14,190 research outputs found
The strong rainbow vertex-connection of graphs
A vertex-colored graph is said to be rainbow vertex-connected if every
two vertices of are connected by a path whose internal vertices have
distinct colors, such a path is called a rainbow path. The rainbow
vertex-connection number of a connected graph , denoted by , is the
smallest number of colors that are needed in order to make rainbow
vertex-connected. If for every pair of distinct vertices, contains a
rainbow geodesic, then is strong rainbow vertex-connected. The
minimum number for which there exists a -vertex-coloring of that
results in a strongly rainbow vertex-connected graph is called the strong
rainbow vertex-connection number of , denoted by . Observe that
for any nontrivial connected graph . In this paper,
sharp upper and lower bounds of are given for a connected graph
of order , that is, . Graphs of order such that
are characterized, respectively. It is also shown that,
for each pair of integers with and , there
exists a connected graph such that and .Comment: 10 page
Superconducting phase with a chiral -wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor
We show that a chiral -wave superconducting pairing may be induced in
the lowest heavy hole band of a hole-doped semiconductor thin film through
proximity contact with an \textit{s}-wave superconductor. The chirality of the
pairing originates from the Berry phase accumulated for a heavy hole
moving along a close path on the Fermi surface. There exist three chiral
gapless Majorana edge states, in consistence with the chiral % -wave
pairing. We show the existence of zero energy Majorana fermions in vortices in
the semiconductor-superconductor heterostructure by solving the
Bogoliubov-de-Gennes equations numerically as well as analytically in the
strong confinement limit.Comment: 5 pages, 4 figure
Activity modulation and allosteric control of a scaffolded DNAzyme using a dynamic DNA nanostructure.
Recognition of the fundamental importance of allosteric regulation in biology dates back to not long after its discovery in the 1960s. Our ability to rationally engineer this potentially useful property into normally non-allosteric catalysts, however, remains limited. In response we report a DNA nanotechnology-enabled approach for introducing allostery into catalytic nucleic acids. Specifically, we have grafted one or two copies of a peroxidase-like DNAzyme, hemin-bound G-quadruplex (hemin-G), onto a DNA tetrahedral nanostructure in such a manner as to cause them to interact, modulating their catalytic activity. We achieve allosteric regulation of these catalysts by incorporating dynamically responsive oligonucleotides that respond to specific "effector" molecules (complementary oligonucleotides or small molecules), altering the spacing between the catalytic sites and thus regulating their activity. This designable approach thus enables subtle allosteric modulation in DNAzymes that is potentially of use for nanomedicine and nanomachines
Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters
Spatial modes have received substantial attention over the last decades and are used in optical communication applications. In fiber-optic communications, the employed linearly polarized modes and phase vortex modes carrying orbital angular momentum can be synthesized by fiber vector eigenmodes. To improve the transmission capacity and miniaturize the communication system, straightforward fiber vector eigenmode multiplexing and generation of fiber-eigenmode-like polarization vortices (vector vortex modes) using photonic integrated devices are of substantial interest. Here, we propose and demonstrate direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters. By exploiting vector vortex modes (radially and azimuthally polarized beams) generated from silicon microring resonators etched with angular gratings, we report data-carrying fiber vector eigenmode multiplexing transmission through a 2-km large-core fiber, showing low-level mode crosstalk and favorable link performance. These demonstrations may open up added capacity scaling opportunities by directly accessing multiple vector eigenmodes in the fiber and provide compact solutions to replace bulky diffractive optical elements for generating various optical vector beams
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