Corporate financial risk prediction is crucial for economic stability and sustainable business operations, yet existing methods struggle with complex interdependencies among financial indicators and temporal dynamics. This study addresses the limitations of conventional approaches in handling high-dimensional financial data, weak temporal pattern recognition, and distributional rigidity across sectors by proposing a novel deep learning framework integrating graph transformer networks (GTN), time-series contrastive learning (TSCL) and meta-learning-based adaptive optimisation (Meta-AO). The hybrid architecture combines graph neural networks with transformer attention mechanisms to model enterprise relationships, employs contrastive learning for robust temporal pattern extraction, and utilises meta-learning for cross-domain adaptation. The findings establish that the proposed framework effectively captures relational structures, temporal dynamics, and distributional shifts in financial data, offering a comprehensive solution for accurate risk prediction across diverse market conditions and enterprise types through its hierarchical feature learning paradigm.
In this article we investigate a class of nonlinear p-Laplacian implicit hybrid fractional differential equations involving a combination of Caputo and Riemann-Liouville fractional derivatives. The primary aim is to establish the existence, uniqueness, and Hyers-Ulam stability of solutions to the proposed problem. To achieve this, we employ fixed point theory as the central analytical tool. The theoretical findings are further supported by an example, which demonstrates the effectiveness of the obtained results.
The main objective of this paper is to investigate the oscillatory behaviour of the solutions of the nonlinear elliptic partial differential equations by using the Riccati technique and the integral average method. Our main goal is to establish (1.1) reduced to an ordinary differential equation by using r = | x |. Radial solutions r often arise in the problems with rotational or spherical symmetry and their study is crucial in various fields such as physics, engineering and biology. If D(r) = 0, equation (1.1) becomes a superlinear elliptic equation. If C(r) = 0, equation (1.1) becomes a sublinear elliptic equation. If either lambda = 1, D(r) = 0 or C(r) = 0, mu = 1, then (1.1) is reduced to linear elliptic partial differential equations. We have provided examples to show the effectiveness of our results.
Emotional computing has high computational costs, poor classification accuracy, lack of psychological theoretical support, and physiological signal acquisition is susceptible to noise interference. In response, this study proposes a deep learning based emotion recognition model that predicts a person's psychological state by using EEG signal data. This study preprocesses the proposed framework and extracts features from image data using discrete wavelet transform (DWT) and power spectral density (PSD). DWT extracts features as frequency bands, while PSD exports statistical features and parameters. Afterwards, this study retrieves spatial (channel) and temporal (brain peak and related latency) features from EEG data, and uses a 3D convolutional neural network for emotion classification to evaluate the proposed model. Meanwhile, this study also employs both subject dependent and subject independent procedures. The results indicate that extracting multidimensional complementary features in both frequency and spatial domains can improve recognition ability.
Trajectory controllability represents the strongest form of controllability and has a wide range of applications. This notion has been extensively studied by many researchers for various types of evolution systems. However, to the best of our knowledge, no work in the existing literature has addressed trajectory controllability for evolution systems governed by almost sectorial operators. Motivated by this gap, the present article establishes sufficient conditions for the trajectory controllability of a class of fractional integro-differential evolution systems driven by almost sectorial operators. In our study, both systems with and without state delays are considered. The fractional derivatives involved are of order r is an element of (0, 1) in the Caputo sense. Existence results are obtained using the Banach fixed point theorem, while the controllability results rely on tools such as properties of Mittag-Leffler functions, Gronwall's inequality, functions of type (M), and other key results from fractional calculus and functional analysis. To further support the theoretical findings, illustrative examples are provided.
Existence, regularity and location of solutions to quasilinear singular elliptic systems with general gradient dependence are established developing a method of sub-supersolution. The abstract theorems involving sub-supersolutions are applied to prove the existence of positive solutions for convective and absorption singular systems.
This paper examines the dynamical behaviour of a rational recursive sequence of higher order given by x(k+1) = (delta(11)x(k) +delta(12)x(k-lambda) + delta(13)x(k-mu) + delta(14)x(k-& vartheta;))/(delta(15)x(k) + delta(14)x(k-lambda) + delta(14)x(k-mu) + delta(14)x(k-& vartheta;)), where the initial conditions x(i), i = -n, -n + 1, ..., 0 with n = max{lambda, mu, & vartheta;} are positive real numbers and delta(i) is an element of & Ropf;(+), i = 11, 12, ..., 18. We derive sufficient conditions for local stability, boundedness, periodicity, and global stability of the system. This study enriches the qualitative theory of rational difference equations by extending stability and periodicity analysis to higher order systems. We examine the existence and absence of 2-cycle periodic solutions under different parameter settings. The analytical results are further supported and illustrated through numerical simulations.
This study integrates Bayesian network (BN) and deep learning (DL) models to create a framework for analysing the impact of organisational inertia on business model innovation strategies in the tourism economy. It also employs artificial intelligence (AI) technology to optimise innovation decisions. By comparing models such as graph neural network (GNN), transformer, and reinforcement learning (RL), the study demonstrates the multi-dimensional performance advantages of the optimised BN model. The experiment focuses on core indicators, including innovation investment ratio, market response speed, innovation success rate, revenue growth rate, customer satisfaction, and competitiveness index in the tourism economy. These results suggest that the optimised model is highly adaptable and effective in addressing organisational inertia and enhancing innovation strategies for enterprises operating in the tourism economy.
The rapid development of computer technology has profoundly influenced many disciplines. Computer technology simplifies many problems, increases speed and accuracy, and extends the application of mathematical modelling problems. As a discipline rooted in mathematics, computer science integrates with mathematical modelling to support practical problem solving and socioeconomic development. In the new era, the training objectives of mathematical modelling in China have evolved. This study examined the role of multimedia augmented reality (AR) technology in computer-based mathematical modelling. Multimedia AR technology was applied, and its advantages were analysed. Results showed that the highest scores in Class A and Class B before the experiment were 49. After the experiment, the highest scores of Class A and Class B were 47 and 78, respectively. The grade of Class A did not change much, but that of Class B improved remarkably. These findings suggest that multimedia AR technology holds considerable value for research in computer mathematical modelling.
Eco-epidemiological models provide an effective framework for examining how population interactions and disease transmission shape ecological outcomes. This work investigates a reaction-diffusion predator-prey system based on the Rosenzweig-MacArthur model with a Holling type-IV functional response, where predators are divided into susceptible and infected classes. Analytical results establish positivity conditions and characterise both local stability and diffusion-driven instability using the Routh-Hurwitz criterion. Numerical simulations display diverse dynamics, including limit cycles, travelling waves, spiral structures, and irregular spatio-temporal activity. The study shows that disease-free systems can produce classical Turing patterns under suitable diffusion settings, whereas the presence of infection disrupts these stationary patterns and leads to wave-like or chaotic behaviour. Bifurcation analysis further reveals transitions from stable equilibria to Hopf oscillations and complex regimes, highlighting the strong influence of disease parameters on coexistence and spatial structure. These findings offer new perspectives on ecological stability, resilience, and disease spread in natural predator-prey communities.
The primary objective of this research is to employ the local fractional Sumudu transform decomposition method (LFSTDM) for solving higher-dimensional linear and nonlinear initial boundary value problems (IBVP) characterised by variable coefficients and fractional local derivatives. The findings demonstrate the efficacy of this method in deriving non-differentiable solutions for established problems involving local fractional derivatives. By effectively reducing computational workload, the LFSTDM emerges as a promising approach for addressing such challenges. The following problem is considered: Lm sigma U (r, tau) + R sigma U(r, tau) + N sigma U(r, tau) = g(r, tau).
This study evaluates the effectiveness of various teaching methods in advanced mathematics education by integrating hierarchical clustering with multiple regression analysis, taking into account the heterogeneity of student groups. A two-stage analytical framework was adopted. First, hierarchical clustering was applied to data such as student performance and classroom participation to classify students into distinct groups. Second, separate multiple regression models were developed for each group to examine the influence of key instructional factors - including teaching methods, frequency of technology use, and timeliness of assignment feedback - on academic performance. The experimental data were drawn from three semesters of student records from a university's mathematics department, supplemented by interaction data from an online learning platform. This study offers a novel approach to advanced mathematics instruction, emphasising the value of differentiated teaching and the benefits of integrating technology with pedagogical content to enhance learning outcomes.
The paper analyses the Reissner-Nordstr & ouml;m black hole in the context of quintessence matter and quantum effects, exploring the behaviour of time-like test particles. It employs the Hamilton-Jacobi formulation to assess its suitability in investigating bound motion around black holes with a quantum-corrected metric.
As space design becomes more intelligent and efficient, virtual simulation technology is continuously updated to provide designers with high-quality virtual reality (VR) landscape renderings. Based on market needs, an optimisation design method using Lumion plotting is proposed to enhance the simulation effect of virtual scene software. The process includes key steps such as data collection of the original scene, creation and import of the 3D model of the scene, preliminary rendering of the space model, placement of plants in the space scene, and optimisation of image details. The process utilises SketchUp software to create space models and import them into Lumion software. The results of four simulation design experiments in different scenarios show that the method used is a highly efficient VR space simulation design approach that requires less time and produces better visual results compared to the SketchUp for V-Ray and 3D Studio Max design methods.
This paper examines whether a solution exists for a specific kind of differential equation: a fuzzy, nonlinear, second-order impulsive functional neutral differential equation with non-instantaneous impulses. We do this by applying the power source Banach fixed point theorem, a key idea in mathematical analysis. The controllability outcomes are also governed by the same system. A fuzzy number with properties such as upper semi-continuity, convexity, normality, and compactly supported intervals is the subject of our study. To illustrate the application and value of our theoretical conclusions, we also provide an instance from reality in the conclusion.
In the complex realm of modern e-commerce, accurately modelling user interests and delivering personalised recommendations are essential for enhancing platform efficiency, user satisfaction, and business value. Traditional recommendation algorithms often struggle with key challenges such as capturing dynamic behavioural changes, effectively integrating multimodal features, and maintaining system stability during inference. To address these limitations, this study proposes the adaptive transformer and stability-enhanced network (ATRMST-Net). ATRMST-Net integrates a transformer-based sequential modelling backbone with a system dynamics-inspired stability control mechanism. A multimodal attention fusion module is designed to effectively aggregate heterogeneous user interaction data, enabling a richer understanding of user preferences. Furthermore, the model incorporates a temporal smoothness regularisation term and a Jacobian response control component to enhance robustness and mitigate the impact of noisy or volatile behaviours. Extensive experiments on multiple real-world e-commerce datasets demonstrate that ATRMST-Net consistently outperforms a range of competitive baselines across standard recommendation metrics. Ablation studies further confirm the individual contributions of each model component. Overall, this work provides a theoretically grounded and practically effective solution for building more stable, interpretable, and accurate recommendation systems in dynamic commercial environments.
This article extends the theory of pseudo almost periodic solutions to systems affected by stochastic processes. It investigates the existence, uniqueness, and exponential stability of (mu(1), mu(2))-pseudo almost periodic mild solutions in p(th) mean sense for a general class of stochastic Lasota-Wazewska model with mixed delays. The study relies on the Banach fixed point theorem, the properties of (mu(1), mu(2))-pseudo almost periodic processes in p(th) mean sense, and some stochastic analysis techniques. Moreover, several sufficient conditions are presented to guarantee our objectives. A numerical example is included to illustrate and support the theoretical findings.
