The isoperimetric problem in the plane with the sum of two Gaussian densities
We consider the isoperimetric problem for the sum of two Gaussian densities in the line and the plane. We prove that the double Gaussian isoperimetric regions in the line are rays and that if the double Gaussian isoperimetric regions in the plane are half-spaces, then they must be bounded by vertical lines.
Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10054850
Journal Name:
Involve
Volume:
11
Issue:
4
Page Range or eLocation-ID:
549-567
ISSN:
1944-4184
Spectropolarimetry enables us to measure the geometry and chemical structure of the ejecta in supernova explosions, which is fundamental for the understanding of their explosion mechanism(s) and progenitor systems. We collected archival data of 35 Type Ia supernovae (SNe Ia), observed with Focal Reducer and Low-Dispersion Spectrograph (FORS) on the Very Large Telescope at 127 epochs in total. We examined the polarization of the Si ii λ6355 Å line ($p_{\rm Si\, \small {II}}$) as a function of time, which is seen to peak at a range of various polarization degrees and epochs relative to maximum brightness. We reproduced the \$\Delta m_{15}\!-\!p_{\rm Si\,more »