Axioms

The problem of the existence of optimal binary cyclically permutable constant-weight (CPCW) codes has been completely solved for codeword weights $k<5$. We consider the smallest open cases, namely $k=5$ and $k=6$. We present such codes for small values of the code length v and derive necessary conditions for the existence of optimal CPCW codes. These necessary conditions can be used to construct such codes, as well as to show that optimal codes with some parameters do not exist. In particular, we use them to prove that an optimal CPCW code does not exist.

The financial market correlation structure exhibits dynamic evolution with implications for systemic risk and diversification benefits; yet, conventional approaches using correlation magnitude monitoring may miss fundamental organizational changes. This study develops an integrated geometric–topological framework synthesizing Riemannian manifold geometry with discrete network topology to characterize market structure transformations, applying the methodology to Turkish financial markets spanning May 2015–May 2025. The analysis employs intrinsic dimensionality estimation, curvature tensor computation, and Forman–Ricci curvature calculation alongside correlation network topology measures across seventeen variables, including sectoral equity indices and macroeconomic indicators. The results document an extraordinary mid-2022 structural break featuring dimensional collapse from $2.4$ to $0.43$ dimensions, network density surge to $0.97$, and Ricci curvature spike to $16.0$, establishing a persistent hypersynchronized regime evident through 2024–2025 with density elevated by $44\%$ and the Ricci curvature being amplified $258\%$ above the baseline. A comparative crisis analysis reveals heterogeneous structural signatures distinguishing COVID-19 geometric vulnerability from currency crisis modular reorganization. Macro-financial linkages identify credit growth as primary structural driver, achieving correlation with geometric resilience. The findings demonstrate that markets undergo permanent structural transformations responding systematically to monetary–credit conditions, with implications for surveillance frameworks, stress testing design, and macroprudential policy.

This paper investigates a novel class of fractional Langevin equations, which introduces a time-varying p(t)-Laplacian operator and parameterized anti-periodic boundary conditions. This approach overcomes the limitations of traditional models characterized by constant diffusion exponents and fixed boundary locations. Under non-compactness conditions, the existence of solutions is established by applying Schaefer’s fixed-point theorem, which significantly relaxes the conventional constraints on the nonlinear term. Moreover, by imposing a Lipschitz condition on the nonlinear term, a Ulam–Hyers-type stability criterion for the coupled system is derived. This work not only extends the relevant stability theory but also provides a rigorous theoretical foundation for error control in practical applications. The effectiveness of the theoretical results is validated through numerical examples.

This paper proposes a novel fishery management model that integrates three critical ecological factors: the prey (fish) fear effect, impulsive nonlinear harvesting, and predator seasonal migration. It is demonstrated that all solutions of the proposed system are uniformly ultimately bounded. We establish the conditions for the local and global asymptotic stability of the prey-extinction periodic solution, derive the permanence criteria for the system, and determine the threshold condition for prey extinction. Numerical simulations are conducted to validate the theoretical findings. These simulations also help identify the key parameters influencing the threshold condition and reveal the complex dynamics of the system. The results provide significant insights for fishery management, suggesting that regulating harvesting intensity and timing, as well as considering predator migration mortality, are crucial for sustaining fish populations and preventing overexploitation.