2,304 research outputs found
Trees with Given Stability Number and Minimum Number of Stable Sets
We study the structure of trees minimizing their number of stable sets for
given order and stability number . Our main result is that the
edges of a non-trivial extremal tree can be partitioned into stars,
each of size or , so that every vertex is included in at most two
distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate
Bound states of neutral particles in external electric fields
Neutral fermions of spin with magnetic moment can interact with
electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation
for such a fermion coupled to a spherically symmetric or central electric field
can be reduced to two simultaneous ordinary differential equations by
separation of variables in spherical coordinates. For a wide variety of central
electric fields, bound-state solutions of critical energy values can be found
analytically. The degeneracy of these energy levels turns out to be numerably
infinite. This reveals the possibility of condensing infinitely many fermions
into a single energy level. For radially constant and radially linear electric
fields, the system of ordinary differential equations can be completely solved,
and all bound-state solutions are obtained in closed forms. The radially
constant field supports scattering solutions as well. For radially linear
fields, more energy levels (in addition to the critical one) are infinitely
degenerate. The simultaneous presence of central magnetic and electric fields
is discussed.Comment: REVTeX, 14 pages, no figur
Short and long distance contributions to
We study the decay of the neutral B meson to within the
framework of the Standard Model, including long distance contributions.Comment: 14 pages, 2 figures; A sign error in the numerical estimation
corrected. Results and figures changed. Results for resonance contributions
also updated to match with the experimetal values in the narrow width
approximatio
Stokes Diagnostis of 2D MHD-simulated Solar Magnetogranulation
We study the properties of solar magnetic fields on scales less than the
spatial resolution of solar telescopes. A synthetic infrared
spectropolarimetric diagnostics based on a 2D MHD simulation of
magnetoconvection is used for this. We analyze two time sequences of snapshots
that likely represent two regions of the network fields with their immediate
surrounding on the solar surface with the unsigned magnetic flux density of 300
and 140 G. In the first region we find from probability density functions of
the magnetic field strength that the most probable field strength at logtau_5=0
is equal to 250 G. Weak fields (B < 500 G) occupy about 70% of the surface,
while stronger fields (B 1000 G) occupy only 9.7% of the surface. The magnetic
flux is -28 G and its imbalance is -0.04. In the second region, these
parameters are correspondingly equal to 150 G, 93.3 %, 0.3 %, -40 G, and -0.10.
We estimate the distribution of line-of-sight velocities on the surface of log
tau_5=-1. The mean velocity is equal to 0.4 km/s in the first simulated region.
The averaged velocity in the granules is -1.2 km/s and in the intergranules is
2.5 km/s. In the second region, the corresponding values of the mean velocities
are equal to 0, -1.8, 1.5 km/s. In addition we analyze the asymmetry of
synthetic Stokes-V profiles of the Fe I 1564.8 nm line. The mean values of the
amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude
asymmetry is increased to 10% while the area asymmetry is only slightly varied.Comment: 24 pages, 12 figure
Spin in relativistic quantum theory
We discuss the role of spin in Poincar\'e invariant formulations of quantum
mechanics.Comment: 54 page
New supersymmetric solutions of N=2, D=5 gauged supergravity with hyperscalars
We construct new supersymmetric solutions, including AdS bubbles, in an N=2
truncation of five-dimensional N=8 gauged supergravity. This particular
truncation is given by N=2 gauged supergravity coupled to two vector multiples
and three incomplete hypermultiplets, and was originally investigated in the
context of obtaining regular AdS bubble geometries with multiple active
R-charges. We focus on cohomogeneity-one solutions corresponding to objects
with two equal angular momenta and up to three independent R-charges.
Curiously, we find a new set of zero and negative mass solitons asymptotic to
AdS_5/Z_k, for k \ge 3, which are everywhere regular without closed timelike
curves.Comment: Latex 3 times, 42 page
A comparison of characteristics of periodic surface micro/nano structures generated via single laser beam direct writing and particle lens array parallel beam processing
Abstract Changing material surface micro/nanostructures using laser beam texturing is a valuable approach in wide applications such as control of cell/bacterial adhesion and proliferation, solar cells and optical metamaterials. Here, we report a comparison of the characteristics of surface micro/nanostructures produced using single beam laser direct writing and particle lens array parallel laser beam patterning. A Nd:YVO4 nanosecond pulsed laser at the wavelength of 532 nm was used in the laser direct writing method to texture the stainless steel surface submerged in water and in air with different scanning patterns. Changes in surface morphology, wettability, surface chemistry, and optical reflectivity were analyzed. In the particle lens array method, an excimer nanosecond laser at 248 nm wavelength was adopted to produce surface patterns on GeSbTe (GST) film coated on a polycarbonate substrate by splitting and focusing a single laser beam into millions of parallel breams. Single beam laser direct writing shows that the surface of high roughness and oxygen percentage content presented high wettability and low reflectivity characteristics. However, the controllability of the type of surface micro/nanopatterns is limited. The parallel laser beam processing using particle lens array allows rapid production of user designed periodic surface patterns at nanoscale overcoming the optical diffraction limit with a high degree of controllability. Controlling the uniformity of the particle lens array is a challenge
Analytical solutions for two heteronuclear atoms in a ring trap
We consider two heteronuclear atoms interacting with a short-range
potential and confined in a ring trap. By taking the Bethe-ansatz-type
wavefunction and considering the periodic boundary condition properly, we
derive analytical solutions for the heteronuclear system. The eigen-energies
represented in terms of quasi-momentums can then be determined by solving a set
of coupled equations. We present a number of results, which display different
features from the case of identical atoms. Our result can be reduced to the
well-known Lieb-Liniger solution when two interacting atoms have the same
masses.Comment: 6 pages, 6 figure
- …