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
Fourteen three-month-old rabbits spontaneously-infected with the microsporidium Encephalilozoon cuniculi Levaditi, Nicolau et Schoen, 1923 were inoculated intravenously with lymphocytes (Ly) from seropositive bovine leukemia virus infected cattle (Ly/BLV) or with fetal lamb kidney cells infected with bovine fetal leukemia (FLK/BLV). Thirteen rabbits were seropositive to BLV at least for a period of three months. Six rabbits died of pulmonary lesions. Chronic inflammatory lesions of ence-phalitozoonosis were found in six rabbits killed between 454 and 548 days of the observation period. Five animals bore subcutaneous granulomas. Immunohistochemically, E. cuniculi was demonstrated in the inflammatory lesions of rabbits studied. Control animals also spontaneously infected with E. cuniculi did not show clinical signs of encephalitozoonosis. Morphological changes were found incidentally in the form of small glial foci and focal interstitial nephritis in these animals. The combined action of BLV - E. cuniculi on the bodies of rabbits is proposed as a suitable model for the study of encephalitozoonosis in man with human immunodeficiency virus (HIV) infection.