Sharp Trudinger-Moser Inequalities On Riemannian Manifolds And Heisenberg Groups

Archival abstract submitte

The Method of Moving spheres on Hyperbolic Space and Symmetry of Solutions to a Class of PDEs

The classification of solutions of semilinear partial differential equations, as well as the classification of critical points of the corresponding functionals, have wide applications in the study of partial differential equations and differential geometry. The classical moving plane method and the moving sphere method on $\mathbb{R}^n$ provide an effective approach to capturing the symmetry of solutions. As far as we know, the moving sphere method has yet to be developed on the hyperbolic space $\mathbb{H}^n$. In the present paper, we focus on the following equation \begin{equation*} P_k u = f(u) \end{equation*} on hyperbolic spaces $\mathbb{H}^n$, where $P_k$ denotes the GJMS operators on $\mathbb{H}^n$ and $f : \mathbb{R} \to \mathbb{R}$ satisfies certain growth conditions. We develop a moving sphere approach for integral equations on $\mathbb{H}^n$, to obtain the symmetry property as well as a characterization result towards positive solutions. Our methods also rely on Helgason-Fourier analysis and Hardy-Littlewood-Sobolev inequalities on hyperbolic spaces together with a Kelvin transform we introduce on $\mathbb{H}^n$ in this paper.Comment: Some references are added and typos fixe

Cloning and biochemical characterization of a novel lipolytic gene from activated sludge metagenome, and its gene product

In this study, a putative esterase, designated EstMY, was isolated from an activated sludge metagenomic library. The lipolytic gene was subcloned and expressed in Escherichia coli BL21 using the pET expression system. The gene estMY contained a 1,083 bp open reading frame (ORF) encoding a polypeptide of 360 amino acids with a molecular mass of 38 kDa. Sequence analysis indicated that it showed 71% and 52% amino acid identity to esterase/lipase from marine metagenome (ACL67845) and Burkholderia ubonensis Bu (ZP_02382719), respectively; and several conserved regions were identified, including the putative active site, GDSAG, a catalytic triad (Ser203, Asp301, and His327) and a HGGG conserved motif (starting from His133). The EstMY was determined to hydrolyse p-nitrophenyl (NP) esters of fatty acids with short chain lengths (≤C8). This EstMY exhibited the highest activity at 35°C and pH 8.5 respectively, by hydrolysis of p-NP caprylate. It also exhibited the same level of activity over wide temperature and pH spectra and in the presence of metal ions or detergents. The high level of stability of esterase EstMY with unique substrate specificities makes it highly valuable for downstream biotechnological applications

NPRF: A Neural Pseudo Relevance Feedback Framework for Ad-hoc Information Retrieval

Pseudo-relevance feedback (PRF) is commonly used to boost the performance of traditional information retrieval (IR) models by using top-ranked documents to identify and weight new query terms, thereby reducing the effect of query-document vocabulary mismatches. While neural retrieval models have recently demonstrated strong results for ad-hoc retrieval, combining them with PRF is not straightforward due to incompatibilities between existing PRF approaches and neural architectures. To bridge this gap, we propose an end-to-end neural PRF framework that can be used with existing neural IR models by embedding different neural models as building blocks. Extensive experiments on two standard test collections confirm the effectiveness of the proposed NPRF framework in improving the performance of two state-of-the-art neural IR models.Comment: Full paper in EMNLP 201

Several Types of Convergence Rates of the M/G/1 Queueing System

We study the workload process of the M/G/1 queueing system. Firstly, we give the explicit criteria for the geometric rate of convergence and the geometric decay of stationary tail. And the parameters ε0 and s0 for the geometric rate of convergence and the geometric decay of the stationary tail are obtained, respectively. Then, we give the explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases. And we give the parameters ε1 and s1 of the rate of convergence and the decay of the stationary tail, respectively, for the subgeometric rate r(n)=exp(sn1/(1+α)), s>0, α>0

Acoustic test facility at Tianjin spacecraft AIT center of China

The China Academy of Space Technology (CAST) designs and builds a new world-class Assembly, Integration and Test Center (AITC) at Tianjin, China. Modal, vibration and acoustic test facilities are built to support the future environmental testing needs of China space station program. The Reverberation Acoustic Test Facility (RATF) is about 4000 m3 in volume and can achieved an empty chamber acoustic overall sound pressure level (OASPL) higher than 156 dB. It is the largest acoustic facility in Asia. Beijing Institute of spacecraft Environment Engineering (BISEE) started its design and construction work from 2012 and put it into use at October of 2015. The RATF will provide an efficient support for environment testing needs of China and world’s space program in the future