摘要：
In this paper, a linearized numerical scheme of nonlinear variable-order fractional diffusion equation with time delay is constructed. We apply the L2-1(sigma) formula to discretize the temporal derivative and second-order central difference scheme to discretize the spatial derivative. The proposed method is unconditionally stable and convergent with O(tau(2)+h(2)), where tau and h are the time and space steps, respectively. Numerical experiment demonstrates the effectiveness and accuracy of the numerical scheme.
期刊：
Results in Physics,2024年56:107253 ISSN：2211-3797
通讯作者：
Zhang, QH
作者机构：
[Zhang, Qing-Hua; Zhang, QH] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.;[Lai, Lemin] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China.;[Lai, Lemin] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China.;[Fei, Shao-Ming] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China.;[Fei, Shao-Ming] Max Planck Inst Math Sci, D-04103 Leipzig, Germany.
通讯机构：
[Zhang, QH ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
关键词：
Steering criteria;Correlation matrices;Special unitary groups
摘要：
We study the steerability for arbitrary dimensional bipartite systems based on the correlation matrices given by local special unitary groups. We present families of steering criteria for bipartite quantum states in terms of parameterized correlation matrices. We show that these steering criteria may detect more steerable states than the existing steering criteria. The results are illustrated by detailed examples.
摘要：
This paper shows that the panic index shadow line difference (ULD) can be an effective predictor of oil returns. We use a candlestick chart to plot the investor panic index (VIX) and subtract the lower shadow from the upper shadow to obtain ULD. The in-sample analysis shows that the ULD can significantly and negatively predict oil returns. The out-of-sample results show that the inclusion of ULD, an exogenous regression variable, in the model not only substantially improves the predictive accuracy of oil returns, but also yields good economic benefits when using its predicted values for portfolio investment. All bivariate regression models that include ULD as an exogenous regression variable obtain higher prediction accuracy than univariate regression models, both for in-sample and out-of-sample predictions. All the robustness tests done in this paper show that ULD is a powerful predictor that significantly improves the predictability of oil returns.
摘要：
Diffusion study of the Ni-Si-V system is significant for the establishment of kinetic database of Ni-based alloys. In this work, the diffusion couple experiment combined with the numerical inverse method was adopted to evaluate the diffusivities and atomic mobilities for the Ni-Si-V fcc phase with high throughput. We prepared 12 fcc Ni-Si-V diffusion couples, which were annealed at 1273, 1373 and 1473 K, and their composition profiles after annealing were then measured by EPMA (Electron Probe Microanalysis). Subsequently, inputting the measured composition profiles as well as the available thermodynamic descriptions into the numerical inverse method incorporated in the CALTPP (CALculation of ThermoPhysical Properties) software, the composition- and temperature-dependent diffusivities and atomic mobilities for the Ni-Si-V fcc phase were simultaneously evaluated. In order to verify the reliability of the present evaluations, the CALTPP-simulated diffusion behaviors such as composition profiles and diffusion paths were compared with the measured ones, demonstrating reasonable agreements with each other. Meanwhile, the high-throughput determinations of diffusivities were confirmed by the ones obtained by the Matano-Kirkaldy method. Furthermore, applying the presently obtained diffusivities and atomic mobilities in combination with thermodynamic descriptions of the Ni-Si-V fcc phase, their diffusion flux, two-dimensional composition profile, activation energy and pre-frequency factor were predicted. It is expected that the presently obtained diffusivities and atomic mobilities of the Ni-Si-V fcc phase can contribute to the establishment of kinetic database of Ni-based alloys for their high-efficiency material design.
摘要：
Abstract: Aiming at the traditional A* algorithm which has the problems of traversing a large number of child nodes, the bottom of the search degree of freedom, and the path search efficiency caused by the large angle of the search direction, the research is carried out, and an improved A* algorithm is proposed. Firstly, in increasing the number of nodes and deleting the repetitive directions, a 16-neighborhood search method is formed, which enlarges the search angle. Then, the search interval is locally adjusted by using the direction information between the current node and the target point on the new neighborhood search method. The weight coefficients of the heuristic function and the evaluation function are improved to reasonably narrow the search neighborhood without the node falling into the local optimal solution. Finally, experiments are conducted in 16 simulated scenarios with different obstacle scales and different raster map sizes. The experimental results show that the improved A* algorithm significantly improves the search efficiency compared with the traditional algorithm, greatly reduces the number of searching sub-nodes, and improves the searching ability of the algorithm.#@#@#摘要: 针对传统的A*算法存在遍历子节点数量多、搜索自由度底、搜索方向夹角大所导致的路径搜索效率不高的问题进行了研究，提出一种改进的A*算法。首先增加节点数量，删除重复方向，建立16邻域搜索方式，扩大搜索角度。然后在新邻域搜索方式上，利用当前节点与目标点的方向信息局部调整搜索区间。改进启发函数和评价函数权重系数，在节点不陷入局部最优解的情况下，合理地缩小了搜索邻域。最后，在不同障碍物比例、不同栅格地图规模等16种模拟场景下进行实验。实验结果显示：改进A*算法相对于传统算法的搜索效率显著提高，极大地减少了搜索子节点的数量，提升了算法搜索的能力。
期刊：
IEEE Transactions on Medical Imaging,2024年43(2):832-845 ISSN：0278-0062
作者机构：
[Xiaofei Huang; Hongfang Gong] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China
摘要：
Research in medical visual question answering (MVQA) can contribute to the development of computer-aided diagnosis. MVQA is a task that aims to predict accurate and convincing answers based on given medical images and associated natural language questions. This task requires extracting medical knowledge-rich feature content and making fine-grained understandings of them. Therefore, constructing an effective feature extraction and understanding scheme are keys to modeling. Existing MVQA question extraction schemes mainly focus on word information, ignoring medical information in the text, such as medical concepts and domain-specific terms. Meanwhile, some visual and textual feature understanding schemes cannot effectively capture the correlation between regions and keywords for reasonable visual reasoning. In this study, a dual-attention learning network with word and sentence embedding (DALNet-WSE) is proposed. We design a module, transformer with sentence embedding (TSE), to extract a double embedding representation of questions containing keywords and medical information. A dual-attention learning (DAL) module consisting of self-attention and guided attention is proposed to model intensive intramodal and intermodal interactions. With multiple DAL modules (DALs), learning visual and textual co-attention can increase the granularity of understanding and improve visual reasoning. Experimental results on the ImageCLEF 2019 VQA-MED (VQA-MED 2019) and VQA-RAD datasets demonstrate that our proposed method outperforms previous state-of-the-art methods. According to the ablation studies and Grad-CAM maps, DALNet-WSE can extract rich textual information and has strong visual reasoning ability.
摘要：
Abstract: This paper is dedicated to the study of a class of tumor immune models with threshold control strategies. The Filippov theory was used to analyze the sliding mode dynamics and global dynamics. It is found that the dynamic behavior of the system changes with the change of thresholds, including the boundary focus branch.#@#@#摘要: 本文致力于研究一类具有阈值控制策略的肿瘤免疫模型。利用Filippov理论分析了滑模动力学和全局动力学。 研究发现，系统的动力学行为随着阁值的改变而改变，包括边界焦点分支。
摘要：
We consider the Alternating Direction Implicit (ADI) method to compute the numerical solution of a continuous Sylvester equation
$$AX+XB=C$$
, based on the recently developed inexact ADI iteration, and we propose classical acceleration techniques to enhance its convergence rate. An extrapolated variant (EADI) and a block successive overrelaxation variant (block SOR-ADI) of the ADI iterative method are described. These relaxation approaches are similar to what is used in Gauss-Seidel and Jacobi methods for linear systems, and, to our knowledge, novel, especially the block SOR-ADI scheme. Convergence properties of these two relaxed variants are analyzed when the matrix A is positive definite and the matrix B is positive semi-definite (not necessarily Hermitian matrices), or conversely. Our numerical experiments suggest that these new schemes are computationally attractive. The convergence rate of the ADI method is usually increased, particularly with the block SOR-ADI variant. A comparison with the well-known Hermitian and skew-Hermitian splitting (HSS) method emphasizes the efficiency of the proposed methods.
摘要：
For Mandelbrot's cascade (Y-n) in an independent and identically distributed (i.i.d.) random environment xi, we are interested in the a.s. convergence rate of the Mandelbrot's martingale (W-n) to its limit W, where W-n=Y-n/E xi Yn is the normalized partition function. We obtain sufficient conditions under which W-Wn has an exponential convergence rate: W-W-n=o(e(-na)) a.s. for some a > 0 explicitly calculated; we also find conditions under which W-Wn has a polynomial convergence rate: W-W-n=o(n(-alpha)) a.s. for some alpha > 0. Similar conclusions hold for Mandelbrot's cascade in a varying environment.
摘要：
Abstract: In this paper, we study the existence and uniqueness of forced traveling wave solu- tion for Lotka-Volterra cooperative model with nonlocal diffusion and time delay in a shifting environment. By constructing a pair of appropriate upper and lower solutions and using the monotone iteration, we prove that there is a traveling wave solution if the speed of the environmental movement .#@#@#摘要: 本文研究了移动环境下具有非局部扩散和时滞的Lotka-Volterra合作模型行波解的存在性。 通过 构造一对合适的上下解，再利用单调迭代，证明了当环境运动速度时，系统存在行波解。
期刊：
Scandinavian Journal of Statistics,2024年 ISSN：0303-6898
通讯作者：
Zhu, EW
作者机构：
[Cai, Bibi; Ling, Shiqing] Hong Kong Univ Sci & Technol, Dept Math, Hong Kong, Peoples R China.;[Zhu, Enwen] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.
通讯机构：
[Zhu, EW ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha, Peoples R China.
关键词：
ARMA model;AR-TFV model;LSE;model checking
摘要：
Abstract This paper studies the autoregressive and moving average (ARMA) model with time‐functional variance (TFV) noises, called the ARMA‐TFV model. We first establish the consistency and asymptotic normality of its least squares estimator (LSE). The Wald tests and portmanteau tests are constructed based on the theory for variable selection and model checking. A simulation study is carried out to assess the performance of our approach in finite samples, and two real examples are given. It should be mentioned that the process generated from the ARMA‐TFV model is not stationary, and the technique in this paper is nonstandard and may provide insights for future research in this area.
通讯机构：
[Tong, QS ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
关键词：
Underwater detection;attention module;non-maximum suppression;lightweight model
摘要：
In recent years, owing to the rapid advancements in deep learning, advanced object detection methods, such as You Only Look Once (YOLO) and Efficient Detector (EfficientDet), have been frequently used to detect underwater organisms. However, due to the complexity of underwater scenarios and deployment limitations, these models often encounter various challenges, such as blurred targets, occlusions, and high model computing costs. On this basis, we propose a YOLO network (CGC-YOLO) based on Cross-Stage Partial Convolutional Block Attention Module (CSPCBAM), Ghost module, and cluster non-maximum suppression (Cluster-NMS). Firstly, CSPCBAM enhances the model’s ability to extract intricate features by amplifying pertinent feature information across both channel and spatial dimensions. This augmentation contributes to an improved detection performance of the model, especially when dealing with fuzzy targets. Secondly, the Ghost module is employed to optimize the model’s efficiency by decreasing its parameters and reducing the computational load in terms of floating-point operations per second (FLOPs). Finally, by introducing Cluster-NMS and Score Penalty Mechanism (SPM) to reweight the confidence of bounding boxes, the model can retain the real object with occlusion. The experimental results show that on the Underwater Robot Picking Competition 2020 (URPC 2020) and brackish water dataset, the mAP@0.5 of our proposed CGC-YOLO reaches 87.2% and 98.6% respectively, which is at least 1 percentage point higher than all other models. The CGC-YOLO has 14.8 FLOPs and speeds of 7.1ms and 6.3ms, respectively, which is also better than all other models. Ablation experiments and qualitative analysis show that CGC-YOLO can deal with fuzzy and obscured objects well, with lower computational cost and faster inference speed.
作者机构：
[Liu, Jian; Zhao, Kang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
通讯机构：
[Zhao, K ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
关键词：
Quadratic asymmetric vibration system;Model updating;No-spillover;Structural modification;Passive control
摘要：
In this paper, the model updating problem of quadratic asymmetric vibration system with no-spillover is considered. Based on the spectral decomposition of a quadratic asymmetric pencil, the original quadratic asymmetric vibration system is updated to a new system such that some natural frequencies are replaced by some suitable chosen or newly measured ones, while the new system preserves no-spillover. The parametric solutions to the model updating problem of quadratic asymmetric vibration system are provided. When the system has repeated natural frequencies, a sufficient condition that the model updating problem can be solved is provided, and the performance of the proposed method is illustrated by some numerical examples.
摘要：
Follow-up experimental designs are frequently employed in a wide range of scientific studies and industries. Lower bounds of average mixture discrepancy for row augmented designs are determined in this paper utilizing the level permutation technique, which is also used to analyse the uniformity of row augmented designs with asymmetrical factorials. Between the row augmented designs and its initial designs or follow-up designs, quantitative relationships of lower bounds of average mixture discrepancy are constructed. Additionally, a proposal is made for the construction algorithm of asymmetrical uniform row augmented designs. Numerical examples indicate that the asymmetrical uniform row augmented designs can be constructed with high efficiency and recommended for use in practice.
作者机构：
[L. Li; Y. Wang] School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, People’s Republic of China;[A. Yang] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, People’s Republic of China
通讯机构：
[A. Yang] S;School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, People’s Republic of China
关键词：
martingale;Lorentz amalgam space;atomic decomposition;duality;fractional integral
摘要：
We develop the martingale theory in the framework of Lorentz amalgam spaces. Atomic decompositions for the martingale Hardy Lorentz amalgam spaces are established. As applications of atomic decompositions, the dual spaces of the martingale Hardy Lorentz amalgam spaces are characterized. Furthermore, when the stochastic basis is regular, the boundedness of the fractional integrals on martingale Hardy Lorentz amalgam spaces is proved. The results obtained here generalized the corresponding known results in martingale Hardy amalgam spaces and various classical martingale Hardy spaces.
作者：
Wang, Ruru;Yan, Yubin;Hendy, A. S.;Qiao, Leijie
期刊：
Computers & Mathematics with Applications,2024年155:126-141 ISSN：0898-1221
通讯作者：
Qiao, LJ
作者机构：
[Wang, Ruru] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.;[Yan, Yubin] Univ Chester, Dept Math, Chester CH1 4BJ, England.;[Hendy, A. S.] Ural Fed Univ, Inst Nat Sci & Math, Dept Computat Math & Comp Sci, 19 Mira St, Ekaterinburg 620002, Russia.;[Hendy, A. S.] Benha Univ, Fac Sci, Dept Math, Banha 13511, Egypt.;[Wang, Ruru; Qiao, Leijie] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China.
通讯机构：
[Qiao, LJ ] S;Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China.
关键词：
3D fractional parabolic integro-differential;equations;Orthogonal spline collocation method;Stability and convergence;Numerical simulations
摘要：
In this paper, we are concerned with constructing a fast and an efficient alternating direction implicit (ADI) scheme for the fractional parabolic integro-differential equations (FPIDE) with a weakly singular kernel in three dimensions (3D). Our constructed scheme is based on a second-order backward differentiation formula (BDF2) for temporal discretization, orthogonal spline collocation (OSC) method for spatial discretization and a second -order fractional quadrature rule proposed by Lubich for the Riemann-Liouville fractional integral. The stability and convergence of the constructed numerical scheme are derived. Finally, some numerical examples are given to illustrate the accuracy and validity of the BDF2 ADI OSC method. Based on the obtained results, the numerical results are in line with the theoretical ones.
期刊：
Journal of Algebra,2024年646:268-293 ISSN：0021-8693
通讯作者：
Zhou, PY
作者机构：
[Liu, Yu] Shaanxi Normal Univ, Sch Math & Stat, Xian 710062, Shannxi, Peoples R China.;[Zhou, Panyue] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Zhou, PY ] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.
关键词：
Twin cotorsion pair;Heart;Integral;Abelian
摘要：
Hearts of twin cotorsion pairs are shown to be quasi-abelian in [14]. But they are not always integral. In this article, we provide a sufficient and necessary condition for the hearts of twin cotorsion pairs being integral (resp. abelian). (c) 2024 Elsevier Inc. All rights reserved.
摘要：
In this paper, we consider the partial quadratic eigenvalue assignment problem (PQEAP) for vibration system by active feedback control, such that some "troublesome" eigenpairs are replaced by some suitable chosen or newly measured ones, while the remaining unknown eigenpairs are kept unchanged. With the assumptions that the mass and stiffness matrices are nonsingular, we give a new proof of the spectral decomposition of quadratic symmetric pencil. And then we provide some necessary and sufficient conditions of the feedback matrices so that the closed-loop can preserve the no spill-over property. With these conditions, we characterize a set of parametric solutions to the PQEAP using receptances, system matrices and a few open-loop eigenpairs. Finally, we propose a gradient-based optimization method for solving the minimum norm solution to the PQEAP. Numerical experiments illustrate the effectiveness and robustness of the proposed algorithm.
摘要：
The U-shaped convolutional neural network (CNN) has attained remarkable achievements in the segmentation of skin lesion. However, given the inherent locality of convolution, this architecture cannot capture long-range pixel dependencies and multiscale global contextual information effectively. Moreover, repeated convolutions and downsampling operations can readily result in the omission of intricate local fine-grained details. In this paper, we proposed a U-shaped network (DBNet-SI) equipped with a dual-branch module that combines shift window attention and inception structures. First, we proposed a dual-branch module that combines shift window attention and inception structures (MSI) to better capture multiscale global contextual information and long-range pixel dependencies. Specifically, we have devised a cross-branch bidirectional interaction module within the MSI module to enable information complementarity between the two branches in the channel and spatial dimensions. Therefore, MSI is capable of extracting distinguishing and comprehensive features to accurately identify the skin lesion boundaries. Second, we have devised a progressive feature enhancement and information compensation module (PFEIC), which progressively compensates for fine-grained features through reconstructed skip connections and integrated global context attention modules. The results of the experiment show the superior segmentation performance of DBNet-SI compared with other deep learning models for skin lesion segmentation in the ISIC2017 and ISIC2018 datasets. Ablation studies demonstrate that our model can effectively extract rich multiscale global contextual information and compensate for the loss of local details.
期刊：
Journal of Mathematical Physics,2024年65(2):021501 ISSN：0022-2488
通讯作者：
Pang, Y
作者机构：
[Lin, Qiang] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Peoples R China.;[Xu, Zhengsheng; Wang, Xingchang; Pang, Yue; Pang, Y] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China.
通讯机构：
[Pang, Y ] H;Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China.
摘要：
This paper considers the global well-posedness of two-dimensional Klein–Gordon equations with exponential nonlinearity. By employing the potential well method, we conduct a comprehensive study on the global existence and finite time blowup of solutions by the requirement of the initial energy at three different initial energy levels.
