67,138 research outputs found
Modularity in orbifold theory for vertex operator superalgebras
This paper is about the orbifold theory for vertex operator superalgebras.
Given a vertex operator superalgebra V and a finite automorphism group G of V,
we show that the trace functions associated to the twisted sectors are
holomorphic in the upper half plane for any commuting pairs in G under the
C_2-cofinite condition. We also establish that these functions afford a
representation of the full modular group if V is C_2-cofinite and g-rational
for any g in G.Comment: 31 page
Markov Selection and -strong Feller for 3D Stochastic Primitive Equations
This paper studies some analytical properties of weak solutions of 3D
stochastic primitive equations with periodic boundary conditions. The
martingale problem associated to this model is shown to have a family of
solutions satisfying the Markov property, which is achieved by means of an
abstract selection principle. The Markov property is crucial to extend the
regularity of the transition semigroup from small times to arbitrary times.
Thus, under a regular additive noise, every Markov solution is shown to have a
property of continuous dependence on initial conditions, which follows from
employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li
formula
On the small time asymptotics of 3D stochastic primitive equations
In this paper, we establish a small time large deviation principle for the
strong solution of 3D stochastic primitive equations driven by multiplicative
noise. Both the small noise and the small, but highly nonlinear, unbounded
nonlinear terms should be taken into consideration
Malliavin Matrix of Degenerate SDE and Gradient Estimate
In this paper, we prove that the inverse of Malliavin matrix is p integrable
for a kind of degenerate stochastic differential equation under some
conditions, which like to Hormander condition, but don't need all the
coefficients of the SDE are smooth. Furthermore, we obtain a uniform estimation
for Malliavin matrix, a gradient estimate, and prove that the semigroup
generated by the SDE is strong Feller. Also some examples are given
Modularity of trace functions in orbifold theory for Z-graded vertex operator superalgebras
We study the trace functions in orbiford theory for Z-graded vertex operator
superalgebras and obtain a modular invariance result. More precisely, let V be
a C_2-cofinite Z-graded vertex operator superalgebra and G a finite
automorphism group of V. Then for any commuting pairs (g,h) in G, the
h\sigma-trace functions associated to the simple g-twisted V-modules are
holomorphic in the upper half plane where \sigma is the canonical involution on
V coming from the superspace structure of V. If V is further g-rational for
every g n G, the trace unctions afford a representation for the full modular
group SL(2,Z).Comment: 14 page
Ergodicity for a class of semilinear stochastic partial differential equations
In this paper, we establish the existence and uniqueness of invariant
measures for a class of semilinear stochastic partial differential equations
driven by multiplicative noise on a bounded domain. The main results can be
applied to SPDEs of various types such as the stochastic Burgers equation and
the reaction-diffusion equations perturbed by space-time white noise
3D tamed Navier-Stokes equations driven by multiplicative L\'{e}vy noise: Existence, uniqueness and large deviations
In this paper, we show the existence and uniqueness of a strong solution to
stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise
with periodic boundary conditions. Then we establish the large deviation
principles of the strong solution on the state space
, where the weak convergence approach plays a
key role.Comment: arXiv admin note: text overlap with arXiv:1801.09565; text overlap
with arXiv:1701.00314 by other author
Twisted representations of vertex operator superalgebras
This paper gives an analogue of A_g(V) theory for a vertex operator
superalgebra V and an automorphism g of finite order. The relation between the
g-twisted V-modules and A_g(V)-modules is established. It is proved that if V
is g-rational, then A_g(V) is finite dimensional semisimple associative algebra
and there are only finitely many irreducible g-twisted V-modules.Comment: 23 page
Ergodicity of the 2D Navier-Stokes Equations with Degenerate Multiplicative Noise
Consider the two-dimensional, incompressible Navier-Stokes equations on the
torus We prove that the semigroup P_t generated by the solutions to stochastic
Navier-stokes equations is asymptotically strong Feller. Moreover, we also
prove that semigroup P_t is exponentially ergodic in some sens
Origin of Cosmic Ray Electrons and Positrons
With experimental results of AMS on the spectra of cosmic ray (CR) ,
, and positron fraction, as well as new measurements of CR
flux by HESS, one can better understand the CR lepton (
and ) spectra and the puzzling electron-positron excess above 10
GeV. In this article, spectra of CR and are fitted with a
physically motivated simple model, and their injection spectra are obtained
with a one-dimensional propagation model including the diffusion and energy
loss processes. Our results show that the electron-positron excess can be
attributed to uniformly distributed sources that continuously inject into the
galactic disk electron-positron with a power-law spectrum cutting off near 1
TeV and a triple power-law model is needed to fit the primary CR electron
spectrum. The lower energy spectral break can be attributed to propagation
effects giving rise to a broken power-law injection spectrum of primary CR
electrons with a spectral hardening above 40 GeV
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