Existence and continuous dependence of mild solutions for fractional abstract differential equations with infinite delay

In this paper, we prove the existence, uniqueness, and continuous dependence of the mild solutions for a class of fractional abstract differential equations with infinite delay. The results are obtained by using the Krasnoselskii's fixed point theorem and the theory of resolvent operators for integral equations

Dirichlet Boundary Value Problems for Second Order pp-Laplacian Difference Equations

In this paper, the solutions to second order Dirichlet boundary value problems of $p$-Laplacian difference equations are investigated. By using critical point theory, existence and multiplicity results are obtained. The proof is based on the Mountain Pass Lemma in combination with variational techniques

Geometry-aware Line Graph Transformer Pre-training for Molecular Property Prediction

Molecular property prediction with deep learning has gained much attention over the past years. Owing to the scarcity of labeled molecules, there has been growing interest in self-supervised learning methods that learn generalizable molecular representations from unlabeled data. Molecules are typically treated as 2D topological graphs in modeling, but it has been discovered that their 3D geometry is of great importance in determining molecular functionalities. In this paper, we propose the Geometry-aware line graph transformer (Galformer) pre-training, a novel self-supervised learning framework that aims to enhance molecular representation learning with 2D and 3D modalities. Specifically, we first design a dual-modality line graph transformer backbone to encode the topological and geometric information of a molecule. The designed backbone incorporates effective structural encodings to capture graph structures from both modalities. Then we devise two complementary pre-training tasks at the inter and intra-modality levels. These tasks provide properly supervised information and extract discriminative 2D and 3D knowledge from unlabeled molecules. Finally, we evaluate Galformer against six state-of-the-art baselines on twelve property prediction benchmarks via downstream fine-tuning. Experimental results show that Galformer consistently outperforms all baselines on both classification and regression tasks, demonstrating its effectiveness.Comment: 9 pages, 5 figure

You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors

In this paper, we propose a novel local descriptor-based framework, called You Only Hypothesize Once (YOHO), for the registration of two unaligned point clouds. In contrast to most existing local descriptors which rely on a fragile local reference frame to gain rotation invariance, the proposed descriptor achieves the rotation invariance by recent technologies of group equivariant feature learning, which brings more robustness to point density and noise. Meanwhile, the descriptor in YOHO also has a rotation equivariant part, which enables us to estimate the registration from just one correspondence hypothesis. Such property reduces the searching space for feasible transformations, thus greatly improves both the accuracy and the efficiency of YOHO. Extensive experiments show that YOHO achieves superior performances with much fewer needed RANSAC iterations on four widely-used datasets, the 3DMatch/3DLoMatch datasets, the ETH dataset and the WHU-TLS dataset. More details are shown in our project page: https://hpwang-whu.github.io/YOHO/.Comment: Accepted by ACM Multimedia(MM) 2022, Project page: https://hpwang-whu.github.io/YOHO

Vibration signal simulation of planetary gearbox based on motion process modeling

In planetary gearbox, multiple gear pair meshing with each other and the vibration transmission paths from gear meshing points to the fixed sensors are time-varying. Therefore, fault diagnosis of the planetary gearbox is more difficult compared to that of fixed-axis gearbox, in which the vibration signal simulation models are very important. This paper constructs vibration signal models based on motion process modeling. This kind of modeling method is easier to understand compare with other methods which mainly based on the theory or physical laws behind the phenomena. The modeling process was presented in a step-by-step procedure according to the motion process of planetary gearbox. Frequency analysis was also implemented and comprehensive diagram was shown to help understand the result

Maternal pre-pregnancy infection with hepatitis B virus and the risk of preterm birth: a population-based cohort study

Background Preterm birth is the leading cause of child death in children younger than 5 years. Large cohort studies in developed countries have shown that maternal hepatitis B virus infection is associated with preterm birth, but there is little reliable evidence from China and other developing countries, where hepatitis B virus prevalence is intermediate or high. Hence, we designed this study to investigate the association between pre-pregnancy hepatitis B virus infection and risk of preterm and early preterm birth. Methods Between Jan 1, 2010, and Dec 31, 2012, we did a population-based cohort study using data from 489 965 rural women aged 21–49 years who had singleton livebirths from 220 counties of China who participated in the National Free Preconception Health Examination Project. Participants were divided into three groups according to their prepregnancy status of hepatitis B virus infection: women uninfected with hepatitis B virus (control group), women who were HBsAg positive and HBeAg negative (exposure group 1), and women who were both HBsAg and HBeAg positive (exposure group 2). The primary outcome was preterm birth (gestation at less than 37 weeks). We used log-binomial regression to estimate adjusted risk ratios (aRR) of preterm birth for women with pre-pregnancy hepatitis B virus infection, and risk of early preterm birth (gestation less than 34 weeks). Findings 489 965 women met inclusion criteria and were included in this study; of these, 20 827 (4·3%) were infected with hepatitis B virus. Compared with women who were not infected with hepatitis B virus, women who were HBsAg positive and HBeAg negative had a 26% higher risk of preterm birth (aRR 1·26, 95% CI 1·18–1·34) and women who were both HBsAg and HBeAg positive had a 20% higher risk of preterm birth (aRR 1·20, 1·08–1·32). Compared with women who were not infected with hepatitis B virus, women who were HBsAg positive and HBeAg negative manifested an 18% higher risk of early preterm birth (gestation less than 34 weeks; aRR 1·18, 1·04–1·34) and women who were both HBsAg and HBeAg positive had a 34% higher risk of early preterm birth (aRR 1·34, 1·10–1·61). Maternal pre-pregnancy hepatitis B virus infection was independently associated with higher risk of preterm birth and early preterm birth. These associations were similar in subgroups of participants as defined by baseline characteristics. Interpretation Besides mother-to-child transmission, the risk of preterm birth in women infected with hepatitis B virus should not be neglected. Comprehensive programmes that focus on early detection of hepatitis B virus infection before pregnancy and provide appropriate medical intervention for women infected with hepatitis B virus before and during pregnancy would be helpful in improving maternal and neonatal outcomes and reducing child mortality