Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems

In this paper we study the existence and multiplicity of homoclinic solutions for the second order Hamiltonian system $\ddot{u}-L(t)u(t)+W_u(t,u)=0$, $\forall t\in\mathbb{R}$, by means of the minmax arguments in the critical point theory, where $L(t)$ is unnecessary uniformly positively definite for all $t\in \mathbb{R}$ and $W_u(t, u)$ sastisfies the asymptotically linear condition.Comment: published in International Mathematical Forum, Vol. 6, 2011, no. 4, 159 - 17

Homoclinic orbits for a class of nonperiodic Hamiltonian systems with some twisted conditions

In this paper, by the Masolv index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian function

Infinitely many periodic solutions for second order Hamiltonian systems

In this paper, we study the existence of infinitely many periodic solutions for second order Hamiltonian systems $\ddot{u}+\nabla_u V(t,u)=0$, where $V(t, u)$ is either asymptotically quadratic or superquadratic as $|u|\to \infty$.Comment: to appear in JDE(doi:10.1016/j.jde.2011.05.021

Infinitely many solutions for Schrödinger–Kirchhoff-type equations involving indefinite potential

In this paper, we study the multiplicity of solutions for the following Schrödinger–Kirchhoff-type equation $$\begin{cases}-\left(a+b\int_{\mathbb{R}^N}|\nabla u|^2dx\right)\triangle u+V(x)u=f(x,u)+g(x,u), \quad x\in \mathbb{R}^N,\\ u\in H^1(\mathbb{R}^N),\end{cases}$$ where $N\geq 3$, $a,\,b>0$ are constants and the potential $V$ may be unbounded from below. Under some mild conditions on the nonlinearities $f$ and $g$, we obtain the existence of infinitely many solutions for this problem. Recent results from the literature are generalized and significantly improved

PM2.5-GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting

When predicting PM2.5 concentrations, it is necessary to consider complex information sources since the concentrations are influenced by various factors within a long period. In this paper, we identify a set of critical domain knowledge for PM2.5 forecasting and develop a novel graph based model, PM2.5-GNN, being capable of capturing long-term dependencies. On a real-world dataset, we validate the effectiveness of the proposed model and examine its abilities of capturing both fine-grained and long-term influences in PM2.5 process. The proposed PM2.5-GNN has also been deployed online to provide free forecasting service.Comment: Pre-print version of a ACM SIGSPATIAL 2020 poster [paper](https://dl.acm.org/doi/10.1145/3397536.3422208). The code is available at [Github](https://github.com/shawnwang-tech/PM2.5-GNN), and the talk is available at [YouTube](https://www.youtube.com/watch?v=VX93vMthkGM

Distribution, occurrence characteristics and geological origin of typical hazardous elements in low-medium ash coal of Huainan coalfield

With the continuous development, processing and utilization of coal resources in our province, the existence of typical harmful elements in coal is bound to have a negative impact on the efficient and clean utilization of coal resources. Based on the mass data analysis of typical hazardous elements in coal of Huainan coalfield, taking the main coal seams (No.13-1, No.11-2, No.8, No.6, No.4 and No.1) as the research objects, the occurrence characteristics and geological genesis of typical hazardous elements were comprehensively analyzed by the means of ICP-MS, AFS, stepwise chemical extraction and cluster analysis. The results were as follows: ① Typical hazardous elements Cr, Co, Se and Pb in coal of Huainan coalfield are “lightly enriched”, Hg is “highly enriched” and other elements are in “normal range”; ② The high value area of As element content in Huainan coalfield was mainly located in the west of coalfield; the high value region of Hg element was located in the east of coalfield, followed by the west; the remaining eight elements (Cr, Mn, Co, Ni, Se, Cd, Sb and Pb) were all higher in coal of Panji mining area of Huainan coalfield (especially near Pansan coal mine). The late magmatic hydrothermal process in Panji-Zhuji region may be the main reason for the relative enrichment of hazardous elements such as Cr, Mn, Co, Ni, Se, Cd, Sb and Pb. ③ There were many ion-exchange States in the occurrence state of Hg, and the inorganic components brought by magmatic hydrothermal action may have little influence on the enrichment degree of Hg element. The magmatic hydrothermal intrusion in the late diagenesis period had no obvious influence on As, and the low content of As in coal may be related to the low content of As in coal-forming plants

Co‐evolutionary adaptations of Acinetobacter baumannii and a clinical carbapenemase‐encoding plasmid during carbapenem exposure

Abstract: OXA‐23 is the predominant carbapenemase in carbapenem‐resistant Acinetobacter baumannii. The co‐evolutionary dynamics of A. baumannii and OXA‐23‐encoding plasmids are poorly understood. Here, we transformed A. baumannii ATCC 17978 with pAZJ221, a blaOXA−23‐containing plasmid from clinical A. baumannii isolate A221, and subjected the transformant to experimental evolution in the presence of a sub‐inhibitory concentration of imipenem for nearly 400 generations. We used population sequencing to track genetic changes at six time points and evaluated phenotypic changes. Increased fitness of evolving populations, temporary duplication of blaOXA−23 in pAZJ221, interfering allele dynamics, and chromosomal locus‐level parallelism were observed. To characterize genotype‐to‐phenotype associations, we focused on six mutations in parallel targets predicted to affect small RNAs and a cyclic dimeric (3′ → 5′) GMP‐metabolizing protein. Six isogenic mutants with or without pAZJ221 were engineered to test for the effects of these mutations on fitness costs and plasmid kinetics, and the evolved plasmid containing two copies of blaOXA−23 was transferred to ancestral ATCC 17978. Five of the six mutations contributed to improved fitness in the presence of pAZJ221 under imipenem pressure, and all but one of them impaired plasmid conjugation ability. The duplication of blaOXA−23 increased host fitness under carbapenem pressure but imposed a burden on the host in antibiotic‐free media relative to the ancestral pAZJ221. Overall, our study provides a framework for the co‐evolution of A. baumannii and a clinical blaOXA−23‐containing plasmid in the presence of imipenem, involving early blaOXA−23 duplication followed by chromosomal adaptations that improved the fitness of plasmid‐carrying cells