Isomorphic Chevalley groups over integral domains
Infinitely many solutions for a semilinear elliptic equation with sign-changing potential.
Trees with equal total domination and total restrained domination numbers
For a graph G = (V,E), a set S ⊆ V(G) is a total dominating set if it is dominating and both ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S ⊆ V(G) is a total restrained dominating set if it is total dominating and ⟨V(G)-S⟩ has no isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. We characterize all trees for which total domination and total restrained...
The logarithmic Sobolev constant of some finite Markov chains
The logarithmic Sobolev constant is always bounded above by half the spectral gap. It is natural to ask when this inequality is an equality. We consider this question in the context of reversible Markov chains on small finite state spaces. In particular, we prove that equality holds for simple random walk on the five cycle and we discuss assorted families of chains on three and four points.
An existence theorem for the Yamabe problem on manifolds with boundary
Let be a compact Riemannian manifold with boundary. We consider the problem (first studied by Escobar in 1992) of finding a conformal metric with constant scalar curvature in the interior and zero mean curvature on the boundary. Using a local test function construction, we are able to settle most cases left open by Escobar’s work. Moreover, we reduce the remaining cases to the positive mass theorem.
On the total restrained domination number of direct products of graphs
Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V∖S is adjacent to a vertex in S as well as to another vertex in V∖S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by , is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds...
A note on -balayages of matrix-exponential Lev́y processes.
The cutoff phenomenon for ergodic Markov processes.
Fixed point theorems for nonexpansive operators with dissipative perturbations in cones
Let be a cone in a Hilbert space , be an accretive mapping (equivalently, be a dissipative mapping) and be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in .
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