2,854 research outputs found
Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations
An algebraic structure related to discrete zero curvature equations is
established. It is used to give an approach for generating master symmetries of
first degree for systems of discrete evolution equations and an answer to why
there exist such master symmetries. The key of the theory is to generate
nonisospectral flows from the discrete spectral
problem associated with a given system of discrete evolution equations. Three
examples are given.Comment: 24 pages, LaTex, revise
Finite-volume effects on octet-baryon masses in covariant baryon chiral perturbation theory
We study finite-volume effects on the masses of the ground-state octet
baryons using covariant baryon chiral perturbation theory (ChPT) up to
next-to-leading order by analyzing the latest lattice Quantum
ChromoDynamics (LQCD) results from the NPLQCD collaboration. Contributions of
virtual decuplet baryons are taken into account using the "consistent" coupling
scheme. We compare our results with those obtained from heavy baryon ChPT and
show that, although both approaches can describe well the lattice data, the
underlying physics is different: In HBChPT, virtual decuplet baryons play a
more important role than they do in covariant ChPT. This is because the virtual
octet baryon contributions to finite-volume corrections are larger in covariant
ChPT than in HBChPT, while the contributions of intermediate decuplet baryons
are smaller, because of relativistic effects. We observe that for the octet
baryon masses, at fixed () finite-volume corrections decrease
as approaches its physical value, provided that the strange quark mass
is at or close to its physical value, as in most LQCD setups.Comment: 15 pages, 5 figure
A Coupled AKNS-Kaup-Newell Soliton Hierarchy
A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is
proposed in terms of hereditary symmetry operators resulted from Hamiltonian
pairs. Zero curvature representations and tri-Hamiltonian structures are
established for all coupled AKNS-Kaup-Newell systems in the hierarchy.
Therefore all systems have infinitely many commuting symmetries and
conservation laws. Two reductions of the systems lead to the AKNS hierarchy and
the Kaup-Newell hierarchy, and thus those two soliton hierarchies also possess
tri-Hamiltonian structures.Comment: 15 pages, late
A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
A bi-Hamiltonian formulation is proposed for triangular systems resulted by
perturbations around solutions, from which infinitely many symmetries and
conserved functionals of triangular systems can be explicitly constructed,
provided that one operator of the Hamiltonian pair is invertible. Through our
formulation, four examples of triangular systems are exhibited, which also show
that bi-Hamiltonian systems in both lower dimensions and higher dimensions are
many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian
systems and illustrate that multi-scale perturbations can lead to
higher-dimensional bi-Hamiltonian systems.Comment: 16 pages, to appear in J. Math. Phy
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PACAP neuropeptide promotes Hepatocellular Protection via CREB-KLF4 dependent autophagy in mouse liver Ischemia Reperfusion Injury.
Organ ischemia reperfusion injury (IRI), associated with acute hepatocyte death, remains an unresolved problem in clinical orthotopic liver transplantation (OLT). Autophagy, an intracellular self-digesting progress, is responsible for cell reprograming required to regain post-stress homeostasis. Methods: Here, we analyzed the cytoprotective mechanism of pituitary adenylate cyclase-activating polypeptide (PACAP)-promoted hepatocellular autophagy in a clinically relevant mouse model of extended hepatic cold storage (4 °C UW solution for 20 h) followed by syngeneic OLT. Results: In contrast to 41.7% of liver graft failure by day 7 post-transplant in control group, PACAP treatment significantly improved graft survival (91.7% by day 14), and promoted autophagy-associated regeneration programs in OLT. In parallel in vitro studies, PACAP-enhanced autophagy ameliorated cellular damage (LDH/ALT levels), and diminished necrosis in H2O2-stressed primary hepatocytes. Interestingly, PACAP not only induced nuclear cAMP response element-binding protein (CREB), but also triggered reprogramming factor Kruppel-like factor 4 (KLF4) expression in IR-stressed OLT. Indeed, CREB inhibition attenuated hepatic autophagy and recreated hepatocellular injury in otherwise PACAP-protected livers. Furthermore, CREB inhibition suppressed PACAP-induced KLF4 expression, whereas KLF4 blockade abolished PACAP-promoted autophagy and neutralized PACAP-mediated hepatoprotection both in vivo and in vitro. Conclusion: Current study documents the essential neural regulation of PACAP-promoted autophagy in hepatocellular homeostasis in OLT, which provides the emerging therapeutic principle to combat hepatic IRI in OLT
Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions
Riemann theta functions are used to construct one-periodic and two-periodic
wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The
basis for the involved solution analysis is the Hirota bilinear formulation,
and the particular dependence of the equations on independent variables
guarantees the existence of one-periodic and two-periodic wave solutions
involving an arbitrary purely imaginary Riemann matrix. The resulting theory is
applied to two nonlinear equations possessing Hirota bilinear forms:
and
where , thereby yielding their one-periodic and two-periodic wave
solutions describing one dimensional propagation of waves
A multiple exp-function method for nonlinear differential equations and its application
A multiple exp-function method to exact multiple wave solutions of nonlinear
partial differential equations is proposed. The method is oriented towards ease
of use and capability of computer algebra systems, and provides a direct and
systematical solution procedure which generalizes Hirota's perturbation scheme.
With help of Maple, an application of the approach to the dimensional
potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and
2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton
type solutions. Two cases with specific values of the involved parameters are
plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure
A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations
A Hamiltonian pair with arbitrary constants is proposed and thus a sort of
hereditary operators is resulted. All the corresponding systems of evolution
equations possess local bi-Hamiltonian formulation and a special choice of the
systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late
Scanning Tunnelling Spectroscopic Studies of Dirac Fermions in Graphene and Topological Insulators
We report novel properties derived from scanning tunnelling spectroscopic (STS) studies of Dirac fermions in graphene and the surface state (SS) of a strong topological insulator (STI), Bi_2Se_3. For mono-layer graphene grown on Cu by chemical vapour deposition (CVD), strain-induced scalar and gauge potentials are manifested by the charging effects and the tunnelling conductance peaks at quantized energies, respectively. Additionally, spontaneous time-reversal symmetry breaking is evidenced by the alternating anti-localization and localization spectra associated with the zero-mode of two sublattices while global time-reversal symmetry is preserved under the presence of pseudo-magnetic fields. For Bi_2Se_3 epitaxial films grown on Si(111) by molecular beam epitaxy (MBE), spatially localized unitary impurity resonances with sensitive dependence on the energy difference between the Fermi level and the Dirac point are observed for samples thicker than 6 quintuple layers (QL). These findings are characteristic of the SS of a STI and are direct manifestation of strong topological protection against impurities. For samples thinner than 6-QL, STS studies reveal the openup of an energy gap in the SS due to overlaps of wave functions between the surface and interface layers. Additionally, spin-preserving quasiparticle interference wave-vectors are observed, which are consistent with the Rashba-like spin-orbit splitting
Finite-dimensional integrable systems associated with Davey-Stewartson I equation
For the Davey-Stewartson I equation, which is an integrable equation in 1+2
dimensions, we have already found its Lax pair in 1+1 dimensional form by
nonlinear constraints. This paper deals with the second nonlinearization of
this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems
with a constraint of Neumann type. The full set of involutive conserved
integrals is obtained and their functional independence is proved. Therefore,
the Hamiltonian systems are completely integrable in Liouville sense. A
periodic solution of the Davey-Stewartson I equation is obtained by solving
these classical Hamiltonian systems as an example.Comment: 18 pages, LaTe
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