Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

Graph-based video fingerprinting using double optimal projection

A double optimal projection method that involves projections for intra-cluster and inter-cluster dimensionality reduction are proposed for video fingerprinting. The video is initially set as a graph with frames as its vertices in a high-dimensional space. A similarity measure that can compute the weights of the edges is then proposed. Subsequently, the video frames are partitioned into different clusters based on the graph model. Double optimal projection is used to explore the optimal mapping points in a low-dimensional space to reduce the video dimensions. The statistics and geometrical fingerprints are generated to determine whether a query video is copied from one of the videos in the database. During matching, the video can be roughly matched by utilizing the statistics fingerprint. Further matching is thereafter performed in the corresponding group using geometrical fingerprints. Experimental results show the good performance of the proposed video fingerprinting method in robustness and discrimination.     

The energy-critical nonlinear wave equation with an inverse-square potential

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.     

An Improved Immune Genetic Algorithm for Solving the Optimization Problems of Computer Communication Networks

1　IntroductionIndesigningacomputercommunicationnet work ,thenetworkaveragedelayisanimportantpa rameterinthenetworkperformance .Inthispaper,weonlyconsiderM /M/1networks,whichmeansthatthemessageprocessingtimeisaprobabilisticdensityfunctionwithnegativepower,thegroupar rivalandsendingisofPoissiondistributionwithasinglequeue .Supposethatthenetworktopologicalstructureandtheestimatesoftheexternaltrafficrequirementsaregiven ,howtoselecttheoptimalroutestobeusedbythecommunicatingnodesinthenetworksoast…     

理想九点五态控制器原理的叙述

用计算的方式叙述理想九点五态控制器的控制原理。为便于人们理解二阶对象的运动中控制的变化过程,将抽象的对象转换为人们熟知的L-R-C电路,通过调节输入电压(即控制作用)的大小和方向来实现对对象性能的调节,并使系统达到理想的性能指标。最后用仿真来验证计算结果的正确性。     

DMT系统中一种易于实现的时域均衡器

总结了DMT系统中时域均衡器(TEQ)的主要设计方法，指出最大缩短信噪比(MSSNR)TEQ的最优设计方法很难实时实现。提出了一种MSSNR TEQ的次优设计方法，它首先估计出目标抽样窗的最优延迟，然后用分步求解法求出TEQ的抽头系数。和最优方法相比，次优方法的计算量大幅度减少，可实时实现，而其缩短信噪比的损失很小。仿真实验验证了次优方法的有效性。     

Profiling Voids Embedded in a Slab by a Non-Linear Model

In this paper, by applying a non linear model for the electromagnetic inverse scattering, a technique for the dielectric profiling of a planarly layered medium is investigated and applied to void localization and diagnostics inside a homogeneous lossless slab (one-dimensional geometry). Data are collected under plane wave multifrequency normal incidence. Suitable finite dimensional representations for the unknown functions are introduced and their influence on the model is discussed. The resulting functional equation is solved by the method of weighted residuals and the solution algorithm amounts to minimizing a non quadratic function, where particular attention is devoted to reduce the occurrence of local minima. Finally, the inversion algorithm is validated by applications to both simulated and experimental data.     

Reducing Huge Gyroscopic Eigenproblems by Automated Multi-level Substructuring

Simulating numerically the sound radiation of a rolling tire requires the solution of a very large and sparse gyroscopic eigenvalue problem. Taking advantage of the automated multi-level substructuring (AMLS) method it can be projected to a much smaller gyroscopic problem, the solution of which however is still quite costly since the eigenmodes are non-real and complex arithmetic is necessary. This paper discusses the application of AMLS to huge gyroscopic problems and the numerical solution of the AMLS reduction. A numerical example demonstrates the efficiency of AMLS.