Global classical solutions near Maxwellians are constructed for the Boltzmann and Landau equations with soft potentials in the whole space. The construction of global solutions is based on refined energy analysis. Our results generalize the classical results in Ukai and Asano (Publ. Res. Inst. Math. Sci. 18 (1982), 477–519) to the very soft potentials for the Boltzmann equation and also extend ...

Denote by Tn,q the set of trees with n vertices and matching number q. Guo [On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379–385] gave the tree in Tn,q with the greatest value of the largest Laplacian eigenvalue. In this paper, we give another proof of this result. Using our method, we can go further beyond Guo by giving the tree in Tn,q with the second largest va...

References 1. Chen F, Sun D, Guo Y, GuoW, Ding Z, Li P, et al. (2015) Spatiotemporal Scan and Age-Period-Cohort Analysis of Hepatitis C Virus in Henan, China: 2005–2012. PLoS ONE 10(6): e0129746. doi: 10.1371/ journal.pone.0129746 PMID: 26075599 2. Chen F, Sun D, Guo Y, GuoW, Ding Z, Li P, et al. (2015) Correction: Spatiotemporal Scan and AgePeriod-Cohort Analysis of Hepatitis C Virus in Henan,...

A unicyclic graph is a graph whose number of edges is equal to the number of vertices. Guo Shu-Guang [S.G. Guo, The largest Laplacian spectral radius of unicyclic graph, Appl. Math. J. Chinese Univ. Ser. A. 16 (2) (2001) 131–135] determined the first four largest Laplacian spectral radii together with the corresponding graphs among all unicyclic graphs on n vertices. In this paper, we extend th...

Nonlinear Benchmark Problem Yi Guo , David J. Hill , Zhong-Ping Jiang Department of Electrical Engineering The University of Sydney, NSW 2006, AUSTRALIA Email: [email protected], [email protected], [email protected] Abstract| In this paper, we study the fuzzy dissipativity design method and apply it to the nonlinear benchmark problem. By representing the nonlinear system with a dynamica...

Abstract. In this paper we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq(s1, . . . , sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang [12] on the renormalization of Euler-Zagier multiple zeta values. We show that our renormalization process pr...

Recently, Guo and Zeng discovered q-analogues of Faulhaber's formulas for the sums of powers. They left it as an open problem to extend the combinatorial interpretation of Faulhaber's formulas as given by Gessel and Viennot to the q case. In this note we will provide such an interpretation.

In this paper, a C0 linear finite element method for biharmonic equations is constructed and analyzed. In our construction, the popular post-processing gradient recovery operators are used to calculate approximately the second order partial derivatives of a C0 linear finite element function which do not exist in traditional meaning. The proposed scheme is straightforward and simple. More import...