8,583 research outputs found
On Distance-Regular Graphs with Smallest Eigenvalue at Least
A non-complete geometric distance-regular graph is the point graph of a
partial geometry in which the set of lines is a set of Delsarte cliques. In
this paper, we prove that for fixed integer , there are only finitely
many non-geometric distance-regular graphs with smallest eigenvalue at least
, diameter at least three and intersection number
Spectral Characterization of the Hamming Graphs
We show that the Hamming graph H(3; q) with diameter three is uniquely determined by its spectrum for q ¸ 36. Moreover, we show that for given integer D ¸ 2, any graph cospectral with the Hamming graph H(D; q) is locally the disjoint union of D copies of the complete graph of size q ¡ 1, for q large enough.Hamming graphs;distance-regular graphs;eigenvalues of graphs
Directional supercontinuum generation: the role of the soliton
In this paper we numerically study supercontinuum generation by pumping a
silicon nitride waveguide, with two zero-dispersion wavelengths, with
femtosecond pulses. The waveguide dispersion is designed so that the pump pulse
is in the normal-dispersion regime. We show that because of self-phase
modulation, the initial pulse broadens into the anomalous-dispersion regime,
which is sandwiched between the two normal-dispersion regimes, and here a
soliton is formed. The interaction of the soliton and the broadened pulse in
the normal-dispersion regime causes additional spectral broadening through
formation of dispersive waves by non-degenerate four-wave mixing and
cross-phase modulation. This broadening occurs mainly towards the second
normal-dispersion regime. We show that pumping in either normal-dispersion
regime allows broadening towards the other normal-dispersion regime. This
ability to steer the continuum extension towards the direction of the other
normal-dispersion regime beyond the sandwiched anomalous-dispersion regime
underlies the directional supercontinuum notation. We numerically confirm the
approach in a standard silica microstructured fiber geometry with two
zero-dispersion wavelengths
Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model
We derive the effective potentials for composite operators in a
Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in
each case they are equivalent to the corresponding effective potentials based
on an auxiliary scalar field. The both effective potentials could lead to the
same possible spontaneous breaking and restoration of symmetries including
chiral symmetry if the momentum cutoff in the loop integrals is large enough,
and can be transformed to each other when the Schwinger-Dyson (SD) equation of
the dynamical fermion mass from the fermion-antifermion vacuum (or thermal)
condensates is used. The results also generally indicate that two effective
potentials with the same single order parameter but rather different
mathematical expressions can still be considered physically equivalent if the
SD equation corresponding to the extreme value conditions of the two potentials
have the same form.Comment: 7 pages, no figur
Quantum-mechanical machinery for rational decision-making in classical guessing game
In quantum game theory, one of the most intriguing and important questions
is, "Is it possible to get quantum advantages without any modification of the
classical game?" The answer to this question so far has largely been negative.
So far, it has usually been thought that a change of the classical game setting
appears to be unavoidable for getting the quantum advantages. However, we give
an affirmative answer here, focusing on the decision-making process (we call
'reasoning') to generate the best strategy, which may occur internally, e.g.,
in the player's brain. To show this, we consider a classical guessing game. We
then define a one-player reasoning problem in the context of the
decision-making theory, where the machinery processes are designed to simulate
classical and quantum reasoning. In such settings, we present a scenario where
a rational player is able to make better use of his/her weak preferences due to
quantum reasoning, without any altering or resetting of the classically defined
game. We also argue in further analysis that the quantum reasoning may make the
player fail, and even make the situation worse, due to any inappropriate
preferences.Comment: 9 pages, 10 figures, The scenario is more improve
Stable rotating dipole solitons in nonlocal optical media
We reveal that nonlocality can provide a simple physical mechanism for
stabilization of multi-hump optical solitons, and present the first example of
stable rotating dipole solitons and soliton spiraling, known to be unstable in
all types of realistic nonlinear media with local response.Comment: 3 pages, 3 figure
On geometric distance-regular graphs with diameter three
In this paper we study distance-regular graphs with intersection array {(t + 1)s. ts. (t - 1)(s + 1 - psi); 1, 2, (t + 1)psi} (1) where s. t. psi are integers satisfying t >= 2 and 1 = 2, there are only finitely many distance-regular graphs of order (s, t) with mallest eigenvalue -t -1, diameter D = 3 and intersection number c(2) = 2 except for Hamming graphs with diameter three. Moreover, we will show that if a distance-regular graph with intersection array (1) for t = 2 exists then (s, psi) = (15, 9). As Gavrilyuk and Makhnev (2013)[9] proved that the case (s, psi) = (15, 9) does not exist, this enables us to finish the classification of geometric distance-regular graphs with smallest eigenvalue -3, diameter D >= 3 and c(2) >= 2 which was started by the first author (Bang, 2013)[1]. (C) 2013 Elsevier Ltd. All rights reserved.X1121Ysciescopu
Analytical theory for dark soliton interaction in nonlocal nonlinear materials with arbitrary degree of nonlocality
We investigate theoretically the interaction of dark solitons in materials
with a spatially nonlocal nonlinearity. In particular we do this analytically
and for arbitrary degree of nonlocality. We employ the variational technique to
show that nonlocality induces an attractive force in the otherwise repulsive
soliton interaction.Comment: submitted for publicatio
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