In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
点云被广泛使用在各种三维应用场景中,但是实际应用中通常存在扫描、标注费时费力等局限性,因此基于小样本数据集的点云分类网络更加符合应用需求.为了有效地提高深度学习分类算法在小样本点云数据集上的分类效果,提出一种针对小样本数...点云被广泛使用在各种三维应用场景中,但是实际应用中通常存在扫描、标注费时费力等局限性,因此基于小样本数据集的点云分类网络更加符合应用需求.为了有效地提高深度学习分类算法在小样本点云数据集上的分类效果,提出一种针对小样本数据集的点云分类方法.针对训练数据集不平衡问题,首先采用基于相似度依赖的Dirichlet中餐馆过程对数据集进行预处理,在无需人工指定聚类个数的前提下对样本进行重新聚类,以提升分类网络在小样本数据集上的性能;然后在重新聚类后的样本上使用模型无关(model agnostic meta learning,MAML)算法训练PointNet++,达到用少量点云样本就能快速适应新任务的能力.所提方法不但降低了模型对数据量的依赖,提高了模型泛化能力,而且成功地把MAML算法从二维图像分类拓展到三维点云分类中;在Modelnet40数据集上的实验结果表明,与PointNet++相比,该方法的训练时间减少了一半,分类准确率平均提高6.67%,验证了该方法在小样本数据集上的有效性.展开更多
In this paper,for a bounded C2 domain,we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive C2 bou...In this paper,for a bounded C2 domain,we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive C2 boundary data.We have a non-existence result,which is the justification for taking into account the restricted boundary data.There is a smooth positive boundary datum that precludes the existence of the positive classical solution.展开更多
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
文摘点云被广泛使用在各种三维应用场景中,但是实际应用中通常存在扫描、标注费时费力等局限性,因此基于小样本数据集的点云分类网络更加符合应用需求.为了有效地提高深度学习分类算法在小样本点云数据集上的分类效果,提出一种针对小样本数据集的点云分类方法.针对训练数据集不平衡问题,首先采用基于相似度依赖的Dirichlet中餐馆过程对数据集进行预处理,在无需人工指定聚类个数的前提下对样本进行重新聚类,以提升分类网络在小样本数据集上的性能;然后在重新聚类后的样本上使用模型无关(model agnostic meta learning,MAML)算法训练PointNet++,达到用少量点云样本就能快速适应新任务的能力.所提方法不但降低了模型对数据量的依赖,提高了模型泛化能力,而且成功地把MAML算法从二维图像分类拓展到三维点云分类中;在Modelnet40数据集上的实验结果表明,与PointNet++相比,该方法的训练时间减少了一半,分类准确率平均提高6.67%,验证了该方法在小样本数据集上的有效性.
基金supported by the National NaturalScience Foundation of China(11971069 and 12126307)。
文摘In this paper,for a bounded C2 domain,we prove the existence and uniqueness of positive classical solutions to the Dirichlet problem for the steady relativistic heat equation with a class of restricted positive C2 boundary data.We have a non-existence result,which is the justification for taking into account the restricted boundary data.There is a smooth positive boundary datum that precludes the existence of the positive classical solution.
