Improving the speed of ghost imaging is one of the main ways to leverage its advantages in sensitivity and imperfect spectral regions for practical applications.Because of the proportional relationship between image r...Improving the speed of ghost imaging is one of the main ways to leverage its advantages in sensitivity and imperfect spectral regions for practical applications.Because of the proportional relationship between image resolution and measurement time,when the image pixels are large,the measurement time increases,making it difficult to achieve real-time imaging.Therefore,a high-quality ghost imaging method based on undersampled natural-order Hadamard is proposed.This method uses the characteristics of the Hadamard matrix under undersampling conditions where image information can be fully obtained but overlaps,as well as deep learning to extract aliasing information from the overlapping results to obtain the true original image information.We conducted numerical simulations and experimental tests on binary and grayscale objects under undersampling conditions to demonstrate the effectiveness and scalability of this method.This method can significantly reduce the number of measurements required to obtain high-quality image information and advance application promotion.展开更多
This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the ...This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.展开更多
本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题...本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题;根据离散系数的性质,利用数学归纳法证明了差分格式的稳定性和收敛性;最后,对具体模型进行数值求解。算例验证了上述理论分析的有效性。展开更多
基金Supported by the National Key R and D Program of China(2020YFA0713100)the Natural Science Foundation of Jiangsu Province(BK20230900)National Natural Science Foundation of China(12141104)。
基金the Science and Technology Development Plan Project of Jilin Province,China(Grant No.20220204134YY)the National Natural Science Foundation of China(Grant No.62301140)+3 种基金Project of the Education Department of Jilin Province(Grant Nos.JJKH20231292KJ and JJKH20240242KJ)Program for Science and Technology Development of Changchun City(Grant No.23YQ11)Innovation and Entrepreneurship Talent Funding Project of Jilin Province(Grant No.2023RY17)the Project of Jilin Provincial Development and Reform Commission(Grant No.2023C042-4).
文摘Improving the speed of ghost imaging is one of the main ways to leverage its advantages in sensitivity and imperfect spectral regions for practical applications.Because of the proportional relationship between image resolution and measurement time,when the image pixels are large,the measurement time increases,making it difficult to achieve real-time imaging.Therefore,a high-quality ghost imaging method based on undersampled natural-order Hadamard is proposed.This method uses the characteristics of the Hadamard matrix under undersampling conditions where image information can be fully obtained but overlaps,as well as deep learning to extract aliasing information from the overlapping results to obtain the true original image information.We conducted numerical simulations and experimental tests on binary and grayscale objects under undersampling conditions to demonstrate the effectiveness and scalability of this method.This method can significantly reduce the number of measurements required to obtain high-quality image information and advance application promotion.
文摘This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.
文摘本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题;根据离散系数的性质,利用数学归纳法证明了差分格式的稳定性和收敛性;最后,对具体模型进行数值求解。算例验证了上述理论分析的有效性。
