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This article aims to investigate whether differences in ESG ratings have an impact on corporate green innovation behavior. A high-order fixed effects model was established using panel data from Chinese companies from 2009 to 2022 to empirically test the impact of ESG rating divergence in the Chinese market on corporate green innovation behavior.The study demonstrates that ESG rating disparity raises the quantity but lowers the quality of businesses’ green innovation efforts because of the short board effect. After a series of robustness tests, the results are still valid.The mechanism investigation reveals that both an external pressure channel and an internal strategy adjustment channel are responsible for the impact of ESG rating disparity on green innovation efforts. The asymmetry of corporate green innovation activities is exacerbated by managers’ self-interest, whereas the asymmetry of green innovation is mitigated by the caliber of government. According to the heterogeneity analysis, the divergence of a business’s ESG rating between large-scale, non-heavy polluting, and places with strong environmental regulations can effectively slow down the asymmetric behavior of enterprise innovation activities. Additional investigation reveals that the phenomenon of ESG rating divergence spreads across industries and geographical areas. The short board effect of ESG rating divergence can be effectively mitigated by improving the quality of enterprise information disclosure and speeding up the digital transformation of businesses. The research conclusion provides marginal contributions on how to improve China’s ESG rating system and how enterprises can identify ESG rating differences and make scientific decisions.

A geometric intrinsic pre-processing algorithm(GPA for short) for solving large-scale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun (in 2022–2023). Different from traditional preconditioning, the authors apply the intrinsic geometric invariance, the Grid matrix G and the discrete PDE mass matrix B , stiff matrix A satisfies commutative operator BG = GB and AG = GA , where G satisfies G m = I , m ≪ dim( G ). A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain. In this paper, the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle, square, tetrahedron, cube, and so on. They give the general form of pre-processing matrix, theory and numerical test of GPA. The conclusion that “the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron” is obtained through research, and it is further found that “commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm”.

Currently, aspect-based multimodal sentiment analysis remains a highly hot research field, aiming to leverage various modalities such as images and text to determine the sentiment orientation of viewpoint entities. Although deep learning methods have made significant progress in this field, some challenges still exist: incomplete alignment of information between modalities, insufficient interaction and low utilization during modal fusion. To solve these problems, this paper proposes a novel multimodal sentiment analysis model called multilayer interactive attention bottleneck transformer (MIABT) network model. The model contains two key modules: (1) the first is the Multimodal Dynamic Gate (MDG) module, which can dynamically interact to align image features and text features; (2) the second is the Multimodal Attention Bottleneck Transformer (MABT) module, which improves performance at lower computational costs by limiting the flow of information between modalities, only sharing necessary relevant information to restrict cross-modal attention. Experimental results show that the model outperforms the baseline model on two public datasets, Twitter-2015 and Twitter-2017, demonstrating that our proposed approach effectively enhances the accuracy of aspect-based multimodal sentiment analysis tasks.

Currently, aspect-based multimodal sentiment analysis remains a highly hot research field, aiming to leverage various modalities such as images and text to determine the sentiment orientation of viewpoint entities. Although deep learning methods have made significant progress in this field, some challenges still exist: incomplete alignment of information between modalities, insufficient interaction and low utilization during modal fusion. To solve these problems, this paper proposes a novel multimodal sentiment analysis model called multilayer interactive attention bottleneck transformer (MIABT) network model. The model contains two key modules: (1) the first is the Multimodal Dynamic Gate (MDG) module, which can dynamically interact to align image features and text features; (2) the second is the Multimodal Attention Bottleneck Transformer (MABT) module, which improves performance at lower computational costs by limiting the flow of information between modalities, only sharing necessary relevant information to restrict cross-modal attention. Experimental results show that the model outperforms the baseline model on two public datasets, Twitter-2015 and Twitter-2017, demonstrating that our proposed approach effectively enhances the accuracy of aspect-based multimodal sentiment analysis tasks.

The discrete Fourier analysis on the 30°-60°-90° triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group G2, which leads to the definition of four families generalized Chebyshev polynomials. The study of these polynomials leads to a Sturm-Liouville eigenvalue problem that contains two parameters, whose solutions are analogues of the Jacobi polynomials. Under a concept of m-degree and by introducing a new ordering among monomials, these polynomials are shown to share properties of the ordinary orthogonal polynomials. In particular, their common zeros generate cubature rules of Gauss type. [ProQuest: [...] denotes formulae omitted.]

HPL (High Performance Linpack) is a widely accepted benchmark for evaluating high-performance computer clusters. It produces performance results by solving large linear systems, which serves as the measurement of the Top-500 supercomputer ranking. With the increasingly wider performance gap between CPU and GPGPU, non-computing-intensive workload becomes more time-critical and impedes the sustained HPL performance more severely. Traditionally on multi-GPGPU platform, a one-to-one mapping between processes and devices is enforced in HPL. While it brings simplicity for implementation, the even share of the system resources among the processes in each node leads to lower system utilization in the major time-critical algorithmic steps of HPL. In this paper, we propose a novel device-centric HPL approach for current main-stream multi-GPGPU platforms, where each process can make full use of the resources of a node, including accelerators, CPU sockets, PCI-e buses and memory/network bandwidth etc. As a result, the workload on the CPU-end and the inter-process communication are greatly boosted due to higher system utilization, while the computation on the device-end remains efficient. Experiment shows that in the case of a single workstation with 4 GPGPUs, our approach can achieve more than 80 % of the theoretical peak and nearly 95 % of the dgemm performance, which is significantly higher than the state-of-the-art counterpart on the same platform. In the case of multi-GPGPU clusters, we also largely improve the sustained performance and efficiency as compared to previous works of HPL incorporating multi-GPGPU features. Further, based on both performance analysis and the experimental results, we believe that our approach may serve as a competitive cornerstone for further optimizations on future heterogeneous platforms.

Several problems of trigonometric approximation on a hexagon and a triangle are studied using the discrete Fourier transform and orthogonal polynomials of two variables. A discrete Fourier analysis on the regular hexagon is developed in detail, from which the analysis on the triangle is deduced. The results include cubature formulas and interpolation on these domains. In particular, a trigonometric Lagrange interpolation on a triangle is shown to satisfy an explicit compact formula, which is equivalent to the polynomial interpolation on a planar region bounded by Steiner's hypocycloid. The Lebesgue constant of the interpolation is shown to be in the order of (log n)². Furthermore, a Gauss cubature is established on the hypocycloid.

In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of (d + 1)! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallel hexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm (FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT) and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a Laplacian-like operator over these domains is explored.

A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible choices of lattices are discussed in the case of lattices that tile and several new results on cubature and interpolation by trigonometric, as well as algebraic, polynomials are obtained.