1,018 research outputs found
PL-006 HBV infection modeling and numerical simulation for anti-HBV infection personalized combination therapy
Uniqueness and Nondegeneracy of Ground States for in
We prove uniqueness of ground state solutions for the
nonlinear equation in , where
and for and for . Here denotes the fractional Laplacian
in one dimension. In particular, we generalize (by completely different
techniques) the specific uniqueness result obtained by Amick and Toland for
and in [Acta Math., \textbf{167} (1991), 107--126]. As a
technical key result in this paper, we show that the associated linearized
operator is nondegenerate;
i.\,e., its kernel satisfies .
This result about proves a spectral assumption, which plays a central
role for the stability of solitary waves and blowup analysis for nonlinear
dispersive PDEs with fractional Laplacians, such as the generalized
Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page
A negative mass theorem for surfaces of positive genus
We define the "sum of squares of the wavelengths" of a Riemannian surface
(M,g) to be the regularized trace of the inverse of the Laplacian. We normalize
by scaling and adding a constant, to obtain a "mass", which is scale invariant
and vanishes at the round sphere. This is an anlaog for closed surfaces of the
ADM mass from general relativity. We show that if M has positive genus then on
each conformal class, the mass attains a negative minimum. For the minimizing
metric, there is a sharp logarithmic Hardy-Littlewood-Sobolev inequality and a
Moser-Trudinger-Onofri type inequality.Comment: 8 page
Anomalous Rashba spin splitting in two-dimensional hole systems
It has long been assumed that the inversion asymmetry-induced Rashba spin
splitting in two-dimensional (2D) systems at zero magnetic field is
proportional to the electric field that characterizes the inversion asymmetry
of the confining potential. Here we demonstrate, both theoretically and
experimentally, that 2D heavy hole systems in accumulation layer-like single
heterostructures show the opposite behavior, i.e., a decreasing, but nonzero
electric field results in an increasing Rashba coefficient.Comment: 4 pages, 3 figure
Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian
In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya
inequalities with best Hardy constants, for domains satisfying suitable
geometric assumptions such as mean convexity or convexity. We then use them to
produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants
for various fractional Laplacians. In the case where the domain is the half
space our results cover the full range of the exponent of the
fractional Laplacians. We answer in particular an open problem raised by Frank
and Seiringer \cite{FS}.Comment: 42 page
Pair production of the heavy leptons in future high energy linear e^{+}e^{-} colliders
The littlest Higgs model with T-parity predicts the existence of the T-odd
particles, which can only be produced in pair. We consider pair production of
the T-odd leptons in future high energy linear collider ().
Our numerical results show that, as long as the T-odd leptons are not too
heavy, they can be copiously produced and their possible signals might be
detected via the processes in future
experiments.Comment: Discussions added, typos and references correcte
Comparison of Radiation Damage in Lead Tungstate Crystals under Pion and Gamma Irradiation
Studies of the radiation hardness of lead tungstate crystals produced by the
Bogoroditsk Techno-Chemical Plant in Russia and the Shanghai Institute of
Ceramics in China have been carried out at IHEP, Protvino. The crystals were
irradiated by a 40-GeV pion beam. After full recovery, the same crystals were
irradiated using a -ray source. The dose rate profiles along
the crystal length were observed to be quite similar. We compare the effects of
the two types of radiation on the crystals light output.Comment: 10 pages, 8 figures, Latex 2e, 28.04.04 - minor grammatical change
Vacuum Polarization Effects in the Lorentz and PCT Violating Electrodynamics
In this work we report new results concerning the question of dynamical mass
generation in the Lorentz and PCT violating quantum electrodynamics. A one loop
calculation for the vacuum polarization tensor is presented. The electron
propagator, "dressed" by a Lorentz breaking extra term in the fermion
Lagrangian density, is approximated by its first order: this scheme is shown to
break gauge invariance. Then we rather consider a full calculation to second
order in the Lorentz breaking parameter: we recover gauge invariance and use
the Schwinger-Dyson equation to discuss the full photon propagator. This allows
a discussion on a possible photon mass shift as well as measurable, observable
physical consequences, such as the Lamb-shift.Comment: Latex file, 19 pages, no figures, includes PACS number
Asymptotic behavior of solutions to the -Yamabe equation near isolated singularities
-Yamabe equations are conformally invariant equations generalizing
the classical Yamabe equation. In an earlier work YanYan Li proved that an
admissible solution with an isolated singularity at to the
-Yamabe equation is asymptotically radially symmetric. In this work
we prove that an admissible solution with an isolated singularity at to the -Yamabe equation is asymptotic to a radial
solution to the same equation on . These results
generalize earlier pioneering work in this direction on the classical Yamabe
equation by Caffarelli, Gidas, and Spruck. In extending the work of Caffarelli
et al, we formulate and prove a general asymptotic approximation result for
solutions to certain ODEs which include the case for scalar curvature and
curvature cases. An alternative proof is also provided using
analysis of the linearized operators at the radial solutions, along the lines
of approach in a work by Korevaar, Mazzeo, Pacard, and Schoen.Comment: 55 page
Two-particle localization and antiresonance in disordered spin and qubit chains
We show that, in a system with defects, two-particle states may experience
destructive quantum interference, or antiresonance. It prevents an excitation
localized on a defect from decaying even where the decay is allowed by energy
conservation. The system studied is a qubit chain or an equivalent spin chain
with an anisotropic () exchange coupling in a magnetic field. The chain
has a defect with an excess on-site energy. It corresponds to a qubit with the
level spacing different from other qubits. We show that, because of the
interaction between excitations, a single defect may lead to multiple localized
states. The energy spectra and localization lengths are found for
two-excitation states. The localization of excitations facilitates the
operation of a quantum computer. Analytical results for strongly anisotropic
coupling are confirmed by numerical studies.Comment: Updated version, 13 pages, 5 figures To appear in Phys. Rev. B (2003
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