The paper concerns a quadratic C0 interior penalty method for solving a fourth-order elliptic variational inequality of the second kind which is arising in a plate friction problem. Optimal error estimate is obtained in the energy norm through the introduction of an enriching operator and the assumption that the solution u ∈ H3(Ω). Numerical experiments are presented to demonstrate the theoretical results.

Load frequency control (LFC) plays a key role in improving power system stability and economic security. This is becoming quite challenging with high renewable power penetration into the power grid, as renewable power is typically random and intermittent energy, which gives rise to a huge impact on power quality. This article proposes a robust distributed economic model predictive control (RDEMPC) to incorporate distributed economic optimization and robust control for achieving the frequency regulation task. The local robust controller consists of a nominal distributed model predictive control (DMPC) and an ancillary feedback law. The ancillary term is designed to effectively cope with the wind disturbance, based on the difference between the actual state and the nominal state. The economic indexes, especially the maintenance cost from the wind-power generation, have been incorporated into the RDEMPC design. The stability of the robust distributed economic model predictive controller can be guaranteed by finding a Lyapunov function for each generation area that decreases with time. Simulation on the multiarea hybrid power system demonstrates the effectiveness of the RDEMPC in both improving the economic performance and reducing the wind speed disturbance.

Given a set X and an integer t, let ℱ be a family of k-subsets of X. The Kruskal-Katona theorem states that if |ℱ|≥tk, then |∂_k-1ℱ|≥tk-1. The minimum degree version of this problem asks: if δ(ℱ)≥tk-1, how small can |∂_k-1ℱ| be? In this article, for the case k=3, we prove that, for every sufficiently large integer t, every extremal hypergraph for this problem contains an isolated copy of K_t+1^3 whenever |X| ≥ ct^2 + o(t^2), with the constant c = 1 + √(928/33). Our proof uses a graph transformation that regularizes the neighborhood structure of extremal graphs, reducing the problem to a counting argument on the neighbors of a disjoint clique family. This gives a quadratic-order threshold for the every-extremal version of the problem, compared with the cubic-order threshold of Füredi and Zhao [SIAM J. Discrete Math. 36(4), 2022].

Given a set X and an integer t, let ℱ be a family of k-subsets of X. The Kruskal–Katona theorem states that if |ℱ|≥tk, then |∂_ℓℱ|≥tℓ. The minimum degree version of this problem asks: if δ(ℱ)≥tk-1, how small can |∂_ℓℱ| be? We call a hypergraph extremal if it achieves the minimum value of |∂_ℓℱ| subject to the degree condition δ(ℱ) ≥tk-1. Füredi and Zhao [SIAM J. Discrete Math. 36(4), 2022] proved that for k=3 and ℓ=2, every extremal graph contains an isolated copy of K_t+1^3 when |X| > 1/4(t+1)^2(t+2). In this article, we study the general case k > ℓ≥ 2. By developing a hypergraph transformation that combines shifting operations with antilexicographic compression, we prove that there exists an extremal hypergraph containing an isolated copy of K^k_t+1 whenever |X| > 1/4(t+1)^2t-1ℓ-2 + 2t.

Introduction Underwater acoustic direction-of-arrival (DOA) estimation is fundamental to submarine detection, offshore exploration, and autonomous underwater vehicle navigation, where accurate source localization under severe multipath propagation and low signal-to-noise ratios remains challenging. Existing methods face critical limitations: traditional uniform arrays require extensive physical sensors to achieve sufficient spatial resolution, resulting in high hardware costs; vector sensor arrays typically neglect sparse array geometries that enable virtual aperture expansion; and conventional matrix-based processing discards multidimensional structural information through vectorization, leading to suboptimal performance.Methods To address these challenges, this paper presents a novel tensor-based DOA estimation framework that integrates hybrid scalar-vector sensor arrays (HSVSAs), fourth-order tensor modeling, and higher-order singular value decomposition (HOSVD). The HSVSA architecture combines vector and scalar sensors in a hybrid configuration to create virtual sensors, improving degrees of freedom while reducing hardware complexity. The tensor model preserves spatial-polarization coupling, enabling robust subspace estimation without iterative optimization.Results Simulations demonstrate that the proposed method outperforms conventional approaches.Discussion The proposed framework offers a practical solution for resource-constrained underwater acoustic applications, with potential for further optimization in real-world scenarios.

In this paper, we study a C0 nonsymmetric interior penalty method for the displacement obstacle problem of Kirchhoff plates on two and three dimensional general polygonal/polyhedral domains. We derive the error in an H2-like energy norm that converges in O(h alpha), where alpha is the index of elliptic regularity. Numerical experiments are performed to illustrate the theoretical results.

In this paper, we study a C0 nonsymmetric interior penalty method for an elliptic distributed optimal control problem with pointwise state constraints. The problem is defined on two or three dimensional convex polygonal/polyhedral domains. We derive the convergence of numerical solutions in an H2-like energy norm by using the weak complementarity form. Numerical experiments are performed to illustrate the theoretical results.

Structural load suppression of wind turbines is one of the important means to improve the economic efficiency of wind farm operation. However, wind turbines are complex systems coupled with multiple control variables. There is no comprehensive solution for the flexible and coordinated control of multiple controllable degrees of freedom. The main difficulty lies in the greater optimization burden of multi-degree-of-freedom systems. This paper proposes a variable degree-of-freedom control system for wind turbines, and uses multivariable model predictive control to design collaborative controllers for generator torque, pitch angle and yaw angle. To avoid the increase in complexity caused by the continuous intervention of yaw control, a yaw control cut-in/cut-out strategy is set, and the non-disturbance of switching is theoretically proved. Simulation results show that the proposed variable degree-of-freedom control system can effectively realize active power control and structural load suppression of wind turbines in a large wind speed range. Note to Practitioners-This paper focuses on efficiently using wind turbines' control degrees of freedom to achieve better structural load suppression. The control strategy of existing commercial wind turbines is decentralized. This paper innovatively considers the organic coordination of generator torque, pitch, and yaw angles, and designs two- and three-degree-of-freedom controllers using model predictive control methods. Considering that the yaw angle control should be reduced in practical applications, this paper designs a switching strategy that can achieve disturbance-free switching between two- and three-degree-of-freedom. These works can provide a new development idea for the control framework of wind turbines and better serve the structural load suppression during the operation of wind turbines.

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive error estimates in the energy norm for both the state and the adjoint state, as well as in the L^2 norm of the control variable. Numerical experiments are provided to demonstrate the robustness and effectiveness of the developed scheme.

Let n equivalent to 0 ( mod 3 ) and H-n,n/3(2) be the 3-graph of order n, whose vertex set is partitioned into two sets Sand T of size 1/3n + 1 and 2/3n-1, respectively, and whose edge set consists of all triples with at least 2 vertices in T. Suppose that n is sufficiently large and H is a 3-uniform hypergraph of order n with no isolated vertex. Zhang and Lu [Discrete Math. 341 (2018), 748-758] conjectured that if deg(u) + deg(v) > 2((n-1 2)-(2n/3 2)) for any two vertices u and v that are contained in some edge of H, then H contains a perfect matching or His a subgraph of H-n,n/3(2). We construct a counter-example to the conjecture. Furthermore, for all gamma > 0 and n is an element of 3Z sufficiently large, we prove that if deg(u) + deg(v) > (3/5 + gamma)n(2) for any two vertices u and v that are contained in some edge of H, then H contains a perfect matching or His a subgraph of H-n,n/3(2). This implies a result of Zhang, Zhao and Lu [Electron. J. Combin. 25 (3), 2018]. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Lateral Control algorithms in autonomous vehicles often necessitates an online fine-tuning procedure in the real world. While reinforcement learning (RL) enables vehicles to learn and improve the lateral control performance through repeated trial and error interactions with a dynamic environment, applying RL directly to safety-critical applications in real physical world is challenging because ensuring safety during the learning process remains difficult. To enable safe learning, a promising direction is to make use of previously gathered offline data, which is frequently accessible in engineering applications. In this context, this paper presents a set of knowledge-guided RL algorithms that can not only fully leverage the prior collected offline data without the need of a physics-based simulator, but also allow further online policy improvement in a smooth, safe and efficient manner. To evaluate the effectiveness of the proposed algorithms on a real controller, a hardware-in-the-loop and a miniature vehicle platform are built. Compared with the vanilla RL, behavior cloning and the existing controller, the proposed algorithms realize a closed-loop solution for lateral control problems from offline training to online fine-tuning, making it attractive for future similar RL-based controller to build upon.

Let n ∈ 3ℤ be sufficiently large. Zhang, Zhao and Lu proved that if H is a 3-uniform hypergraph with n vertices and no isolated vertices, and if deg(u)+deg(v) > 2/3n^2 - 8/3n + 2 for any two vertices u and v that are contained in some edge of H, then H admits a perfect matching. In this paper, we prove that the rainbow version of Zhang, Zhao and Lu's result is asymptotically true. More specifically, let δ > 0 and F_1, F_2, …, F_n/3 be 3-uniform hypergraphs on a common set of n vertices. For each i ∈ [n/3], suppose that F_i has no isolated vertices and deg_F_i(u)+deg_F_i(v) > ( 2/3 + δ)n^2 holds for any two vertices u and v that are contained in some edge of F_i. Then { F_1, F_2, …, F_n/3} admits a rainbow matching. Note that this result is asymptotically tight.

A digraph is considered supereulerian if it possesses a spanning closed ditrail. Let n be positive integer and Dn,n be a bipartite digraph, whose vertices are divided into two equal parts of size n. If Dn,n is strongly connected and δ−+δ+≥n+1, where δ− is its minimum in-degree and δ+ is its minimum out-degree, then Dn,n is supereulerian digraph.

Distributed model predictive control is an effective method to realize the power system load frequency control (LFC). However, the frequency stability of the multi-area power system becomes quite challenging with incorporating high wind power penetration, as it brings strong uncertainties. This paper proposes a tube-based distributed model predictive control (DMPC) for the LFC of the interconnected power system. In the scheme, the high penetrated wind power is taken as an independent generation area, in which the virtual inertia control system is incorporated for enhancing the inertia response. The wind turbines are operated under the de-load mode for participating in the frequency regulation, just like the thermal power plants. The tube-based DMPC consists of a nominal MPC and an ancillary feedback law, which aims at restraining the wind speed uncertainty. The neighboring areas' information is incorporated into the ancillary controller as a feedback term, realizing effective coordination between generation areas. The input-to-state stability of the power system under the proposed tube-based DMPC can be guaranteed based on the Schur property and the bounded disturbance condition. The simulation on a four-area interconnected power system demonstrates the effectiveness of proposed algorithm on alleviating the frequency fluctuation caused by varying load and uncertain wind speed.

This paper proposes and analyzes a novel fully discrete finite element scheme with an interpolation operator for stochastic Cahn -Hilliard equations with functionaltype noise. The nonlinear term satisfies a one-sided Lipschitz condition and the diffusion term is globally Lipschitz continuous. The novelties of this paper are threefold. Firstly, the L 2 -stability ( L infinity in time) and H 2 -stability ( L 2 in time) are proved for the proposed scheme. The idea is to utilize the special structure of the matrix assembled by the nonlinear term. None of these stability results has been proved for the fully implicit scheme in existing literature due to the difficulty arising from the interaction of the nonlinearity and the multiplicative noise. Secondly, higher moment stability in L 2 -norm of the discrete solution is established based on the previous stability results. Thirdly, the Holder continuity in time for the strong solution is established under the minimum assumption of the strong solution. Based on these findings, the strong convergence in H - 1 -norm of the discrete solution is discussed. Several numerical experiments including stability and convergence are also presented to validate our theoretical results.

Achieving high attack success rate (ASR) with minimal perturbed distortion has consistently been a prominent and challenging research topic in the field of adversarial examples. In this paper, a novel method to optimize communication signal adversarial examples is proposed by focusing on low-frequency components of perturbations (LFCP). Observations on model attention towards DCT coefficients reveal the crucial role of LFCP within adversarial examples in altering the model’s predictions. As a result, selectively preserving LFCP is established as the fundamental concept of the optimization strategy. By utilizing the binary search algorithm, which considers the inconsistency in the model’s predictions as a constraint, LFCP can be effectively identified, and the aim of minimizing perturbed distortion while maintaining ASR can be achieved. Experimental results conducted on a publicly available dataset, six adversarial attacks and two DNN models, indicate that the proposed method not only significantly minimizes perturbed distortion for FGSM, BIM, PGD, and MI-FGSM but also achieves a modest improvement in ASR. Notably, even for DeepFool and BS-FGM, which introduce small perturbations and exhibit high ASRs, the proposed method can still deliver feasible performance.

We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general second-order elliptic boundary value problems can be used to solve the elliptic optimal control problems with pointwise state constraints. We establish concrete error estimates and numerical experiments are shown to support the theoretical results.

Mobile crowdsensing services are divided into two categories: opportunistic and participatory. In opportunistic mobile crowdsensing services, users do not need to specify the crowdsensing tasks to be completed. Compared with participatory crowdsensing services, the application scope is wider and more user-friendly. In participatory crowdsensing, the service provider assumes that the user can successfully complete the data collection task. However, such an approach cannot work in an opportunistic crowdsensing service because in opportunistic crowdsensing, the user’s execution of the task is uncertain, which brings great challenges to the quality of the crowdsensing service. This article is based on the assumption of the user coverage probability model and transforms the opportunistic mobile crowdsensing value maximization problem into an ordered submodularity value function model with budget constraints. This model is also good at representing participatory crowdsourcing problems. To the best of our knowledge, this is the first study to apply the ordered submodularity feature to a mobile crowdsensing service. Furthermore, we combine the properties of ordered submodular and auction models and propose an ordered submodularity-proportional share mechanism (O-PSM) to solve the allocation and payment problems in opportunistic mobile crowdsensing services. Specifically, in the allocation stage, the winning users are selected based on the proportional share threshold, and in the payment stage, the payment price for the winning users is designed based on critical value theory. We prove that the mechanism satisfies the economic characteristics of individual rationality, truthfulness, and budget feasibility. In the experimental section, the mechanism design based on ordered submodularity is shown to enable the service provider to obtain a higher value and a lower payment.

Let n,s be positive integers such that n is sufficiently large and n≥4s+7. Suppose H is a 3-uniform hypergraph of order n. If H contains no isolated vertex and deg⁡(u)+deg⁡(v)>2((n−12)−(n−s2))+1 for any two vertices u and v that are contained in some edge of H, then H either contains a matching of size s or is a subgraph of Hn,s, where Hn,s is the 3-graph of order n whose vertex set is partitioned into two sets S and T of size n−2s+1 and 2s−1, respectively, and whose edge set consists of all triples with at least 2 vertices in T. This result improves our previous one (Zhang and Lu, 2019 [26]).