1,168 research outputs found
Traveling Wave Solutions of a Reaction-Diffusion Equation with State-Dependent Delay
This paper is concerned with the traveling wave solutions of a
reaction-diffusion equation with state-dependent delay. When the birth function
is monotone, the existence and nonexistence of monotone traveling wave
solutions are established. When the birth function is not monotone, the minimal
wave speed of nontrivial traveling wave solutions is obtained. The results are
proved by the construction of upper and lower solutions and application of the
fixed point theorem
Direct Measurement of Piezoelectric Response around Ferroelectric Domain Walls in Crystals with Engineered Domain Configuration
We report the first investigation of the piezoelectric response on a
nanoscale in the poled ferroelectric crystals with engineered configuration of
domains. Piezoresponse force microscopy of tetragonal 0.63PMN-0.37PT
relaxor-based ferroelectric crystals reviled that the d33 piezoelectric
coefficient is significantly reduced within the distance of about 1 um from the
uncharged engineered domain wall. This finding is essential for understanding
the mechanisms of the giant piezoresponse in relaxor-based crystals and for
designing new piezoelectric materials
On the -spectral radius of hypergraphs
For real and a hypergraph , the -spectral radius
of is the largest eigenvalue of the matrix , where is the adjacency matrix of , which is a
symmetric matrix with zero diagonal such that for distinct vertices of
, the -entry of is exactly the number of edges containing both
and , and is the diagonal matrix of row sums of . We study
the -spectral radius of a hypergraph that is uniform or not necessarily
uniform. We propose some local grafting operations that increase or decrease
the -spectral radius of a hypergraph. We determine the unique
hypergraphs with maximum -spectral radius among -uniform hypertrees,
among -uniform unicyclic hypergraphs, and among -uniform hypergraphs with
fixed number of pendant edges. We also determine the unique hypertrees with
maximum -spectral radius among hypertrees with given number of vertices
and edges, the unique hypertrees with the first three largest (two smallest,
respectively) -spectral radii among hypertrees with given number of
vertices, the unique hypertrees with minimum -spectral radius among the
hypertrees that are not -uniform, the unique hypergraphs with the first two
largest (smallest, respectively) -spectral radii among unicyclic
hypergraphs with given number of vertices, and the unique hypergraphs with
maximum -spectral radius among hypergraphs with fixed number of pendant
edges
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