skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Surjective word maps and Burnside’s $$p^aq^b$$ p a q b theorem
Award ID(s):
1840702
PAR ID:
10091627
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Inventiones mathematicae
Volume:
213
Issue:
2
ISSN:
0020-9910
Page Range / eLocation ID:
589 to 695
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Bridge Weigh-in-Motion (B-WIM) is the concept of using measured strains on a bridge to calculate the axle weights of trucks as they pass overhead at full highway speed. There exist a consensus that conventional instrumentation faces substantial practical problems that halts the feasibility of this theory, namely cost, installation time and complexity. This article will go through a new concept by moving toward the first Portable Bridge Weigh-In-Motion (P-B-WIM) system. The system introduce flying sensor concept which consist of a swarm of drones that have accelerometers and able to latch bridge girders to record acceleration data. Some perching mechanisms have been introduce in this paper to allow drones to latch bridges girders. At the same time, a new algorithm is developed to allow the B-WIM system to use the acceleration data to estimate the truck weigh instead of the strain measurements. The algorithm uses the kalman-filter-based estimation algorithm to estimate the state vectors (displacement and velocities) using limited measured acceleration response (from drones). The estimated state vector is used to feed a moving force identification (MFI) algorithm that shows good results in estimating a quarter car model weight. 
    more » « less
  2. Abstract Whole rock compositions at Buldir Volcano, western Aleutian arc, record a strong, continuous trend of iron depletion with decreasing MgO, classically interpreted as a calc-alkaline liquid line of descent. In contrast, olivine-hosted melt inclusions have higher total iron (FeO*) than whole rocks and show little change in FeO* with decreasing MgO. To investigate this discrepancy and determine the conditions required for strong iron depletion, we conducted oxygen fugacity (ƒO2) buffered, water-saturated crystallization experiments at 800 MPa and ƒO2 = QFM + 1.6 ± 0.4 (1$$\sigma$$) (where QFM refers to the quartz-fayalite-magnetite buffer) on a high-Al, basaltic starting material modeled after a Buldir lava. Experimental conditions were informed by olivine-hosted melt inclusions that record minimum entrapment pressures as high as 570 MPa, >6 wt % H2O, and ƒO2 of QFM + 1.4 (±0.2), making Buldir one of the most oxidized and wettest arc volcanoes documented globally. The experiments produce melts with Si-enrichment and Fe-depletion signatures characteristic of evolved, calc-alkaline magmas at the lowest MgO, although FeO* remains roughly constant over most of the experimental temperature range. Experiments saturate CrAl-spinel and olivine at 1160°C, followed by clinopyroxene and Al-spinel at 1085°C, hornblende at 1060°C, and, finally, plagioclase and magnetite between 1040°C and 960°C. Hornblende crystallization, not magnetite, generates the largest increase in SiO2 and largest decrease in FeO* in coexisting melts. Compositions of melt inclusions are consistent with experimental melts and reflect crystallization of a basaltic parent magma at high PH2O. In contrast, the whole rock compositional trends are influenced by magma mixing and phenocryst redistribution and accumulation. The crystallization experiments and natural liquids (melt inclusions and groundmass glass) from Buldir suggest that for an oxidized, hydrous primary basalt starting composition, significant Fe depletion from the melt will not occur until intermediate to late stages of magma crystallization (< ~4.5 wt % MgO). We conclude that the Buldir whole rock trend cannot be reproduced by crystallization at arc-relevant oxygen fugacities and is not a true liquid line of descent, warranting caution when interpreting volcanic trends globally. 
    more » « less