30,262 research outputs found
Linear colorings of subcubic graphs
A linear coloring of a graph is a proper coloring of the vertices of the
graph so that each pair of color classes induce a union of disjoint paths. In
this paper, we prove that for every connected graph with maximum degree at most
three and every assignment of lists of size four to the vertices of the graph,
there exists a linear coloring such that the color of each vertex belongs to
the list assigned to that vertex and the neighbors of every degree-two vertex
receive different colors, unless the graph is or . This confirms
a conjecture raised by Esperet, Montassier, and Raspaud. Our proof is
constructive and yields a linear-time algorithm to find such a coloring
Cracking pressure control of parylene checkvalve using slanted tensile tethers
MEMS check valves with fixed cracking pressures are important in micro-fluidic applications where the pressure, flow directions and flow rates all need to be carefully controlled. This work presents a new surface-micromachined parylene check valve that uses residual thermal stress in the parylene to control its cracking pressure. The new check valve uses slanted tethers to allow the parylene tensile stress to apply a net downward force on the valving seat against the orifice. The angle of the slanted tethers is made using a gray-scale mask to create a sloped sacrificial photoresist with the following tether parylene deposition. The resulted check valves have both the cracking pressures and flow profiles agreeable well with our theoretical analysis
Constraining fast radio burst progenitors with gravitational lensing
Fast Radio Bursts (FRBs) are new transient radio sources discovered recently.
Because of the angular resolution restriction in radio surveys, no optical
counter part has been identified yet so it is hard to determine the progenitor
of FRBs. In this paper we propose to use radio lensing survey to constrain FRB
progenitors. We show that, different types of progenitors lead to different
probabilities for a FRB to be gravitationally lensed by dark matter halos in
foreground galaxies, since different type progenitors result in different
redshift distributions of FRBs. For example, the redshift distribution of FRBs
arising from double stars shifts toward lower redshift than of the FRBs arising
from single stars, because double stars and single stars have different
evolution timescales. With detailed calculations, we predict that the FRB
sample size for producing one lensing event varies significantly for different
FRB progenitor models. We argue that this fact can be used to distinguish
different FRB models and also discuss the practical possibility of using
lensing observation in radio surveys to constrain FRB progenitors.Comment: 14 pages, including 6 figures and 1 tabl
Search for strong gravitational lensing effect in the current GRB data of BATSE
Because gamma-ray bursts (GRBs) trace the high-z Universe, there is an
appreciable probability for a GRB to be gravitational lensed by galaxies in the
universe. Herein we consider the gravitational lensing effect of GRBs
contributed by the dark matter halos in galaxies. Assuming that all halos have
the singular isothermal sphere (SIS) mass profile in the mass range and all GRB samples follow
the intrinsic redshift distribution and luminosity function derived from the
Swift LGRBs sample, we calculated the gravitational lensing probability in
BATSE, Swift/BAT and Fermi/GBM GRBs, respectively. With an derived probability
result in BATSE GRBs, we searched for lensed GRB pairs in the BATSE 5B GRB
Spectral catalog. The search did not find any convincing gravitationally lensed
events. We discuss our result and future observations for GRB lensing
observation.Comment: 18 pages, 8 figure
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