Mathematics

The economic operation of hydropower stations has the potential to increase water use efficiency. However, there are some challenges, such as the fixed and unchangeable flow characteristic curve of the hydraulic turbines, and the large number of variables in optimal load distribution, which limit the progress of research. In this paper, we propose a new optimal method of the economic operation of hydropower stations based on improved Long Short-Term Memory neural network (I-LSTM) and Random Forest (RF) algorithm. Firstly, in order to accurately estimate the water consumption, the LSTM model’s hyperparameters are optimized using improved particle swarm optimization, and the I-LSTM method is proposed to fit the flow characteristic curve of the hydraulic turbines. Secondly, the Random Forest machine learning algorithm is introduced to establish a load-distribution model with its powerful feature extraction and learning ability. To improve the accuracy of the load-distribution model, we use the K-means algorithm to cluster the historical data and optimize the parameters of the Random Forest model. A Hydropower Station in China is selected for a case study. It is shown that (1) the I-LSTM method fits the operating characteristics under various working conditions and actual operating characteristics of hydraulic turbines, ensuring that they are closest to the actual operating state; (2) the I-LSTM method is compared with Support Vector Machine (SVM), Extreme Learning Machine (ELM) and Long Short-Term Memory neural network (LSTM). The prediction results of SVM have a large error, but compared with ELM and LSTM, MSE is reduced by about 46% and 38% respectively. MAE is reduced by about 25% and 21%, respectively. RMSE is reduced by about 27% and 24%, respectively; (3) the RF algorithm performs better than the traditional dynamic programming algorithm in load distribution. With the passage of time and the increase in training samples, the prediction accuracy of the Random Forest model has steadily improved, which helps to achieve optimal operation of the units, reducing their average total water consumption by 1.24%. This study provides strong support for the application of intelligent low-consumption optimization strategies in hydropower fields, which can bring higher economic benefits and resource savings to renewable energy production. Full article

In this study, the portfolio optimization problem is explored, using a combination of classical and quantum computing techniques. The portfolio optimization problem with specific objectives or constraints is often a quadratic optimization problem, due to the quadratic nature of, for example, risk measures. Quantum computing is a promising solution for quadratic optimization problems, as it can leverage quantum annealing and quantum approximate optimization algorithms, which are expected to tackle these problems more efficiently. Quantum computing takes advantage of quantum phenomena like superposition and entanglement. In this paper, a specific problem is introduced, where a portfolio of loans need to be optimized for 2030, considering `Return on Capital’ and `Concentration Risk’ objectives, as well as a carbon footprint constraint. This paper introduces the formulation of the problem and how it can be optimized using quantum computing, using a reformulation of the problem as a quadratic unconstrained binary optimization (QUBO) problem. Two QUBO formulations are presented, each addressing different aspects of the problem. The QUBO formulation succeeded in finding solutions that met the emission constraint, although classical simulated annealing still outperformed quantum annealing in solving this QUBO, in terms of solutions close to the Pareto frontier. Overall, this paper provides insights into how quantum computing can address complex optimization problems in the financial sector. It also highlights the potential of quantum computing for providing more efficient and robust solutions for portfolio management. Full article

Accurate traffic prediction is pivotal when constructing intelligent cities to enhance urban mobility and to efficiently manage traffic flows. Traditional deep learning-based traffic prediction models primarily focus on capturing spatial and temporal dependencies, thus overlooking the existence of spatial and temporal heterogeneities. Heterogeneity is a crucial inherent characteristic of traffic data for the practical applications of traffic prediction. Spatial heterogeneities refer to the differences in traffic patterns across different regions, e.g., variations in traffic flow between office and commercial areas. Temporal heterogeneities refer to the changes in traffic patterns across different time steps, e.g., from morning to evening. Although existing models attempt to capture heterogeneities through predefined handcrafted features, multiple sets of parameters, and the fusion of spatial–temporal graphs, there are still some limitations. We propose a self-supervised learning-based traffic prediction framework called Traffic Prediction with Self-Supervised Learning (TPSSL) to address this issue. This framework leverages a spatial–temporal encoder for the prediction task and introduces adaptive data masking to enhance the robustness of the model against noise disturbances. Moreover, we introduce two auxiliary self-supervised learning paradigms to capture spatial heterogeneities and temporal heterogeneities, which also enrich the embeddings of the primary prediction task. We conduct experiments on four widely used traffic flow datasets, and the results demonstrate that TPSSL achieves state-of-the-art performance in traffic prediction tasks. Full article

The perishable nature of vegetable commodities poses challenges for superstores, as reselling them is often unfeasible due to their short freshness period. Reliable market demand analysis is crucial for boosting revenue. This study simplifies the pricing and replenishment decision-making process by making reasonable assumptions about the selling time, wastage rate, and replenishment time for vegetable commodities. A single-objective planning model with the objective of profit maximization was constructed by fitting historical data using the nonparametric method of support vector regression (SVR). The study reveals a specific relationship between sales volume and cost-plus pricing for each category and predicts future cost changes using an LSTM model. Combining these findings, we substitute the relationship between sales volume and pricing as well as the LSTM prediction data into the model, and solve it using genetic algorithms in machine learning to derive the optimal replenishment volume and pricing strategy. Practical results show that the method can provide reasonable pricing and replenishment strategies for vegetable superstores, and after careful accounting, we arrive at an expected profit of RMB 22,703.14. The actual profit of the supermarket was RMB 19,732.89. The method, therefore, increases the profit of the vegetable superstore by 13.08%. By optimizing inventory management and pricing decisions, the superstore can better meet the challenges of vegetable commodities and achieve sustainable development. Full article

In this article, when $2\le p\le 4$, we establish the $C_{\mathrm{loc}}^{0,1}$-regularity of weak solutions to the degenerate parabolic p-Laplacian equation ${\partial }_{t}u=-{\displaystyle \sum _{i=1}^6}{X}_i^{*}(|{\nabla }_{\mathcal{H}}u{|}^{p-2}{X}_{i}u)$ on the group SU(3) granted with horizontal vector fields $X_1, \dots , X_6$. Compared to the Heisenberg group, ${\mathbb{H}}^n$, we obtained the optimal range of p; that is, $2\le p\le 4$. Full article

Skewness and bimodality properties are frequently observed when analyzing environmental data such as wind speeds, precipitation levels, and ambient temperatures. As an alternative to modeling data exhibiting these properties, we propose a flexible extension of the skew-logistic distribution. The proposal corresponds to a weighted version of the skewed logistic distribution, defined by a parametric weight function that allows shapes with up to three modes for the resulting density. Parameter estimation via the maximum likelihood approach is discussed. Simulation experiments are carried out to evaluate the performance of the estimators. Applications to environmental data illustrating the utility of the proposal are presented. Full article

Vulnerabilities are often accompanied by cyberattacks. CVE is the largest repository of open vulnerabilities, which keeps expanding. ATT&CK models known multi-step attacks both tactically and technically and remains up to date. It is valuable to correlate the vulnerability in CVE with the corresponding tactic and technique of ATT&CK which exploit the vulnerability, for active defense. Mappings manually is not only time-consuming but also difficult to keep up-to-date. Existing language-based automated mapping methods do not utilize the information associated with attack behaviors outside of CVE and ATT&CK and are therefore ineffective. In this paper, we propose a novel framework named VTT-LLM for mapping Vulnerabilities to Tactics and Techniques based on Large Language Models, which consists of a generation model and a mapping model. In order to generate fine-tuning instructions for LLM, we create a template to extract knowledge of CWE (a standardized list of common weaknesses) and CAPEC (a standardized list of common attack patterns). We train the generation model of VTT-LLM by fine-tuning the LLM according to the above instructions. The generation model correlates vulnerability and attack through their descriptions. The mapping model transforms the descriptions of ATT&CK tactics and techniques into vectors through text embedding and further associates them with attacks through semantic matching. By leveraging the knowledge of CWE and CAPEC, VTT-LLM can eventually automate the process of linking vulnerabilities in CVE to the attack techniques and tactics of ATT&CK. Experiments on the latest public dataset, ChatGPT-VDMEval, show the effectiveness of VTT-LLM with an accuracy of 85.18%, which is 13.69% and 54.42% higher than the existing CVET and ChatGPT-based methods, respectively. In addition, compared to fine-tuning without outside knowledge, the accuracy of VTT-LLM with chain fine-tuning is 9.24% higher on average across different LLMs. Full article

Digital financial inclusion and common prosperity are pivotal elements in promoting the sustainable socioeconomic development of China. This study introduces a novel Multi-Criteria Decision Analysis (MCDA) method to evaluate the Common Prosperity Index (CPI). Using this index, alongside the Digital Financial Inclusion Index (DFII) released by Peking University, it examines the evolution of the coupling coordination relationship between digital financial inclusion and common prosperity within the Yangtze River Delta (YRD) urban agglomeration from 2011 to 2021. By integrating gravity models and social network analysis, in this paper, we thoroughly investigate the spatiotemporal evolution characteristics of the spatial network of this coupling coordination relationship. The results indicate that both the DFII and CPI generally exhibit an upward trend, but the decline in the coupling degree reflects a weakened interaction strength between them. Specifically, Anhui significantly lags behind Jiangsu, Zhejiang, and Shanghai in the development of digital financial inclusion and common prosperity, indicating regional development imbalances. Furthermore, the strength of spatial connections in city coupling coordination has significantly increased, with Nanjing’s siphon effect on cities in Anhui becoming markedly stronger, and the number of core cities in the network increasing, which demonstrates a geographical proximity feature in network development. Additionally, the overall network characteristics are transitioning towards higher density and “small-world” properties, suggesting a trend toward network stabilization. The disparity in centrality among cities has decreased, with an overall enhancement in centrality, where the spatial spillover effects from core areas such as Hangzhou-Ningbo, Nanjing-Changzhou, and Shanghai-Suzhou-Wuxi significantly promote the development of peripheral cities. Based on these findings, this paper proposes policy recommendations for the sustainable development of digital financial inclusion and common prosperity in the YRD region. Full article

In this paper, we concentrate on the propagation dynamics of stochastic reaction–diffusion equations, including the existence of travelling wave solution and asymptotic wave speed. Based on the stochastic Feynman–Kac formula and comparison principle, the boundedness of the solution of stochastic reaction–diffusion equations can be obtained so that we can construct a sup-solution and a sub-solution to estimate the upper bound and the lower bound of wave speed. Full article

Reversible data hiding (RDH) is an advanced data protection technology that allows the embedding of additional information into an original digital medium while maintaining its integrity. Color images are typical carriers for information because of their rich data content, making them suitable for data embedding. Compared to grayscale images, color images with their three color channels (RGB) enhance data embedding capabilities while increasing algorithmic complexity. When implementing RDH in color images, researchers often exploit the inter-channel correlation to enhance embedding efficiency and minimize the impact on image visual quality. This paper proposes a novel RDH method for color images based on inter-channel correlation modeling and improved skewed histogram shifting. Initially, we construct an inter-channel correlation model based on the relationship among the RGB channels. Subsequently, an extended method for calculating the local complexity of pixels is proposed. Then, we adaptively select the pixel prediction context and design three types of extreme predictors. The improved skewed histogram shifting method is utilized for data embedding and extraction. Finally, experiments conducted on the USC-SIPI and Kodak datasets validate the superiority of our proposed method in terms of image fidelity. Full article

Supersonic flow over a half-angle wedge (θ = 15°) with an upstream Mach number of 2.0 was investigated using 2D Euler equations where sea level conditions were considered. The investigation employed the Steger–Warming flux vector splitting (FVS) method executed in MATLAB 9.13.0 (R2022b) software. The study involved a meticulous comparison between theoretical calculations and numerical results. Particularly, the research emphasized the angle of oblique shock and downstream flow properties. A substantial iteration count of 2000 iteratively refined the outcomes, underscoring the role of advanced computational resources. Validation and comparative assessment were conducted to elucidate the superiority of the Steger–Warming flux vector splitting (FVS) scheme over existing methodologies. This research serves as a link between theoretical rigor and practical applications in high-speed aerospace design, enhancing the efficiency of aircraft components. Full article

White light cystoscopy is the gold standard for the diagnosis of bladder cancer. Automatic and accurate tumor detection is essential to improve the surgical resection of bladder cancer and reduce tumor recurrence. At present, Transformer-based medical image segmentation algorithms face challenges in restoring fine-grained detail information and local boundary information of features and have limited adaptability to multi-scale features of lesions. To address these issues, we propose a new multi-scale detail-enhanced reverse attention network, MDER-Net, for accurate and robust bladder tumor segmentation. Firstly, we propose a new multi-scale efficient channel attention module (MECA) to process four different levels of features extracted by the PVT v2 encoder to adapt to the multi-scale changes in bladder tumors; secondly, we use the dense aggregation module (DA) to aggregate multi-scale advanced semantic feature information; then, the similarity aggregation module (SAM) is used to fuse multi-scale high-level and low-level features, complementing each other in position and detail information; finally, we propose a new detail-enhanced reverse attention module (DERA) to capture non-salient boundary features and gradually explore supplementing tumor boundary feature information and fine-grained detail information; in addition, we propose a new efficient channel space attention module (ECSA) that enhances local context and improves segmentation performance by suppressing redundant information in low-level features. Extensive experiments on the bladder tumor dataset BtAMU, established in this article, and five publicly available polyp datasets show that MDER-Net outperforms eight state-of-the-art (SOTA) methods in terms of effectiveness, robustness, and generalization ability. Full article

We consider a nonlinear Dirichlet problem driven by the $(p(z),q)$-Laplacian and with a logistic reaction of the equidiffusive type. Under a nonlinearity condition on a quotient map, we show existence and uniqueness of positive solutions and the result is global in parameter $\lambda$. If the monotonicity condition on the quotient map is not true, we can no longer guarantee uniqueness, but we can show the existence of a minimal solution $u_{\lambda }^{*}$ and establish the monotonicity of the map $\lambda ⟼u_{\lambda }^{*}$ and its asymptotic behaviour as the parameter $\lambda$ decreases to the critical value ${\widehat{\lambda }}_1(q)>0$ (the principal eigenvalue of $(-{\Delta }_q,W_0^{1,q}(\Omega ))$). Full article

In this article, we delve into the study of statistical solitons on submanifolds of Kenmotsu statistical manifolds, introducing the presence of concircular vector fields. This investigation is further extended to study the behavior of almost quasi-Yamabe solitons on submanifolds with both concircular and concurrent vector fields. Concluding our research, we offer a compelling example featuring a 5-dimensional Kenmotsu statistical manifold that accommodates both a statistical soliton and an almost quasi-Yamabe soliton. This example serves to reinforce and validate the principles discussed throughout our study. Full article

The conventional approach of the local convergence analysis of an iterative method on ${\mathbb{R}}^m$, with m a natural number, depends on Taylor series expansion. This technique often requires the calculation of high-order derivatives. However, those derivatives may not be part of the proposed method(s). In this way, the method(s) can face several limitations, particularly the use of higher-order derivatives and a lack of information about a priori computable error bounds on the solution distance or uniqueness. In this paper, we address these drawbacks by conducting the local convergence analysis within the broader framework of a Banach space. We have selected an important family of high convergence order methods to demonstrate our technique as an example. However, due to its generality, our technique can be used on any other iterative method using inverses of linear operators along the same line. Our analysis not only extends in ${\mathbb{R}}^m$ spaces but also provides convergence conditions based on the operators used in the method, which offer the applicability of the method in a broader area. Additionally, we introduce a novel semilocal convergence analysis not presented before in such studies. Both forms of convergence analysis depend on the concept of generalized continuity and provide a deeper understanding of convergence properties. Our methodology not only enhances the applicability of the suggested method(s) but also provides suitability for applied science problems. The computational results also support the theoretical aspects. Full article

Currently, various light-emitting diode (LED) lighting systems are being developed because LEDs are one of the most used lighting sources for work environments, buildings, homes, and public roads in terms of some of their applications. Similarly, they have low energy consumption, quick responses, and excellent optimal performance in their operation. However, these systems still need to precisely regulate lighting, maintain stable voltage and current in the presence of faults and disturbances, and have a wide range of operations in the event of trajectory changes or monitoring tasks regarding the desired voltage and current. This work presents the design and application of two types of robust controllers (structure-at-infinity control and geometric control) applied to an LED driver using a buck converter. The controllers aim to follow the desired trajectories, attenuate disturbances at the power supply input, and compensate for faults in the actuator (MOSFET) to keep the capacitor voltage and inductor current stable. When comparing the results obtained with the two controllers, it was observed that both present excellent performance in the presence of constant disturbances. However, in scenarios in which variable faults and path changes are implemented, the structure-at-infinity control method shows an overimpulse of output voltage and current ranging from 39 to 42 volts and from 0.3 to 0.45 A, with a margin of error of 1%, and it can generate a failure in the LED driver using a buck converter. On the other hand, when using geometric control, the results are satisfactory, achieving attenuating constant disturbances and variable faults, reaching the desired voltage (40 v to 35 v) and current (0.3 to 0.25 A) with a margin of error of 0.05%, guaranteeing a system without overvoltages or the accelerated degradation of the components due to magnetic conductivity. Full article

In this paper, the fixed-time and preassigned-time synchronization issues of fully quaternion-valued fuzzy memristive neural networks are studied based on the dynamic event-triggered control mechanism. Initially, the fuzzy rules are defined within the quaternion domain and the relevant properties are established through rigorous analysis. Subsequently, to conserve resources and enhance the efficiency of the controller, a kind of dynamic event-triggered control mechanism is introduced for the fuzzy memristive neural networks. Based on the non-separation analysis, fixed-time and preassigned-time synchronization criteria are presented and the Zeno phenomenon under the event-triggered mechanism is excluded successfully. Finally, the effectiveness of the theoretical results is verified through numerical simulations. Full article

This article investigates certain fixed-point results enjoying nonlinear almost contraction conditions in the setup of relational metric space. Some examples are constructed in order to indicate the profitability of our results. As a practical use of our findings, we demonstrate the existence of a unique solution to a specific first-order boundary value problem. Full article

We prove a strong theorem on the partial non-defectivity of secant varieties of embedded homogeneous varieties developing a general set-up for families of subvarieties of Grassmannians. We study this type of problem in the more general set-up of joins of embedded varieties. Joins are defined by taking a closure. We study the set obtained before making the closure (often called the open part of the join) and the set added after making the closure (called the boundary of the join). For a point q of the open part, we give conditions for the uniqueness of the set proving that q is in the open part. Full article