As the development of High-Speed Railways (HSRs) shifts from scale expansion to quality and efficiency, high-density timetables face increasing challenges regarding operational stability. Traditional capacity metrics often prioritize volume over service quality, neglecting the economic and service implications of delays. To reconcile theoretical capacity with practical reliability, this paper proposes a novel Reliable Value (RV)-oriented framework for HSR timetabling. We construct a Reserve Capacity Incremental Heuristic Optimization Framework that employs a synergetic integrated stochastic optimization strategy. This methodology treats reserve capacity as a systematically varied analytical parameter rather than a static constant, integrating redundancy layout planning with dynamic recovery adjustments under stochastic delay scenarios. The RV metric quantitatively combines efficiency (Expected Running Time) and robustness (Indirect Capacity Loss). A case study on the Beijing–Shanghai high-speed railway corridor demonstrates a non-linear relationship between reserve capacity allocation and system value. The results identify an optimal saturation interval of 5 to 14 min, where the marginal gains in reliability maximize the overall system value without excessively compromising operational efficiency. These findings provide theoretical support for transitioning from static capacity planning to proactive, value-based resilience engineering through optimized redundancy allocation.

Column generation is a fundamental technique for solving large-scale combinatorial optimization problems such as unit commitment and vehicle routing, yet its performance is often limited by dual oscillation. This study explores the intrinsic cause of this phenomenon from the perspective of shadow price theory and demonstrates that dual oscillation arises from the lack of marginal interpretability of Lagrange multipliers when multiple dual solutions coexist. To address this issue, an improved column generation framework is proposed in which traditional multipliers are replaced with minimum-norm multipliers that possess clear economic meaning and act as directional shadow prices. A generalized pricing subproblem is formulated, and partial minimum-norm multipliers are obtained through convex quadratic optimization to guide column generation. Numerical experiments on a simplified single-period unit commitment case and large-scale cutting stock problems showed that the proposed approach eliminated invalid column generation and achieved speedy convergence to the optimal solution within only two iterations for the unit commitment case, and the classical column generation exhibited slow convergence with dual oscillation in large-scale scenarios while the improved algorithm achieved fast and stable convergence. The results indicate that the stabilization method enhances the consistency of dual variables and provides a more robust foundation for the theoretical and practical development of column generation algorithms.

Orthogonal Linear Discriminant Analysis (OLDA) has been widely studied for dimensionality reduction, as the orthogonality constraints on its projection matrix enable more effective elimination of redundant features compared to conventional Linear Discriminant Analysis (LDA). However, most existing methods for solving OLDA rely on iterative optimization to sequentially construct orthogonal components, incurring massive repeated high-cost matrix operations and thus leading to substantial computational inefficiency. To address this limitation, we propose QR decomposition-based Fast OLDA (QR-FOLDA), a method built upon a theoretical result (Theorem 1) established in this work: the optimal solutions of LDA remain valid under any full-rank linear transformation. By leveraging this property, QR-FOLDA applies QR decomposition directly to the optimal LDA solution, thereby enforcing orthogonality while avoiding the repeated high-cost matrix operations typically involved in iterative optimization procedures. Experimental evaluations conducted on nine real-world datasets across various domains show that QR-FOLDA not only achieves substantial improvements in computational efficiency compared to existing OLDA methods but also delivers superior classification performance. These findings position QR-FOLDA as a theoretically sound and practically efficient solution for orthogonal discriminant analysis.

Wireless sensor network (WSN) coverage optimization is a critical factor in improving network service quality, yet it faces challenges such as deployment uniformity, high-dimensional optimization, and the balance between exploration and exploitation under limited node resources. To address the shortcomings of the cultural historical optimization algorithm (CHOA), including insufficient global exploration, lack of dynamic regulation, and limited local exploitation accuracy, this paper proposes a film and television strategy-based multi-strategy cultural historical optimization algorithm (FTSCHOA). The proposed algorithm enhances performance through three synergistic mechanisms: a DE-style evolutionary operator that strengthens global exploration and population diversity; a film-and-television strategy that balances exploration and exploitation via random perturbations and adaptive parameter regulation; and a memory-based neighborhood local search that performs refined exploitation around high-quality solution sets to improve local optimization accuracy. Extensive experiments conducted on the CEC2017 and CEC2022 benchmark suites with dimensions of 10, 20, 30, and 50 demonstrate that FTSCHOA outperforms comparative algorithms in terms of optimization accuracy, convergence speed, and stability. The Friedman mean rank test indicates that FTSCHOA consistently achieves the best average ranking, while the Wilcoxon rank-sum test confirms that its performance differences with respect to competing algorithms are statistically significant (p<0.05). When applied to WSN coverage optimization in a 100 m×100 m monitoring region, FTSCHOA achieves coverage rates of 0.9351 and 0.9738 with 25 and 30 sensor nodes, respectively, which are significantly higher than those obtained by PSO, GWO, CHOA, and other algorithms. Moreover, the resulting node deployments exhibit greater uniformity, fewer coverage holes, and lower redundancy. The experimental results demonstrate that FTSCHOA effectively overcomes the limitations of traditional algorithms and provides an efficient and practical solution for WSN node deployment optimization, with strong potential for application in real-world scenarios such as environmental monitoring and smart agriculture.

The control systems for models described by non-commensurate fractional-order differential equations are based on their transformation into large commensurate-order systems, which impose difficulties in determining control laws. In this context, in this paper, a new control method for this class of systems is proposed. The results obtained are based on Lyapunov methods for differential equations with fractional exponents and on the application of the Yakubovich–Kalman–Popov lemma adapted for this class of systems. The stability criterion is presented as a frequency criterion and represented graphically by familiar frequency plots similar to those of the Nyquist or Popov type. If the parameters that define the model can be defined in a closed domain, the frequency criterion can be interpreted as “Popov’s circle criterion”. The two numerical applications present two important cases. The first studies the stability criterion in the case where the viscosity coefficients determine non-commensurate fractional-order exponents in the dynamic model of the system. The second example studies the complex problem of the human–machine system in which the human model imposes dynamics determined by non-commensurate fractional-order systems. The proposed investigation methods allow for a reduction in computational effort by several orders of magnitude for non-commensurate fractional-order systems, eliminate stability conditions that use matrix-based criteria for large-scale systems, and introduce standard frequency-domain criteria.

This paper studies a three-dimensional second-order rational difference system, which generalizes earlier scalar and bidimensional models. We derive explicit closed-form solutions for general initial conditions and identify special cases that simplify the system’s structure. These explicit solutions are particularly significant, as they not only enable rigorous stability analysis but also provide a precise analytical characterization of the system’s long-term behavior, offer deeper insight into its underlying periodic structure, and establish a solid theoretical foundation for potential future applications in the control, prediction, and optimization of multivariable dynamical systems. The analysis carefully addresses conditions ensuring well-defined solutions, avoiding singularities. Numerical simulations illustrate various dynamic behaviors, including oscillations, convergence, and sensitivity to parameters, confirming the richness and robustness of the system’s temporal evolution.

For D:={z∈C:|z|<1}, this paper derives refined conditions for the inclusion of special functions in lemniscate and nephroid domains focusing on solutions to the differential equations of the form znF″(z)+a(z)zn−1F′(z)+b(z)F(z)+d(z)=0,n∈{1,2},z∈D, with normalization F(0)=1, where a(z), b(z) and d(z) are analytic in D. Using advanced techniques from geometric function theory, we generalize and improve existing results, particularly for classes of functions defined by differential equations. Specific applications include generalized Bessel functions, regular Coulomb wave functions, and associated Laguerre polynomials, where we derive improved bounds for their inclusion in lemniscate domains. Additionally, we present open problems, supported by numerical experiments, to guide future research in this direction.

Recall that in On a general second order derivative, Sci. Rep. Tokyo Kyoiku Daigaku A, 5(124–127)(1956), 111–114, Ozaki, Ono and Umezawa proved a result that if f(z) is analytic and satisfies |f″(z)|<1 in the unit disc D=z:z<1, then |f′(z)−1|<1 and so, f(z) is univalent in D, because Re{f′(z)}>0 in D implies univalence by the Noshiro–Warschawski Theorem. In this paper, we obtain another sufficient condition for univalence of f(z) by applying a hypothesis for modulus of arg{f″(z)}.

This paper presents the notion of primal weak structures as a generalized mathematical framework obtained by relaxing the axioms of classical topological spaces. We formally define primal weak structures and provide a detailed investigation of their fundamental properties. Particular attention is given to the operator cw⋄, whose essential characteristics and related properties are analyzed to obtain a comprehensive characterization of primal weak structures. Furthermore, we introduce new constructions denoted by σ(w,P), π(w,P), β(w,P), and α(w,P), and demonstrate that they generate generalized primal topological spaces. These results establish a unifying connection between primal weak structures and existing generalized topological frameworks. In addition, several separation axioms are proposed to distinguish between different classes of primal weak structure spaces. Overall, primal weak structures constitute a flexible and robust class of mathematical models with strong connections to classical topology and significant potential for future applications. The operators and constructions developed in this work provide a solid foundation for further research in this area.

Using the instanton partition function for five-dimensional U(1) gauge theory with eight supercharges and a single adjoint massive hypermultiplet on the Ω background, we give explicit expression for non-perturbative corrections to the topological string theory in the holomorphic limit. It was argued that in this case the theory is compactified on the twisted affine line bundle over C×T2. We perform calculations in two ways. First we modify the integration contour by adding poles responsible for non-perturbative physics in accordance with a recent proposal. Then, we compute the genus zero Gopakumar–Vafa invariants for our case and evaluate the non-perturbative corrections to the partition function. We check that both calculations give the same result.