B. Dejene

Int. J. Mol. Sci. 2025, 26(7), 3183; https://doi.org/10.3390/ijms26073183 - 29 Mar 2025

Cited by 1 | Viewed by 670

Abstract

The morphological, structural, and thermoluminescence (TL) properties of LiF:SiO₅ doped with Ce³⁺ solid powder phosphor were systematically analyzed. X-ray diffraction (XRD) confirmed the crystalline nature of single-phase LiF:SiO₅:Ce³⁺ nanoparticles (NPs), with crystalline size (D) determined using the Williamson–Hall [...] Read more.

The morphological, structural, and thermoluminescence (TL) properties of LiF:SiO₅ doped with Ce³⁺ solid powder phosphor were systematically analyzed. X-ray diffraction (XRD) confirmed the crystalline nature of single-phase LiF:SiO₅:Ce³⁺ nanoparticles (NPs), with crystalline size (D) determined using the Williamson–Hall (W–H) and Scherrer methods. Ce³⁺ doping induced structural modifications, reflected in variations of full width at half maximum (FWHM), strain, and stress values. The TL glow curve revealed two distinct peaks at approximately 64 °C and 134 °C, shedding light on the electron capture and release mechanisms following beta irradiation. A dose-dependent study demonstrated that TL intensity increased proportionally with radiation exposure, showing a superlinearity relationship up to 6 Gy. Additionally, investigations into different heating rates indicated only a slight shift in peak of the temperature, confirming the thermal stability of the materials. This study provides valuable insights into the TL behavior of LiF:SiO₅:Ce³⁺, making it a promising candidate for radiation dosimetry and luminescence applications. Full article

(This article belongs to the Special Issue Research on Luminescent Materials and Their Luminescence Mechanism)

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14 pages, 268 KB

Open AccessArticle

Oscillation and Asymptotic Behavior of Third-Order Neutral Delay Differential Equations with Mixed Nonlinearities

by Balakrishnan Sudha, George E. Chatzarakis and Ethiraju Thandapani

Mathematics 2025, 13(5), 783; https://doi.org/10.3390/math13050783 - 27 Feb 2025

Viewed by 684

Abstract

In the present article, we create new sufficient conditions for the oscillatory and asymptotic behavior of solutions of third-order nonlinear neutral delay differential equations with several super-linear and sub-linear terms. The results are obtained first by applying the arithmetic–geometric mean inequality along with [...] Read more.

In the present article, we create new sufficient conditions for the oscillatory and asymptotic behavior of solutions of third-order nonlinear neutral delay differential equations with several super-linear and sub-linear terms. The results are obtained first by applying the arithmetic–geometric mean inequality along with the linearization method and then using comparison method as well as the integral averaging technique. Finally, we show the importance and novelty of the main results by applying them to special cases of the studied equation. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

17 pages, 332 KB

Open AccessFeature PaperArticle

Finite and Infinte Time Blow Up of Solutions to Wave Equations with Combined Logarithmic and Power-Type Nonlinearities

by Milena Dimova, Natalia Kolkovska and Nikolai Kutev

Mathematics 2025, 13(2), 319; https://doi.org/10.3390/math13020319 - 20 Jan 2025

Cited by 1 | Viewed by 931

Abstract

In this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. The nonlinearity includes a logarithmic term and several power-type terms with nonnegative variable coefficients. Two new [...] Read more.

In this paper, we investigate the global behavior of the weak solutions to the initial boundary value problem for the nonlinear wave equation in a bounded domain. The nonlinearity includes a logarithmic term and several power-type terms with nonnegative variable coefficients. Two new necessary and sufficient conditions for blow up of the weak solutions are established. The first one addresses the blow up of the global weak solutions at infinity. The second necessary and sufficient condition is obtained in the case of strong superlinearity and concerns blow up of the weak solutions for a finite time. Additionally, we derive new sufficient conditions on the initial data that guarantee blow up for either finite or infinite time. A comparison with previous results is also given. Full article

16 pages, 384 KB

Open AccessArticle

Investigating Oscillations in Higher-Order Half-Linear Dynamic Equations on Time Scales

by Ahmed M. Hassan, Sameh S. Askar, Ahmad M. Alshamrani and Monica Botros

Symmetry 2025, 17(1), 116; https://doi.org/10.3390/sym17010116 - 13 Jan 2025

Viewed by 665

Abstract

This study presents novel and generalizable sufficient conditions for determining the oscillatory behavior of solutions to higher-order half-linear neutral delay dynamic equations on time scales. Utilizing the Riccati transformation technique in combination with Taylor monomials, we derive new and comprehensive oscillation criteria that [...] Read more.

This study presents novel and generalizable sufficient conditions for determining the oscillatory behavior of solutions to higher-order half-linear neutral delay dynamic equations on time scales. Utilizing the Riccati transformation technique in combination with Taylor monomials, we derive new and comprehensive oscillation criteria that cover a wide range of cases, including super-linear, half-linear, and sublinear equations. These results extend and improve upon existing oscillation criteria found in the literature by introducing more general conditions and providing a broader applicability to different types of dynamic equations. Furthermore, the study highlights the role of symmetry in the underlying equations, demonstrating how symmetry properties can be leveraged to simplify the analysis and provide additional insights into oscillatory behavior. To demonstrate the practical relevance of our findings, we include illustrative examples that show how these new criteria, along with symmetry-based perspectives, can be effectively applied to various time scales. Full article

(This article belongs to the Special Issue Differential/Difference Equations and Its Application: Volume II)

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26 pages, 1404 KB

Open AccessFeature PaperArticle

Research on Three-Dimensional Extension of Barzilai-Borwein-like Method

by Tianji Wang and Qingdao Huang

Mathematics 2025, 13(2), 215; https://doi.org/10.3390/math13020215 - 10 Jan 2025

Viewed by 705

Abstract

The Barzilai-Borwein (BB) method usually uses BB stepsize for iteration so as to eliminate the line search step in the steepest descent method. In this paper, we modify the BB stepsize and extend it to solve the optimization problems of three-dimensional quadratic functions. [...] Read more.

The Barzilai-Borwein (BB) method usually uses BB stepsize for iteration so as to eliminate the line search step in the steepest descent method. In this paper, we modify the BB stepsize and extend it to solve the optimization problems of three-dimensional quadratic functions. The discussion is divided into two cases. Firstly, we study the case where the coefficient matrix of the quadratic term of quadratic function is a special third-order diagonal matrix and prove that using the new modified stepsize, this case is R-superlinearly convergent. In addition to that, we extend it to n-dimensional case and prove the rate of convergence is R-linear. Secondly, we analyze that the coefficient matrix of the quadratic term of quadratic function is a third-order asymmetric matrix, that is, when the matrix has a double characteristic root and prove the global convergence of this case. The results of numerical experiments show that the modified method is effective for the above two cases. Full article

(This article belongs to the Section E: Applied Mathematics)

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17 pages, 289 KB

Open AccessArticle

Nonlinear Neutral Delay Differential Equations: Novel Criteria for Oscillation and Asymptotic Behavior

by Belal Batiha, Nawa Alshammari, Faten Aldosari, Fahd Masood and Omar Bazighifan

Mathematics 2025, 13(1), 147; https://doi.org/10.3390/math13010147 - 2 Jan 2025

Cited by 6 | Viewed by 1178

Abstract

This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of [...] Read more.

This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a careful analysis of the monotonic properties of solutions and their derivatives, paving the way for a deeper understanding of this complex behavior. The research is particularly significant as it extends the scope of previous studies by addressing more complex forms of neutral differential equations. Using the linearization technique, strict conditions are developed that exclude the existence of positive solutions, which allows the formulation of innovative criteria for determining the oscillatory behavior of the studied equations. This research highlights the theoretical and applied aspects of this mathematical phenomenon, which contributes to enhancing the scientific understanding of differential equations with neutral conditions. To demonstrate the effectiveness of the results, the research includes two illustrative examples that prove the validity and importance of the proposed methodology. This work represents a qualitative addition to the mathematical literature, as it lays new foundations and opens horizons for future studies in this vital field. Full article

(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications, 2nd Edition)

24 pages, 328 KB

Open AccessArticle

Quasilinear Fractional Neumann Problems

by Dimitri Mugnai and Edoardo Proietti Lippi

Mathematics 2025, 13(1), 85; https://doi.org/10.3390/math13010085 - 29 Dec 2024

Viewed by 578

Abstract

We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also provide the weak formulation of solutions without regularity assumptions and we provide an example, [...] Read more.

We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also provide the weak formulation of solutions without regularity assumptions and we provide an example, even in the linear case, for which no regularity can indeed be assumed. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

16 pages, 275 KB

Open AccessArticle

Existence of Nontrivial Solutions for Boundary Value Problems of Fourth-Order Differential Equations

by Hongyu Li

Axioms 2024, 13(11), 766; https://doi.org/10.3390/axioms13110766 - 4 Nov 2024

Cited by 1 | Viewed by 1143

Abstract

This article investigates the solvability problem of fourth-order differential equations with two-point boundary conditions; specifically, conclusions regarding sign-changing solutions are obtained. The methods used in this article are fixed-point theorems on lattices. Firstly, under some sublinear conditions, the existence of three nontrivial solutions [...] Read more.

This article investigates the solvability problem of fourth-order differential equations with two-point boundary conditions; specifically, conclusions regarding sign-changing solutions are obtained. The methods used in this article are fixed-point theorems on lattices. Firstly, under some sublinear conditions, the existence of three nontrivial solutions is demonstrated, including a sign-changing solution, a negative solution and a positive solution. Secondly, under some unilaterally asymptotically linear and superlinear conditions, the existence of at least one sign-changing solution is proved. Finally, this article provides several specific examples to illustrate the obtained conclusions. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems)

32 pages, 552 KB

Open AccessArticle

Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty

by Tak Kuen Siu

J. Risk Financial Manag. 2024, 17(10), 436; https://doi.org/10.3390/jrfm17100436 - 29 Sep 2024

Cited by 1 | Viewed by 1456

Abstract

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used [...] Read more.

This paper aims to leverage Bayesian nonlinear expectations to construct Bayesian lower and upper estimates for prices of Ether options, that is, options written on Ethereum, with conditional heteroscedasticity and model uncertainty. Specifically, a discrete-time generalized conditional autoregressive heteroscedastic (GARCH) model is used to incorporate conditional heteroscedasticity in the logarithmic returns of Ethereum, and Bayesian nonlinear expectations are adopted to introduce model uncertainty, or ambiguity, about the conditional mean and volatility of the logarithmic returns of Ethereum. Extended Girsanov’s principle is employed to change probability measures for introducing a family of alternative GARCH models and their risk-neutral counterparts. The Bayesian credible intervals for “uncertain” drift and volatility parameters obtained from conjugate priors and residuals obtained from the estimated GARCH model are used to construct Bayesian superlinear and sublinear expectations giving the Bayesian lower and upper estimates for the price of an Ether option, respectively. Empirical and simulation studies are provided using real data on Ethereum in AUD. Comparisons with a model incorporating conditional heteroscedasticity only and a model capturing ambiguity only are presented. Full article

(This article belongs to the Special Issue Featured Papers in Finance and Society Wellbeing—in Honor of Professors Joe Gani and Chris Heyde)

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