811 research outputs found
Infinitely Many Homoclinic Orbits for 2 n
By establishing a new proper variational framework and using the critical point
theory, we establish some new existence criteria to guarantee that the 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian Δn(r(t−n)φp(Δnu(t−1)))+q(t)φp(u(t))=f(t,u(t+n),…,u(t),…,u(t−n)), n∈ℤ(3), t∈ℤ, has infinitely many homoclinic orbits, where φp(s) is p-Laplacian operator; φp(s)=|s|p−2s(1<p<∞)r, q, f are nonperiodic in t. Our conditions on the potential are rather relaxed, and some existing results in the literature are improved
Geodesic Distance Function Learning via Heat Flow on Vector Fields
Learning a distance function or metric on a given data manifold is of great
importance in machine learning and pattern recognition. Many of the previous
works first embed the manifold to Euclidean space and then learn the distance
function. However, such a scheme might not faithfully preserve the distance
function if the original manifold is not Euclidean. Note that the distance
function on a manifold can always be well-defined. In this paper, we propose to
learn the distance function directly on the manifold without embedding. We
first provide a theoretical characterization of the distance function by its
gradient field. Based on our theoretical analysis, we propose to first learn
the gradient field of the distance function and then learn the distance
function itself. Specifically, we set the gradient field of a local distance
function as an initial vector field. Then we transport it to the whole manifold
via heat flow on vector fields. Finally, the geodesic distance function can be
obtained by requiring its gradient field to be close to the normalized vector
field. Experimental results on both synthetic and real data demonstrate the
effectiveness of our proposed algorithm
Sneutrino DM in the NMSSM with inverse seesaw mechanism
In supersymmetric theories like the Next-to-Minimal Supersymmetric Standard
Model (NMSSM), the lightest neutralino with bino or singlino as its dominant
component is customarily taken as dark matter (DM) candidate. Since light
Higgsinos favored by naturalness can strength the couplings of the DM and thus
enhance the DM-nucleon scattering rate, the tension between naturalness and DM
direct detection results becomes more and more acute with the improved
experimental sensitivity. In this work, we extend the NMSSM by inverse seesaw
mechanism to generate neutrino mass, and show that in certain parameter space
the lightest sneutrino may act as a viable DM candidate, i.e. it can annihilate
by multi-channels to get correct relic density and meanwhile satisfy all
experimental constraints. The most striking feature of the extension is that
the DM-nucleon scattering rate can be naturally below its current experimental
bounds regardless of the higgsino mass, and hence it alleviates the tension
between naturalness and DM experiments. Other interesting features include that
the Higgs phenomenology becomes much richer than that of the original NMSSM due
to the relaxed constraints from DM physics and also due to the presence of
extra neutrinos, and that the signatures of sparticles at colliders are quite
different from those with neutralino as DM candidate.Comment: 33 page
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