We extend the Calderbank-Shor-Steane (CSS) quantum code construction to Gaussian integer rings & Zopf;q[i], where q is a positive integer whose prime divisors all satisfy p = 1 (mod 4). Using nested principal ideal codes with Hermitian dual containment C perpendicular to H 2 C_ C1 C_ C2, we construct quantum stabilizer codes with dimension K = |C2|/|C1|. To address the challenges of decoding over rings with zero divisors, we introduce an algebraic error model where correctable errors are characterized by the coset structure of C2 relative to C1. This framework operates independently of specific physical noise assumptions, focusing on deterministic coset distinguishability. The associated coset-based decoder is shown to require exactly|epsilon | = [C2 : C1] membership tests, where the coset index is analytically determined by the norm quotient N(alpha 1)/N(alpha 2). Examples over & Zopf;25[i], & Zopf;85[i], and & Zopf;325[i] demonstrate codes encoding K E {5, 17, 5} logical states. Numerical simulations confirm the coding gain of the proposed scheme and provide benchmarks for its performance under additive noise. These results establish that ring-theoretic coset structures provide an algebraically rigorous and computationally efficient foundation for structured error correction over Gaussian integer rings. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The 6 February 2023 earthquakes in Türkiye inflicted widespread damage on transportation infrastructure, resulting in complex, spatially heterogeneous deformation patterns, most notably along the Hatay Airport access road. Situated atop the alluvial deposits of the former Amik Lake basin, this roadway is inherently susceptible to liquefaction-induced settlement and ground instability. This study examines the underlying damage mechanisms affecting this strategically important corridor using advanced signal-processing methodologies that go beyond conventional analytical techniques. High-precision post-event GNSS measurements were employed to characterize the post-earthquake roadway surface profile and its spatial irregularity structure. The statistical characteristics and persistence of the resulting deformation signals were evaluated using Detrended Fluctuation Analysis (DFA), thereby assessing randomness and long-range dependence. Complementarily, the Continuous Wavelet Transform (CWT) was applied to spatially resolve deformation energy and to delineate critical damage hotspot areas along the road alignment. Google Earth Engine-based remote sensing validation was also incorporated. These results provide a quantitative and mathematically grounded interpretation of post-event geometric irregularities and the inferred deformation processes driven by soil–structure interaction and liquefaction phenomena. Collectively, the study underscores the efficacy of fractal and wavelet-based analytical frameworks as robust decision-support tools for post-earthquake damage evaluation and for informing prioritization of targeted rehabilitation and mitigation strategies.
Airline baggage policies generally rely on uniform weight allowances combined with excess-baggage fees. From a payload-allocation perspective, this design may obscure the scarcity value of the aircraft payload and generate implicit incidence patterns across passengers. We study a Total Weight Allocation (TWA) benchmark in which passengers receive tradable baggage rights derived from a fixed per-passenger payload allowance net of body weight and trade these rights in a competitive market. When the payload capacity binds, the TWA implements a payload-efficient allocation by equalizing the marginal valuations of discretionary baggage capacity, exactly under quasi-linear preferences. Efficiency is independent of the initial assignment of rights, whereas incidence depends on endowments: conditional on baggage demand and travel needs, lower-body-weight passengers tend to be net sellers and higher-body-weight passengers tend to be net buyers. A non-tradable seating baseline preserves feasibility without changing the tradable baggage margin. The theoretical results extend to convex weight-cost formulations and multidimensional payload constraints. An illustrative numerical exercise based on assumed parameter distributions reports model-implied efficiency gains relative to non-tradable uniform baggage allowances and the transfer patterns implied by tradable rights; it is not an empirical calibration or a route-specific prediction. A per-kg fee equal to the payload shadow price can replicate the benchmark trading allocation while transferring scarcity rents from passengers to the airline, highlighting the efficiency–incidence trade-off in baggage-policy design.
Deformation-induced anisotropic hardening strongly influences springback, strain localisation, forming limits and unloading-sensitive response in metallic sheet materials, and must therefore be represented reliably in finite-element simulations of sheet-forming operations. Existing syntheses have clarified the phenomenology of load-path effects and catalogued broad classes of constitutive models, but they have generally devoted less attention to the practical questions that govern engineering adoption: which observed behaviours justify which model family, what test information is minimally required for calibration, and what implementation burden follows at the FE level. This article presents a critical narrative review of deformation-induced anisotropic hardening in metallic sheet materials from the viewpoint of model selection, calibration and finite-element deployment. Experimentally observed responses are reorganised into a three-layer framework linking observable hardening signatures, constitutive evolution modes and representative model families. Prior syntheses are positioned explicitly to define the distinct contribution of the present review in terms of calibration burden, identifiability, implementation readiness and decision-oriented model choice. Crystal-plasticity-based approaches are discussed as supporting virtual laboratories for mechanism interpretation and synthetic calibration data generation. Computational issues relevant to industrial deployment are reviewed in terms of local stress updates, consistent elastoplastic tangents and parameter-identification workflows. The scope is restricted to constitutive descriptions of anisotropy evolution in metallic sheet materials up to the onset of localised necking. The overall aim is to provide a practical map for choosing, calibrating and implementing anisotropic hardening models in sheet-forming simulations.
Achieving sustainable development is one of the most important goals for countries. Achieving this depends on accurately identifying its determinants. This study aims to identify the various factors that contribute to sustainable development in the United States. For this purpose, the effects of globalization, energy uncertainty, ecological footprint, and ESG-based uncertainty on sustainable development were examined for the period from 2002 to 2022. The study examined the stationarity of the variables, the long-term relationship, and the coefficients related to this relationship using appropriate methods that also account for structural breaks, respectively. The robustness of the results was tested with three different long-term estimators, for example, ARDL, FMOLS, and CCR. Accordingly, ecological footprint, energy uncertainty, and globalization were found to have negative effects on sustainable development, while ESG-based uncertainty had positive effects. These results are expected to inform the United States' approach to achieving sustainable development by ensuring that the ESG has been planned, implemented, and reported as a market commitment to answer the sustainable development progress and emphasizing globalization in a sustainable manner.
