Search Results (30)

Fractional heat conduction models extend classical formulations by incorporating fractional differential operators that capture multiscale relaxation effects. In this work, we introduce an electrical analogy that represents the action of these operators via generalized longitudinal impedance and admittance elements, thereby clarifying their physical role in energy transfer: fractional derivatives account for the redistribution of heat accumulation and dissipation within micro-scale heterogeneous structures. This analogy unifies different classes of fractional models—diffusive, wave-like, and mixed—as well as distinct fractional operator types, including the Caputo and Atangana–Baleanu forms. It also provides a general computational methodology for solving heat conduction problems through the concept of thermal impedance, defined as the ratio of surface temperature variations (relative to ambient equilibrium) to the applied heat flux. The approach is illustrated for a semi-infinite sample, where different models and operators are shown to generate characteristic spectral patterns in thermal impedance. By linking these spectral signatures of microstructural relaxation to experimentally measurable quantities, the framework not only establishes a unified theoretical foundation but also offers a practical computational tool for identifying relaxation mechanisms through impedance analysis in microscale thermal transport. Full article

This paper investigates the structural properties of solutions of vector equilibrium systems and mixed variational inequalities in topological vector spaces. Based on Himmelberg-type fixed point theorem, combined with the analysis of set-valued mapping and quasi-monotone conditions, the existence criteria of solutions for two classes of generalized equilibrium problems with weak compactness constraints are constructed. This work introduces an innovative application of the measurable selection theorem of semi-continuous function space to eliminate the traditional compactness constraints, and provides a more universal theoretical framework for game theory and the economic equilibrium model. In the analysis of mixed variational problems, the topological stability of the solution set under the action of generalized monotone mappings is revealed by constructing a new KKM class of mappings and introducing the theory of pseudomonotone operators. In particular, by replacing the classical compactness assumption with pseudo-compactness, this study successfully extends the research boundary of scholars on variational inequalities, and its innovations are mainly reflected in the following aspects: (1) constructing a weak convergence analysis framework applicable to locally convex topological vector spaces, (2) optimizing the monotonicity constraint of mappings by introducing a semi-continuous asymmetric condition, and (3) in the proof of the nonemptiness of the solution set, the approximation technique based on the family of relatively nearest neighbor fields is developed. The results not only improve the theoretical system of variational analysis, but also provide a new mathematical tool for the non-compact parameter space analysis of economic equilibrium models and engineering optimization problems. This work presents a novel combination of measurable selection theory and pseudomonotone operator theory to handle non-compact constraints, advancing the theoretical framework for economic equilibrium analysis. Full article

This work shows a three-dimensional (3D) layerwise model for static and free vibration analyses of functionally graded piezomagnetic materials (FGPM) spherical shell structures where magnetic and elastic fields are completely coupled. The 3D magneto-elastic governing equations for spherical shells are made of the three equations of equilibrium in three-dimensional form and the three-dimensional divergence equation for the magnetic induction. Governing equations are written in the orthogonal mixed curvilinear reference system ($\alpha$, $\beta$, z) allowing the analysis of several curved and flat geometries (plates, cylindrical shells and spherical shells) thanks to proper considerations of the radii of curvature. The static cases, actuator and sensor configurations and free vibration investigations are proposed. The resolution method uses the imposition of the Navier’s harmonic forms in the two in-plane directions and the exponential matrix methodology in the transverse normal direction. Single-layered and multilayered simply-supported FGPM structures have been investigated. In order to understand the behavior of FGPM structures, numerical values and trends along the thickness direction for displacements, stresses, magnetic potential, magnetic induction and free vibration modes are proposed. In the results section, a first assessment phase is proposed to demonstrate the validity of the formulation and to fix proper values for the convergence of results. Therefore, a new benchmark section is presented. Different cases are proposed for several material configurations, load boundary conditions and geometries. The possible effects involved in this problem (magneto-elastic coupling and effects related to embedded materials and thickness values of the layers) are discussed in depth for each thickness ratio. The innovative feature proposed in the present paper is the exact 3D study of magneto-elastic coupling effects in FGPM plates and shells for static and free vibration analyses by means of a unique and general formulation. Full article

The growing penetration of renewable energy sources (RES) has exacerbated operational flexibility deficiencies in modern power systems under time-varying conditions. To address the limitations of existing flexibility management approaches, which often exhibit excessive conservatism or risk exposure in managing supply–demand uncertainties, this study introduces a data-driven distributionally robust optimization (DRO) framework for power system scheduling. The methodology comprises three key phases: First, a meteorologically aware uncertainty characterization model is developed using Copula theory, explicitly capturing spatiotemporal correlations in wind and PV power outputs. System flexibility requirements are quantified through integrated scenario-interval analysis, augmented by flexibility adjustment factors (FAFs) that mathematically describe heterogeneous resource participation in multi-scale flexibility provision. These innovations facilitate the formulation of physics-informed flexibility equilibrium constraints. Second, a two-stage DRO model is established, incorporating demand-side resources such as electric vehicle fleets as flexibility providers. The optimization objective aims to minimize total operational costs, encompassing resource activation expenses and flexibility deficit penalties. To strike a balance between robustness and reduced conservatism, polyhedral ambiguity sets bounded by generalized moment constraints are employed, leveraging Wasserstein metric-based probability density regularization to diminish the probabilities of extreme scenarios. Third, the bilevel optimization structure is transformed into a solvable mixed-integer programming problem using a zero-sum game equivalence. This problem is subsequently solved using an enhanced column-and-constraint generation (C&CG) algorithm with adaptive cut generation. Finally, simulation results demonstrate that the proposed model positively impacts the flexibility margin and economy of the power system, compared to traditional uncertainty models. Full article

This paper studies nonlinear mixed variational-like inequalities under generalized quasimonotone mappings in Banach spaces. The main objective of this work is to relax the well-known KKM (Knaster–Kuratowski–Mazurkiewicz) condition which is extensively used in the literature to prove the existence of solutions for variational inequalities and equilibrium problems, and to establish the existence of solutions for the nonlinear mixed variational-like inequalities, which uncovers another approach of solving variational inequalities. Further, we propose an iterative algorithm to find approximate solutions to our problem and to study its convergence criteria. Finally, as an application, we find a gap function for nonlinear mixed variational-like inequalities, which uncovers another way of solving our variational-like inequalities using the methods of solutions and algorithms of the optimization problems. Full article

Motivated by the operational scenarios of lock scheduling, we propose a serial-lock chain navigation problem (SLCNP) modeled on the Three Gorges-Gezhouba Dam (TGGD) for the first time. Ship grouping, synchronized moving, and grouped waiting operations are integrated into the ship navigation process. A mixed integer programming (MIP) model that incorporates real-world constraints such as ship priority, service fairness, traffic flow equilibrium, and phased ship placement is presented to optimize ship throughput and ship stay time. To solve the SLCNP, a sort-pick strategy-based swarm intelligence algorithm (SPSSIA) framework is developed that integrates the characteristics of SLCNP through a hybrid multi-section encoding method and a two-stage heuristic decoding approach. A swarm intelligence evolution mechanism is used to improve the search ability and robustness of the framework. Several instances are generated based on real data to verify the correctness and effectiveness of the model and algorithm. Computational results demonstrate the applicability and effectiveness of the proposed SPSSIA. Further analysis of the experimental results indicates that the key impact factors significantly influence the navigational performance of the TGGD system. The results of this study will provide practical guidance for the operational processes of inland river hubs with comparable characteristics. Full article

Unconventional events exacerbate the imbalance between regional transportation demand and limited road network resources. Scientific and efficient path planning serves as the foundation for rapidly restoring equilibrium to the road network. In real large-scale road networks, especially during emergencies, it is usually difficult to obtain or predict accurate dynamic traffic network flows in real-time, which is used to support equilibrium path planning. Moreover, the traditional iterative methods cannot meet the real-time demand of emergency equilibrium path planning decision generation. To solve the above problems, this paper proposes a hybrid control architecture for path planning based on equilibrium traffic assignment theory. The architecture introduces the travelers’ real-time travel data and constructs a spatio-temporal neural network, which captures the evolution of traffic network loads. Adaptive multi-graph fusion technology is used to mix the background traffic flow data and the traveler’s real-time Origin–Destination (OD) data, to mine the dynamic correlation between the traffic state and the travelers’ travel. Based on the real-time prediction of dynamic network states, equilibrium mapping learning is carried out to pre-allocate potential travel demands and construct equilibrium traffic graphs based on system optimization traffic assignment. Finally, individual evacuation path strategies are generated online in a data-driven manner in real time to achieve improved resilience in the transportation system. Full article

This paper is to study finite horizon linear quadratic (LQ) non-zero sum Nash game for discrete-time infinite Markov jump stochastic systems (IMJSSs). Based on the theory of stochastic analysis, a countably infinite set of coupled generalized algebraic Riccati equations are solved and a necessary and sufficient condition for the existence of Nash equilibrium points is obtained. From a new perspective, the finite horizon mixed robust $H_2/H_{\infty }$ control is investigated, and summarize the relationship between Nash game and $H_2/H_{\infty }$ control problem. Moreover, the feasibility and validity of the proposed method has been proved by applying it to a numerical example. Full article

This research addresses the efficient integration and sizing of flexible alternating current transmission systems (FACTS) in electrical distribution networks via a convex optimization approach. The exact mixed-integer nonlinear programming (MINLP) model associated with FACTS siting and sizing aims for the minimization of the expected annual operating costs of the network (i.e., energy losses and FACTS purchasing costs). The constraints of this problem include power equilibrium equalities, voltage regulation bounds, and device capacities, among others. Due to the power equilibrium constraints per node and period, the MINLP model is a non-convex optimization problem. To transform the exact MINLP model into a mixed-integer convex one, the approximation of the product between two variables in the complex domain is relaxed through its hyperbolic equivalent, which generates a set of convex cones. The main advantage of the proposed mixed-integer convex model is that it ensures the global optimum of the problem, even when considering objective multiplexes. Numerical simulations in the IEEE 33-, 69-, and 85-bus grids demonstrate the effectiveness and robustness of FACTS integration via the proposed convex approach in comparison with the exact solution of the MINLP model in the GAMS software as well as with combinatorial optimization algorithms (i.e., the black widow optimizer and the vortex search algorithm). All simulations were carried out in MATLAB with Yalmip optimization and the Gurobi and Mosek solvers. The simulation results show that, for a fixed operation of the FACTS devices (i.e., a VAR compensator) during the day, the annual operating costs are reduced by 12.63%, 13.97%, and 26.53% for the IEEE 33-, 69-, and 85-bus test systems, respectively, while for the operation variable, the reductions are by 14.24%, 15.79%, and 30.31%, respectively. Full article

Optimizing the train plan for high-speed rail systems should consider both the passengers’ demands and enterprise’s benefits. The choice of the departure time period is the most important factor affecting the passenger demand distribution. In this paper, the optimization problem of a train operation plan based on time period preference is studied for a high-speed rail corridor. First, according to the travel process of the passengers, the extended service network for a high-speed rail system is established. The main factors that influence the passengers’ travel choices are analyzed, and the departure time period preference, stop time and flexible pricing strategy based on the time period preference are put forward. The generalized travel cost function, including the convenience, ticket fare and stop time costs, is constructed, and a two-level programming model is established based on the function. The upper-level planning model is formulated as a mixed 0–1 programming problem that aims at maximizing the revenue of the railway enterprise. It is mainly constrained by passenger travel demand and solved by improved genetic algorithms. The lower-level model is a user equilibrium (UE) model. The Frank–Wolfe algorithm is used to allocate multiple groups of OD (origin and destination) passenger flows to each train so that the generalized travel expenses of all the passengers with the same OD are minimized and equal. Finally, the train operation plan is solved based on the Lan-xi (Lanzhou–Xi’an) high-speed rail data, and the validity of both the model and algorithm is verified. Full article

The paper explores the emergence and consequence of contract farming as a new subsector of agriculture in a small open developing economy, applying the theory of finite change in a general equilibrium framework. In this paper, we analyze the entry of a cash crop-producing foreign contract farming (CF) subsector within the agricultural sector of a country. Entry requires a cash crop price that is substantially above the price of the food crop already being produced within the country. CF (a) increases GDP and hence aggregate economic welfare; (b) may make income distribution more skewed; (c) reduces domestic production of food and hence, (d) increases food import and hence food insecurity. Thus, CF might imply a trade-off between inequality and growth. We employ a variant of the 3 × 3 mixed specific factor-Heckscher Ohlin general equilibrium model of production and trade where introduction of a new policy may lead to the emergence of a new sector resulting in finite changes where we show the possibilities of sectoral diversification with combinations of contract farming vis-à-vis traditional agriculture under some plausible conditions. Our results seem to be consistent when compared to some empirically robust conclusions found in the literature and some secondary data available on the FAO website. We also argue that the food insecurity problem gets aggravated as more and more countries engage in contract farming. Policy simulations identify critical parameters confirming the dominance of distribution over the growth effect in terms of a social welfare function. Simulations imply that there could be a food insecurity problem, as rises in GDP could result in increasing inequality so that government—to preserve social welfare—could restrict the extent of contract farming if non-food-producing sectors expand, causing terms-of-trade deterioration of food-importing nations. Full article

With the growing proportion of advanced metering infrastructures and intelligent controllable equipment in power grids, demand response has been regarded as an effective and easily implemented approach to meet the demand–supply equilibrium. This paper innovatively proposes generalized demand-side resources combining the demand response with an energy storage system and constructs a configuration model to obtain scheduling plans. Firstly, this paper analyzes the characteristics of generalized demand-side resources and models the translational loads, reducible loads and energy storage system. Secondly, a deterministic energy storage configuration model aiming at achieving the lowest operation cost of distribution networks is established, from which the scheduling scheme of generalized demand-side resources can be obtained. Then, the fuzzy membership function and the probability density function are used to represent the uncertainty of the demand response, the prediction error of renewable energy output and the generalized demand-side resources that do not participate in the demand response. Therefore, this paper simulates daily operations to modify the capacity of energy storage. The problem is solved by using Monte Carlo simulation, fuzzy chance-constrained programming and mixed-integer programming. Finally, the effectiveness of this model is demonstrated with case studies in a 33-node distribution network. The results show that the uncertainty of this system is solved effectively. When only considering generalized demand-side resources, the total cost is reduced by 9.5%. After considering the uncertainty, the total cost is also decreased 0.3%. Simultaneously, the validity of the model is verified. Full article

Fixed point theory provides an important structure for the study of symmetry in mathematics. In this article, a new iterative method (general Picard–Mann) to approximate fixed points of nonexpansive mappings is introduced and studied. We study the stability of this newly established method which we find to be summably almost stable for contractive mappings. A number of weak and strong convergence theorems of such iterative methods are established in the setting of Banach spaces under certain geometrical assumptions. Finally, we present a number of applications to address various important problems (zero of an accretive operator, mixed equilibrium problem, convex optimization problem, split feasibility problem, periodic solution of a nonlinear evolution equation) appearing in the field of nonlinear analysis. Full article

In this work, we consider bilevel problems: variational inequality problems over the set of solutions of the generalized mixed equilibrium problems. Two new inertial extragradient methods are proposed for solving these problems. Under appropriate conditions, we prove strong convergence theorems for the proposed methods by the regularization technique. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms. Full article

This paper is devoted to introducing a new viscosity approximation method using the implicit midpoint rules for finding a common element in the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a general system of variational inequalities and the set of common fixed points of a finite family of nonexpansive mappings in a symmetric Hilbert space. Then, we prove a strong convergence theorem regarding the proposed iterative scheme under some suitable conditions on the parameters. Finally, we provide two numerical results to show the consistency and accuracy of the scheme. One of them, moreover, compares the behavior of our scheme with the iterative scheme of Ke and Ma (Fixed Point Theory Appl 190, 2015). Full article