Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant

This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad \partial_t u + \partial_x p(v) =\displaystyle -\frac{\alpha}{(1+t)^\lambda} u, \end{equation} with null-Dirichlet boundary condition or null-Neumann boundary condition on $u$. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends time-asymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang (1999, J. Differential Equations, 156, 439-458), and Jiang and Zhu (2009, Discrete Contin. Dyn. Syst., 23, 887-918), we obtain a general result when the initial perturbation belongs to the same space. In addition, our main novelty lies in the facts that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave

Geo-Social Group Queries with Minimum Acquaintance Constraint

The prosperity of location-based social networking services enables geo-social group queries for group-based activity planning and marketing. This paper proposes a new family of geo-social group queries with minimum acquaintance constraint (GSGQs), which are more appealing than existing geo-social group queries in terms of producing a cohesive group that guarantees the worst-case acquaintance level. GSGQs, also specified with various spatial constraints, are more complex than conventional spatial queries; particularly, those with a strict $k$NN spatial constraint are proved to be NP-hard. For efficient processing of general GSGQ queries on large location-based social networks, we devise two social-aware index structures, namely SaR-tree and SaR*-tree. The latter features a novel clustering technique that considers both spatial and social factors. Based on SaR-tree and SaR*-tree, efficient algorithms are developed to process various GSGQs. Extensive experiments on real-world Gowalla and Dianping datasets show that our proposed methods substantially outperform the baseline algorithms based on R-tree.Comment: This is the preprint version that is accepted by the Very Large Data Bases Journa

The Relationship between Virtual Reality Technology and Anxiety State of Parturient Women with Labor Pain

As per the authors' request, the sequence of the affiliations have been adjusted accordingly

In silico enzyme modelling

The 2013 Nobel Prize in Chemistry went to Martin Karplus, Michael Levitt and Arieh Warshel for their pioneering work on computer modelling, specifically, the \u27development of multiscale models of complex chemical systems\u27 (1). This award not only recognises the critical contributions by the three laureates to the field of molecular simulations, but also underscores the broad impact that computer simulations have made in fields as diverse as chemistry, biophysics, enzymology and material sciences. This review will present an overview of computational enzymology, a rapidly maturing field where multiscale modelling plays a key role in deciphering enzymatic catalysis (2-4)

Exploration and Discussion on Rural Financial Innovation in the New Period

With the deepening of urban and rural planning, in the new period, if rural financial development wants to adapt to the development trend of society, it needs to carry out corresponding innovations to improve the rural economy and promote urban and rural construction. This paper mainly analyzes the necessity of rural financial innovation in the new period, the problems existing in rural financial development and the rural financial innovation strategy in the new period for reference