33,210 research outputs found
Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equation
Let be a complete smooth metric measure space with
-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic
gradient estimates for positive solutions of a weighted nonlinear parabolic
equation \begin{align*} \displaystyle \Big(\Delta_f - \frac{\partial}{\partial
t}\Big) u(x,t) +q(x,t)u^\alpha(x,t) = 0, \end{align*} where and is an arbitrary constant. As
Applications we prove a Liouville-type theorem for positive ancient solutions
and Harnack-type inequalities for positive bounded solutions.Comment: 18 page
A generalized Gaussian process model for computer experiments with binary time series
Non-Gaussian observations such as binary responses are common in some
computer experiments. Motivated by the analysis of a class of cell adhesion
experiments, we introduce a generalized Gaussian process model for binary
responses, which shares some common features with standard GP models. In
addition, the proposed model incorporates a flexible mean function that can
capture different types of time series structures. Asymptotic properties of the
estimators are derived, and an optimal predictor as well as its predictive
distribution are constructed. Their performance is examined via two simulation
studies. The methodology is applied to study computer simulations for cell
adhesion experiments. The fitted model reveals important biological information
in repeated cell bindings, which is not directly observable in lab experiments.Comment: 49 pages, 4 figure
The effect of cross-organizational governance on supply chain resilience:A mediating and moderating model
Bis(2,2′-bipyridine)-1κ2 N,N′;3κ2 N,N′-hexa-μ-methacrylato-1:2κ6 O:O′;2:3κ6 O:O′-(nitrato-2κ2 O,O′)-1,3-dicobalt(II)-2-terbium(III)
In the title trinuclear cobalt–terbium complex, [Co2Tb(C4H5O2)6(NO3)(C10H8N2)2], the central TbIII and each of the CoII ions are bridged by three carboxylate groups of the methacrylate anions. The TbIII cation is coordinated by six O atoms from six methacrylate anions and two O atoms from a chelating nitrate anion in a distorted square-antiprismatic geometry. Each CoII ion is coordinated by three O atoms from three methylacrylate anions and two N atoms of a 2,2′-bypiridine ligand in a distorted square-pyramidal geometry. In the crystal structure, π–π stacking between the pyridine rings [centroid–centroid distances = 3.682 (8) and 3.760 (8) Å] is observed and weak intermolecular C—H⋯O hydrogen bonding is also present
- …