We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of Cao (2014)., Ji Liu, Jia-Shan Zheng., and Obsahuje seznam literatury
We obtain the boundedness of Calderón-Zygmund singular integral operators T of non-convolution type on Hardy spaces Hp(X) for 1/(1 + ε) < p < 1, where X is a space of homogeneous type in the sense of Coifman and Weiss (1971), and ε is the regularity exponent of the kernel of the singular integral operator T. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón’s identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was used in the literature., Yayuan Xiao., and Obsahuje bibliografii
Let $G$ be a weighted hypergraph with edges of size at most 2. Bollobás and Scott conjectured that $G$ admits a bipartition such that each vertex class meets edges of total weight at least $(w_1-\Delta_1)/2+2w_2/3$, where $w_i$ is the total weight of edges of size $i$ and $\Delta_1$ is the maximum weight of an edge of size 1. In this paper, for positive integer weighted hypergraph $G$ (i.e., multi-hypergraph), we show that there exists a bipartition of $G$ such that each vertex class meets edges of total weight at least $(w_0-1)/6+(w_1-\Delta_1)/3+2w_2/3$, where $w_0$ is the number of edges of size 1. This generalizes a result of Haslegrave. Based on this result, we show that every graph with $m$ edges, except for $K_2$ and $K_{1,3}$, admits a tripartition such that each vertex class meets at least $\lceil{2m}/5\rceil$ edges, which establishes a special case of a more general conjecture of Bollobás and Scott., Qinghou Zeng, Jianfeng Hou., and Obsahuje bibliografické odkazy
Na Přírodovědecké fakultě Masarykovy univerzity byl 10. března 2011, měsíc před 60. výročím jeho úmrtí (12. 4. 1951) uspořádán složkami Jednoty českých matematiků a fyziků v součinnosti s vedením fakulty seminář, jako vzpomínka na matematika a fyzika Bohuslava Hostinského., Martin Černohorský., and Obsahuje bibliografii