Search

In this paper, we propose an application of hyperfunction theory to numerical integration. Hyperfunction theory is a generalized version of function theory where functions with singularities such as poles, discontinuities and delta impulses are expressed in terms of complex analytic functions. This feature of hyperfunction theory allows us to construct a numerical integration method for analytic functions. Theoretical error estimates show that our method converges geometrically, and numerical examples show that our method is very efficient especially for integrals with strong end-point singularities. In addition, we present an automatic integration method based on our hyperfunction method. [ABSTRACT FROM AUTHOR]

Let M be a CR manifold. The main results of this paper are the following:(A)When M is real analytic, a semi-global Hartogs extension phenomenon occurs for real analytic CR functions if and only if M is nowhere strictly pseudoconvex and dimRM⩾3.(B)When M is a standard manifold, the Hartogs–Bochner extension phenomenon occurs for non-CR-confined domains if and only if M is nowhere strictly pseudoconvex and dimCRM⩾2.(C)If M is a smooth submanifold of Cn foliated by complex curves, a semi-global Hartogs–Bochner extension phenomenon occurs for smooth non-CR-confined domains if and only if dimCRM⩾2.(D)If M is a real analytic nowhere strictly pseudoconvex manifold and if Ω is a sufficiently small domain in M, a hyperfunction which is real analytic in a neighborhood of bΩ and CR in a neighborhood of Ω is in fact real analytic on Ω. [Copyright &y& Elsevier]

Zinc oxide nanoparticles (ZnONPs) have been widely used in food storage containers and food additives in daily life. However, the impact of oral intake of ZnONPs on nervous system is extremely limited, especially on children and adolescents. In this study, four weeks old mice were treated with either vehicle or ZnONPs suspension solution at 26 mg/kg by intragastric administration for 30 days. Our results demonstrated that oral ZnONPs exposure could induce pathological changes in gut and abnormal excitement of enteric neurons. Interestingly, we found that ZnONPs caused enhancement of 5-hydroxytryptamine (5-HT) in gut by activation of its biosynthesis, transport and receptors, and subsequently resulting in increased level of 5-HT in brain via gut-brain communication by blood. Our data also showed that there were no apparent changes on the expressions of interleukin (Il)-6 , Il-1β , C–C motif chemokine ligand 2 (Ccl2), tumor necrosis factor (Tnf) in gut and zinc chelator Mt2 in gut and cortex. Meanwhile, no significant changes were observed on the expressions of tryptophan hydroxylase type 1, 5-HT receptor 3A (Htr3a) and Htr4 in hippocampus and cortex. Our study indicate that oral ZnONPs exposure causes hyperfunction of 5-HT in gut in young mice which may further spread to brain via gut-brain communication. • ZnONPs caused pathological changes and impaired endothelial tight junctions in gut. • ZnONPs caused abnormal excitement of enteric neurons and enhancement of 5-HT in gut. • ZnONPs caused activation of biosynthesis, transport and receptors of 5-HT in gut. • ZnONPs caused enhancement of 5-HT in brain via gut-brain communication by blood. [ABSTRACT FROM AUTHOR]