A New Scheme on Synchronization of Commensurate Fractional-Order Chaotic Systems Based on Lyapunov Equation by Hua Wang, Hang-Feng Liang, Peng Zan, Zhong-Hua Miao

“…A simple but practical method to synchronize many familiar fractional-order chaotic systems has been put forward. A new theorem is proposed for a class of cascade fractional-order systems and it is applied in chaos synchronization. …”
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Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation by Mohamed El-Borhamy, Tamer Medhat, Manal E. Ali

“…In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El-Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain.…”
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An Improved Approach of Classical Upper Bound Theory for Stability Analysis of Layered Slopes by ZeRun Tian, YanHong Zhang, XiTong Wei, Fei Li, YaFeng Guo

“…Considering the possible global or local failure modes of the layered slope, the equations for the critical height of the above modes are derived based on the upper limit theorem by using rotational failure mechanisms or rotational and translational failure mechanisms. …”
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Evolution Game Model of Travel Mode Choice in Metropolitan by Chaoqun Wu, Yulong Pei, Jingpeng Gao

“…Second, backward induction is used to solve for Nash equilibrium of the game based on the Folk Theorem. Third, the sensitivity analysis suggests that a payoff reduction of travel by any mode will result in a rising proportion of inhabitants travelling by that mode and falling proportions of inhabitants travelling by other modes. …”
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Two Bootstrap Strategies for a k-Problem up to Location-Scale with Dependent Samples by Jean-François Quessy, François Éthier

“…To this end, two bootstrap strategies based on the multiplier central limit theorem are proposed, both exploiting a representation of the test statistics in terms of a Hadamard differentiable functional. …”
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Application of first-order logic to identify organizers and perpetrators of illegal actions in teams of a limited circle of people by A. М. Sobol, E. I. Kozlova, Yu. A. Chernyavsky

“…There are three main families of inference algorithms in first-order logic: direct inference and its application to deductive databases and production systems; backward inference procedures and logic programming systems; theorem proving systems based on the resolution method. …”
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Anti-aliased metasurfaces beyond the Nyquist limit by Seokwoo Kim, Joohoon Kim, Kyungtae Kim, Minsu Jeong, Junsuk Rho

“…Prevailing metasurface research has often relied on the conventional Nyquist sampling theorem to assess sampling appropriateness, however, our findings reveal that the Nyquist criterion is insufficient guidance for sampling in metasurface. …”
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Barr-Zee diagrams at a high-energy muon collider by Samuel Homiller, Jackie Lodman, Aditya Parikh, Matthew Reece

“…These loop corrections lead to kinematic features in the differential cross sections of these processes, dictated by the optical theorem. We demonstrate this connection in the context of the singlet-doublet and doublet-triplet extensions to the SM, explore the detectability of these features at a muon collider experiment, and discuss how these measurements can be used to ascertain the underlying model parameters.…”
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Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems by Seng-Kin Lao, Lap-Mou Tam, Hsien-Keng Chen, Long-Jye Sheu

“…In order to ensure the stability of the error signal between two fractional-order systems, the arguments of all eigenvalues of the Jacobian matrix of the erroneous system should be within a region defined in Matignon’s theorem. Sometimes, the arguments depend on the state variables of the driving system, which makes it difficult to prove the stability. …”
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Design, implementation and formal verification of BGP proxy for mimic router by Jin ZHANG, Qiang GE, Weihai XU, Yiming JIANG, Hailong MA, Hongtao YU

“…To ensure the safety and correctness of the critical ‘mimic bracket’ components such as protocol proxies of mimic routers, a BGP (border gateway protocol) proxy was designed and implemented, and formal methods were applied to verify the safety and correctness of the BGP proxy.The BGP packets communicated between the peer routers and the master actor were monitored by the BGP proxy.The BGP sessions with the slave actors on behalf of peer routers were established, ensuring the consistency of the BGP protocol states for all actors.The formal specification of the BGP proxy was written based on separation logic.The VeriFast theorem prover was used to prove that the program had no memory safety problems such as null pointer reference.Furthermore, the formal verification of high-level attributes of each module in BGP proxy was also conducted to strictly ensure that the implementation met the specification.The implementation to proof code ratio of BGP proxy is about 1.8:1, and the implementation to proof labor hour ratio is about 1:3.The formally verified BGP proxy consume 0.16 seconds to process 100 000 BGP routes, which is about 7 times as long as the unverified one.Works done provide a reference for applying formal methods to verify the safety and correctness of critical components in mimic defense equipment and systems.…”
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Origins and conservation of topological polarization defects in resonant photonic-crystal diffraction by Yin Xuefan, Inoue Takuya, Peng Chao, Noda Susumu

“…Unlike Bloch states, the polarization defects live and evolve in an unbound momentum space, obeying a local conservation law as a direct consequence of Stokes’ theorem, but the total charge number is countless.…”
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Trajectory tracking sliding mode control for vertical take-off and landing aircraft based on double loop and global Lipschitz stability. by Liang Du

“…To tackle this issue, the paper leverages the global asymptotic stability theorem for dynamic systems and develops a closed-loop system with global Lipschitz continuity, guaranteeing robust stability across both loops. …”
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Periodic Solution for a Kind of Third-Order Neutral-Type Differential Equation by Axiu Shu, Bo Du

“…This paper is devoted to the use of properties of neutral-type operators with a variable parameter and Mawhin’s continuation theorem for overcoming the above difficulties. The neutral term in the third-order neutral differential equation in this paper contains a variable parameter which is different from third-order neutral-type equations that have been studied. …”
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Research on Upper Bound Limit Stability Analysis of Multi-Step High Steep Slope by Zhen Wang

“…In order to explore the stability of multi-step high steep slope, this paper considers layer distribution of soil and builds a slope failure mechanism which meets requirements of velocity separation based on plastic mechanics principles, then derives the calculation method of external force power and internal energy dissipation power in failure area using numerical analysis theory, and proposes a loop algorithm for slope stability analysis combining upper bound limit analysis theorem and strength reduction principle. At the same time, in order to enhance the applicability of the upper bound limit analysis method, this paper develops a slope stability calculation system of upper bound limit analysis combined with computer programming technology and evaluates the accuracy of the calculation system through slope engineering practice in open-pit mine. …”
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On the analytic generalization of particle deflection in the weak field regime and shadow size in light of EHT constraints for Schwarzschild-like black hole solutions by Reggie C. Pantig

“…Abstract In this paper, an analytic generalization of the weak field deflection angle (WDA) is derived by utilizing the current non-asymptotically flat generalization of the Gauss–Bonnet theorem. The derived formula is valid for any Schwarzschild-like spacetime, which deviates from the classical Schwarzschild case through some constant parameters. …”
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Research on Aircraft Attitude Control Method Based on Linear Active Disturbance Rejection by Zhiguo Song, Changjian Zhao, Huiqiang Zhang, Tian Dong, Aojia Ma, Dawei Yan

“…Finally, the stability proof of the dual-loop attitude control method is given based on the Lyapunov theorem of stability. Simulation results show that compared with the traditional PID attitude control method, the dual-loop ADRC attitude control method has better control quality in tracking speed, tracking error, and system anti-interference ability. …”
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Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory by Zulfiqar Ali, Syed Husnine, Imran Naeem

“…Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. …”
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IMPACT OF HARDENING ON SLIGHTLY CURVED ELASTICITY-PLASTICITY CRACK TIP DISPLACEMENT UNDER QUASI-STATIC LOADS by YANG DaPeng, WANG JunJie, ZHAO Yao, LI TianYun, CHEN JianQiao

“…In this article,elastic-plastic curved crack tip opening displacement in hardened material under quasi-static loads has been mainly studied,and curved crack tip opening displacement has been calculated as a practical application of a second order perturbation method and theorem of surname KA,where the effects of quasi-static applied stresses and quasi-static normal and shear stresses on the boundaries of plasticity area are synthetically taken into considerations. …”
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Global dynamics of a simple model for wild and sterile mosquitoes by Yu Ichida, Yukihiko Nakata

“…In this paper, we combine a geometric approach called the time-scale transformation and blow-up technique with the center manifold theorem to provide a complete understanding of dynamical systems near the origin. …”
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Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses by Zhenguo Luo, Liping Luo, Jianhua Huang, Binxiang Dai

“…By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. …”
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