5,058 research outputs found
Gevrey Smoothing Effect for Solutions of the Non-Cutoff Boltzmann Equation in Maxwellian Molecules Case
In this paper we study the Gevrey regularity for the weak solutions to the
Cauchy problem of the non-cutoff spatially homogeneous Botlzmann equation for
the Maxwellian molecules model with the singularity exponent . We
establish that any weak solution belongs to the Gevrey spaces for any positive
time.Comment: 35 page
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Bayesian Model Selection Approach to Multiple Change-Points Detection with Non-Local Prior Distributions
We propose a Bayesian model selection (BMS) boundary detection procedure using non-local prior distributions for a sequence of data with multiple systematic mean changes. By using the non-local priors in the BMS framework, the BMS method can effectively suppress the non-boundary spike points with large instantaneous changes. Further, we speedup the algorithm by reducing the multiple change points to a series of single change point detection problems. We establish the consistency of the estimated number and locations of the change points under various prior distributions. From both theoretical and numerical perspectives, we show that the non-local inverse moment prior leads to the fastest convergence rate in identifying the true change points on the boundaries. Extensive simulation studies are conducted to compare the BMS with existing methods, and our method is illustrated with application to the magnetic resonance imaging guided radiation therapy data
Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps
We give three families of parabolic rational maps and show that every Cantor
set of circles as the Julia set of a non-hyperbolic rational map must be
quasisymmetrically equivalent to the Julia set of one map in these families for
suitable parameters. Combining a result obtained before, we give a complete
classification of the Cantor circles Julia sets in the sense of quasisymmetric
equivalence. Moreover, we study the regularity of the components of the Cantor
circles Julia sets and establish a sufficient and necessary condition when a
component of a Cantor circles Julia set is a quasicircle.Comment: 39 pages, 10 figures and 1 table, to appear in Discrete and Continous
Dynamical Systems-
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