The Magnus expansion is attractive for periodically driven quantum systems because every finite truncation exponentiates an anti-Hermitian generator and therefore preserves unitarity. Its practical failure in interacting fermionic systems is nevertheless subtle: a low-order approximation may remain unitary while becoming progressively less accurate as additional terms are retained. We establish order-resolved breakdown signatures for a half-filled, periodically driven one-dimensional Fermi-Hubbard chain. The one-period propagator is computed numerically exactly in the fixed-particle sector and compared with Magnus approximants through fourth order. Failure is defined operationally by a successive-order error ratio (rₙ=εₙ/εₙ₋₁≥ 1), not by an unsupported claim of divergence of the infinite series. Across a raw (9×29) interaction-frequency grid ((U/J=0…,8), (ω/J=2…,16)), at least one added order loses improvement at 36.40% of the 261 sampled points. The smallest sampled frequency above which all retained orders improve throughout the remaining high-frequency tail rises from (ω/J=2.5) at (U=0) to (11.5) at (U/J=8). At (U/J=4), the highest (r₄=1) crossing occurs at (ω/J=7.719), followed by a monotone sampled tail from (ω/J=8). High-frequency error exponents approach the expected omitted-order scaling. A norm-based convergence certificate is consistently more conservative than the observed finite-order boundary. These results show that Magnus breakdown in the Hubbard model is order dependent, interaction shifted, and detectable before unitarity is lost.

College English, as a compulsory course with both instrumental and humanistic attributes, bears a unique mission of integrating language training with value guidance. Curriculum ideological and political education plays an indispensable role in accomplishing the significant mission. This paper attempts to analyze the feasibility and necessity of innovating ideological and political teaching approaches and proposes multi-dimensional innovative teaching approaches, aiming to construct an integrated and blended teaching mode. These proposed innovative approaches can effectively achieve the full infiltration of moral education into all aspects of language teaching, realize the organic integration of language knowledge transmission, ability development, value shaping and guidance, and provide operable reform references for College English curriculum ideological and political construction in the new era.

Thomistic Biblicism may be understood as an approach that brings together the philosophical and theological resources of Thomas Aquinas with the witness of Sacred Scripture, particularly through the complementary relationship between faith and reason. At the heart of this approach is Aquinas’s effort to articulate the intellectual content of Christian faith by drawing upon Aristotelian philosophy without reducing revelation to philosophy. Biblical Thomism, in particular, seeks to recover the profoundly biblical character of Aquinas’s theology by examining the dynamic relationship between Scripture and speculative theology, as well as the interaction between doctrine, moral teaching, and Christian life. The present study proposes the expression “logical conviviality” to describe this relationship. Conviviality, from the Latin con-vivere, meaning “to live with,” suggests a harmonious and mutually enriching coexistence. Applied to Thomistic Biblicism, it refers to the ordered coexistence of biblical revelation, rational inquiry, metaphysical reflection, and theological tradition. Thomism, as a systematic philosophical and theological tradition, cannot simply be identified with a form of Biblicism that accepts isolated biblical texts without philosophical or theological interpretation. Rather, Aquinas integrates Scripture with reason, tradition, metaphysics, and rigorous logical analysis. The “logical conviviality of Thomistic Biblicism,” therefore, denotes a relationship in which reason does not compete with revelation but serves it, while revelation provides the horizon within which reason operates. This paper examines this relationship through three major works of Aquinas: The Summa Theologiae, the Summa Contra Gentiles, and the Commentary on the Sentences of Peter Lombard. It argues that, for Aquinas, Scripture provides the foundational content of sacred doctrine, while logic, philosophy, and metaphysics provide the intellectual means through which that content is clarified, defended, and contemplated.

Artificial intelligence has become increasingly embedded in the practices through which human beings acquire, organize, evaluate, communicate, and act upon information. The philosophical problem raised by this development is therefore not exhausted by the familiar observation that artificial intelligence sometimes produces false information. More fundamental is the question of whether systems that generate apparently knowledgeable discourse can participate appropriately in epistemic practices when they do not possess the kinds of beliefs, experiences, intentions, understanding, or testimonial commitments ordinarily associated with human knowers. This paper develops the concept of epistemic impropriety as a normative framework for examining that problem. Epistemic impropriety is distinguished from epistemic error and epistemic harm: an error concerns falsity or inadequate justification; a harm concerns damage suffered in one's capacity as a knower; impropriety concerns the violation or distortion of norms governing responsible inquiry, testimony, justification, interpretation, authority, and epistemic agency. The paper argues that the central epistemic danger of generative artificial intelligence lies in the possibility that linguistic plausibility may acquire the social authority normally associated with justified knowledge. This danger manifests itself in hallucination, the manufacture of apparent understanding, the illusion of comprehensiveness, the substitution of plausibility for justification, algorithmic opacity, automation bias, synthetic testimony, epistemic injustice, hermeneutical exclusion, epistemic infantilization, and the gradual displacement of human intellectual agency. At the same time, the paper rejects the simplistic conclusion that artificial intelligence is epistemically worthless. AI may function as an epistemic technology, a cognitive aid, and a participant in distributed practices of inquiry without thereby becoming an autonomous knower or epistemic authority in the full human sense. The appropriate philosophical response is consequently neither technological rejection nor uncritical enthusiasm, but the cultivation of a critical human–AI epistemic relationship governed by provenance, transparency, evidential calibration, contestability, pluralism, human judgment, and responsibility. The ultimate question is not merely whether artificial intelligence can generate answers, but whether its participation enables human beings to become better knowers.

This paper presents the findings of a research on an artificial intelligence-based hybrid Support Vector Machine–Bat Optimization Algorithm (SVM-BOA) model developed for spectrum sensing in the Ultra High Frequency (UHF) television band (470 – 694 MHz). The main objective is to enhance detection accuracy, probability of detection, probability of false alarm, and computational efficiency for efficient spectrum utilization. Experimental spectrum measurements were conducted across Kano, Kaduna, and the Federal Capital Territory (FCT), Abuja, Nigeria, to assess the level of spectrum occupancy and identify available Television White Space (TVWS) channels. Relevant signal features, including received signal power level, noise power level, and frequency, were extracted from the field data collected and used to train and test the proposed model. The model was developed and implemented in MATLAB computing environment. The new model was validated using test data for classification of channel status as either free or occupied. The developed model achieved a detection accuracy of 97.67% at a threshold of −99.5dB, based on metric from confusion matrix, outperforming baseline SVM (78.57%) and other benchmark optimization-based SVM models, including Grid Search SVM (92.86%), Random Search SVM (89.29%), Genetic Algorithm SVM (92.86%), and Particle Swarm Optimization SVM (92.78%). It also attained a probability of detection (Pd) of 1.00 (100%) and a probability of false alarm (Pfa) of 0.1053 (10.53%), which satisfies the sensing performance requirements of the Institute of Electrical and Electronics (IEEE 802.22) standards under low-signal conditions. These findings suggest that the hybrid SVM-BOA approach will offer superior classification accuracy and computational efficiency relative to conventional techniques and comparable hybrid models, signifying a strong potential for the improvement of spectrum utilization in next-generation cognitive radio networks.

The search for eco-friendly corrosion inhibitors for mild steel has driven interest in the valorization of expired pharmaceutical products as green alternatives to conventional toxic inhibitors. The present study investigated the synergistic inhibition behaviour of expired ciprofloxacin and iodide ions for mild steel in synthetic acid rain solution using gravimetric, surface morphology analysis and molecular dynamic simulation approaches. The results showed that the corrosion inhibition performance significantly improved in ciprofloxacin-iodide system and the inhibition performance reach approximately 97 % at low concentration. The surface morphology analysis showed that the inhibitor molecules are adsorbed on the mild steel surface, thereby decreasing the corrosion rate. The adsorption process follows the Frumkin adsorption isotherm. The experimental results correlated with the molecular dynamics simulation results. The findings in this research provide a practical strategy for the potential reuse of expired ciprofloxacin waste and the development of novel corrosion inhibitors.

The removal of synthetic dyes such as Methylene Blue from aqueous effluents is a critical environmental challenge. This study investigates the efficacy of activated Carbon derived from Pterocarpus santalinoides Fruit as a low-cost and renewable adsorbent of Methylene Blue dye. The Pterocarpus santalinoides activated carbon was analyzed using scanning electron microscopy and Fourier transform infra-red spectroscopy. The Box-Behnken design of response surface methodology (RSM) method was adopted to optimize the adsorption process variables such as contact time (20 – 100 min), adsorbent dose (0.1 – 0.5 g), initial dye concentration (10 – 50 mg/l), and temperature (30 – 60 ℃). The characterization result revealed the good adsorptive properties of the Pterocarpus santalinoides activated carbon. The ANOVA result indicates that quadratic model was reliable for predicting methylene blue removal with R2 of 0.9267 and 0.9618 for adsorption capacity. The optimum condition for the maximum removal efficiency of 95.90 % and adsorption capacity of 5.70 mg/g were achieved at contact time (56.33 min), adsorbent dose (0.43 g), MB concentration (36.26 mg/l) and temperature (55.91 ℃). Both Henry and Langmuir isotherms were well fitted to the adsorption data. The adsorption kinetics was best described by the Psuedo–second order model indicating a chemisorption-dominated process. Equilibrium Isotherm data showed a high correlation with the Langmuir model suggesting a monolayer adsorption on a homogeneous surface. This study successfully demonstrated the efficiency of Box Behnken Design of Response Surface Methodology (BBD – RSM) as a powerful tool for modeling and optimizing the adsorption process, providing a clear path-way for maximizing the efficiency of Pterocarpus santalinoides based activated Carbon for dye wastewater treatment and environmental remediation.