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
Jako Bouveretův syndrom je označována obstrukce v oblasti duodena impaktovaným žlučovým kamenem, který vycestuje cholecystoduodenální či cholecystogastrickou píštělí. Onemocnění je vzácné, vyskytuje se zejména u starších žen s četnými komorbiditami a vysokým operačním rizikem. K diagnóze se zpravidla dospěje endoskopicky nebo pomocí zobrazovacích metod. Pokud stav nelze řešit endoskopicky, je indikováno operační řešení. Autoři prezentují případ Bouveretova syndromu u 79leté pacientky, u níž se zdařilo zdokumentovat všechny fáze vyšetřovacího a léčebného procesu. Součástí sdělení je přehled literatury týkající se diagnostiky a terapie tohoto vzácného syndromu., Bouveret syndrome is a gastric outlet obstruction caused by impaction of a gallstone that passes through a cholecystoduodenal or cholecystogastric fistula. It is a rare disease, most common in elderly women with multiple comorbidities and high surgical risk. The diagnosis can be made either radiologically or endoscopically. Endoscopic extraction is the preferred therapeutic option. Surgical intervention is indicated when endoscopic methods fail. We describe a case of Bouveret syndrome in a 79 years old woman. The report is followed by a review of literature on the diagnostics and treatment of this rare syndrome., and P. Kocián, M. Bocková, J. Schwarz