381,543 research outputs found
On the Convergence of a Modified Kaehler-Ricci flow
We study the convergence of a modified Kaeher-Ricci flow defined by Zhou
Zhang. We show that the flow converges to a singular metric when the limit
class is degenerate. This proves a conjecture of Zhang
Variational rotating solutions to non-isentropic Euler-Poisson equations with prescribed total mass
This paper proves the existence of variational rotating solutions to the
compressible non-isentropic Euler-Poisson equations with prescribed total mass.
This extends the result of the isentropic case [Auchmuty and Beals, Arch.
Ration. Mech. Anal., 1971] to the non-isentropic case. Compared with the
previous result of variational rotating solutions in non-isentropic case [Wu,
Journal of Differential Equations, 2015], to keep the constraint of a
prescribed finite total mass, the author establishes a new variational
structure the non-isentropic Euler-Poisson equations
On local holomorphic maps preserving invariant (p,p)-forms between bounded symmetric domains
Let be irreducible bounded symmetric domains. We
study local holomorphic maps from into
preserving the invariant -forms induced from the normalized Bergman
metrics up to conformal constants. We show that the local holomorphic maps
extends to algebraic maps in the rank one case for any and in the rank at
least two case for certain sufficiently large . The total geodesy thus
follows if for any or if
with rank and sufficiently large. As
a consequence, the algebraic correspondence between quasi-projective varieties
preserving invariant -forms is modular, where is
a torsion free, discrete, finite co-volume subgroup of Aut. This solves
partially a problem raised by Mok
Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws
In this paper we study large time behaviors toward shock waves and
rarefaction waves under periodic perturbations for 1-D convex scalar
conservation laws. The asymptotic stabilities and decay rates of shock waves
and rarefaction waves under periodic perturbations are proved
Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-d convex scalar viscous conservation laws
This paper studies the asymptotic stability of shock profiles and rarefaction
waves under space-periodic perturbations for one-dimensional convex scalar
viscous conservation laws. For the shock profile, we show that the solution
approaches the background shock profile with a constant shift in the norm at exponential rates. The new phenomena contrasting
to the case of localized perturbations is that the constant shift cannot be
determined by the initial excessive mass in general, which indicates that the
periodic oscillations at infinities make contributions to this shift. And the
vanishing viscosity limit for the shift is also shown. The key elements of the
poof consist of the construction of an ansatz which tends to two periodic
solutions as respectively, and the anti-derivative
variable argument, and an elaborate use of the maximum principle. For the
rarefaction wave, we also show the stability in the
norm.Comment: 43 pages, 3 figure
The CR immersion into a sphere with the degenerate CR Gauss map
It is a classical problem in algebraic geometry to characterize the algebraic
subvariety by using the Gauss map. In this note, we try to develop the analogue
theory in CR geometry. In particular, under some assumptions, we show that a CR
map between spheres is totally geodesic if and only if the CR Gauss map of the
image is degenerate
On the self-similar solution to full compressible Navier-Stokes equations without heat conductivity
In this work, we establish a class of globally defined, large solutions to
the free boundary problem of compressible Navier-Stokes equations with constant
shear viscosity and vanishing bulk viscosity. We establish such solutions with
initial data perturbed arbound any self-similar solution when \gamma > 7/6. In
the case when 7/6 < \gamma < 7/3, as long as the self-similar solution has
bounded entropy, a solution with bounded entropy can be constructed. It should
be pointed out that the solutions we obtain in this fashion do not in general
keep being a small perturbation of the self-similar solution due to the second
law of thermodynamics, i.e., the growth of entropy. If in addition, in the case
when 11/9 < \gamma < 5/3, we can construct a solution as a global-in-time small
perturbation of the self-similar solution and the entropy is uniformly bounded
in time
Non-invasive dynamic or wide-field imaging through opaque layers and around corners
In turbid media, scattering of light scrambles information of the incident
beam and represents an obstacle to optical imaging. Noninvasive imaging through
opaque layers is challenging for dynamic and wide-field objects due to
unreliable image reconstruction processes. We here propose a new perspective to
solve these problems: rather than using the full point-spread-function (PSF),
the wave distortions in scattering layers can be characterized with only the
phase of the optical-transfer-function (OTF, the Fourier transform of PSF),
with which diffraction-limit images can be analytically solved. We then develop
a method that exploits the redundant information dynamic objects, and can
reliably and rapidly recover OTFs' phases within several iterations. It enables
not only noninvasive video imaging at 25 ~ 200 Hz of a moving object hidden
inside turbid media, but also imaging under weak illumination that is
inaccessible with previous methods. Furthermore, by scanning a localized
illumination on the object plane, we propose a wide-field imaging approach,
with which we demonstrate an application where a photoluminescent sample hidden
behind four-layers of opaque polythene films is imaged with a modified
multi-photon excitation microscopy setup.Comment: Revised version with a new experiment adde
ARJA: Automated Repair of Java Programs via Multi-Objective Genetic Programming
Recent empirical studies show that the performance of GenProg is not
satisfactory, particularly for Java. In this paper, we propose ARJA, a new GP
based repair approach for automated repair of Java programs. To be specific, we
present a novel lower-granularity patch representation that properly decouples
the search subspaces of likely-buggy locations, operation types and potential
fix ingredients, enabling GP to explore the search space more effectively.
Based on this new representation, we formulate automated program repair as a
multi-objective search problem and use NSGA-II to look for simpler repairs. To
reduce the computational effort and search space, we introduce a test filtering
procedure that can speed up the fitness evaluation of GP and three types of
rules that can be applied to avoid unnecessary manipulations of the code.
Moreover, we also propose a type matching strategy that can create new
potential fix ingredients by exploiting the syntactic patterns of the existing
statements. We conduct a large-scale empirical evaluation of ARJA along with
its variants on both seeded bugs and real-world bugs in comparison with several
state-of-the-art repair approaches. Our results verify the effectiveness and
efficiency of the search mechanisms employed in ARJA and also show its
superiority over the other approaches. In particular, compared to jGenProg (an
implementation of GenProg for Java), an ARJA version fully following the
redundancy assumption can generate a test-suite adequate patch for more than
twice the number of bugs (from 27 to 59), and a correct patch for nearly four
times of the number (from 5 to 18), on 224 real-world bugs considered in
Defects4J. Furthermore, ARJA is able to correctly fix several real
multi-location bugs that are hard to be repaired by most of the existing repair
approaches.Comment: 30 pages, 26 figure
Holomorphic maps from the complex unit ball to Type IV classical domains
We prove rigidity results for holomorphic proper maps from the complex unit
ball to the Type IV bounded symmetric domain where . In addition, a classification result is
established when $m=n+1.
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