一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.     

非齐度量测度空间上Morrey-Herz空间上的广义分数次积分算子及其交换子

设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性.     

基于级联卷积神经网络的前列腺磁共振图像分类

针对深度学习训练成本高，以及基于磁共振图像的前列腺癌临床诊断需要大量医学常识且极为耗时的问题，本文提出了一种基于级联卷积神经网络（Convolutional Neural Network，CNN）和磁共振图像的前列腺癌（Prostate Cancer，PCa）自动分类诊断方法，该网络以Faster-RCNN作为前网络，对前列腺区域进行提取分割，用于排除前列腺附近组织器官的干扰；以基于ResNet改进的网络结构CNN40_bottleneck作为后网络，用于对前列腺区域病变进行分类.后网络由瓶颈结构串联组成，其中使用批量标准化（Batch Normalization，BN）、全局平均池化（Global Average Pooling，GAP）进行优化.实验结果证明，本文方法对前列腺癌诊断结果较好，而且缩减了训练时间和参数量，有效降低了训练成本.     

Solutions with concentration for conservation laws with discontinuous flux and its applications to numerical schemes for hyperbolic systems

Measure-valued weak solutions for conservation laws with discontinuous flux are proposed and explicit formulae have been derived. We propose convergent discontinuous flux-based numerical schemes for the class of hyperbolic systems that admit nonclassical -shocks, by extending the theory of discontinuous flux for nonlinear conservation laws to scalar transport equation with a discontinuous coefficient. The article also discusses the concentration phenomenon of solutions along the line of discontinuity, for scalar transport equations with a discontinuous coefficient. The existence of the solutions for transport equation is shown using the vanishing viscosity approach and the asymptotic behavior of the solutions is also established. The performance of the numerical schemes for both scalar conservation laws and systems to capture the -shocks effectively is displayed through various numerical experiments.     

On the analysis of vibration equation involving a fractional derivative with Mittag-Leffler law

The present article deals with a fractional extension of the vibration equation for very large membranes with distinct special cases. The fractional derivative is considered in Atangana-Baleanu sense. A numerical algorithm based on homotopic technique is employed to examine the fractional vibration equation. The stability analysis is conducted for the suggested scheme. The maple software package is utilized for numerical simulation. In order to illustrate the effects of space, time, and order of Atangana-Baleanu derivative on the displacement, the outcomes of this study are demonstrated graphically. The results revel that the Atangana-Baleanu fractional derivative is very efficient in describing vibrations in large membranes.     

On the impulsive implicit Ψ-Hilfer fractional differential equations with delay

In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam-Hyers-Mittag-Leffler stability results for impulsive implicit Ψ-Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam-Hyers and generalized Ulam-Hyers stability are the specific cases of Ulam-Hyers-Mittag-Leffler stability. Extended version of the Gronwall inequality, abstract Gronwall lemma, and Picard operator theory are the primary devices in our investigation. We provide an example to illustrate the obtained results.     

Hydrogen‐Bonded Films for Zero‐Order Release of Leuprolide

Leuprolide has been widely used in androgen deprivation therapy for the treatment of advanced prostate cancer, but its use is still limited due to its short half‐life. Herein, hydrogen‐bonded layer‐by‐layer films are fabricated from PEGylated leuprolide (PEG‐LEU) and tannic acid (TA). Because of its dynamic nature, the film disintegrates gradually in water and releases PEG‐LEU and TA. The in vitro release profile indicated perfect zero‐order kinetics, which is explained by the unique release mechanism. When implanted subcutaneously in male rats, the films maintain a constant serum drug level. For a 60‐bilayer film, the serum drug level is maintained constant for ≈24 days. No initial burst release is observed, suggesting that the in vivo release also follows zero‐order kinetics. Initially, an increase in the level of serum testosterone is induced by the released drug, followed by testosterone suppression to a constant level below the castrate level, which could be maintained as long as a constant serum drug level is maintained. Since the new drug carriers avoid an initial burst release of the drug and maintain a constant serum drug level and hence a constant serum testosterone level below the castrate level, these carriers are highly promising for androgen deprivation therapy.