We continue our work (Y. Li, C. Zhao in J Differ Equ 212:208–233, 2005) to study the structure of positive solutions to the equation ε m Δmu − u m−1 + f(u) = 0 with homogeneous Neumann boundary condition in a smooth bounded domain of (N ≥ 2). First, w . . .

The expansion of space, and other geometric properties of cosmological models, can be studied using geometrically defined notions of relative velocity. In this paper, we consider test particles undergoing radial motion relative to comoving (geodesic) . . .

We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the "core" of the so . . .

We study the relationship between full-disk solar radiative flux at different wavelengths and average solar photospheric magnetic-flux density, using daily measurements from the Kitt Peak magnetograph and other instruments extending over one or more s . . .

Given n points in the plane, a covering path is a polygonal path that visits all the points. If no three points are collinear, every covering path requires at least n/2 segments, and n−1 straight line segments obviously suffice even if the covering pa . . .

Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p > 0 of countable cardinality. Let N be a normal (respectively, characteristic) subgroup of π 1(C). Under th . . .

It is shown that for a constant t∈N, every simple topological graph on n vertices has O(n)edges if the graph has no two sets of t edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of the intersecti . . .

Public sociology is an attempt to redress the issues of public engagement and disciplinary identity that have beset the discipline over the past several decades. While public sociology seeks to rectify the public invisibility of sociology, this paper . . .

We study the space – time distributions of intensity fluctuations in 2 – 3 hour sequences of multi-spectral, high-resolution, high-cadence, broad-band filtergram images of the Sun made by the SOT – FG system aboard the Hinode spacecraft. In the freque . . .

We study biplane graphs drawn on a finite planar point set \(S\) in general position. This is the family of geometric graphs whose vertex set is \(S\) and can be decomposed into two plane graphs. We show that two maximal biplane graphs—in the sense th . . .