468 research outputs found
Capacities from the Chiu-Tamarkin complex
In this paper, we construct a sequence of symplectic
capacities based on the Chiu-Tamarkin complex , a
-equivariant invariant coming from the microlocal theory of
sheaves. We compute for convex toric domains, which
are the same as the Gutt-Hutchings capacities. Our method also works for the
prequantized contact manifold . We define a sequence of
"contact capacities" on the prequantized contact
manifold , and we compute them for prequantized convex toric
domains.Comment: Major revision. We add a discussion on the -action at the end of
Subsection 0.3. More details are provided in Subsection 1.4, Section 2 and
Section 4. We rewrite Section 3. Comments are welcome
A Note on Homoclinic Orbits for Second Order Hamiltonian Systems
In this paper, we study the existence for the homoclinic orbits for the
second order Hamiltonian systems. Under suitable conditions on the potential
, we apply the direct method of variations and the Fourier analysis to prove
the existence of homoclinc orbits
Forced Oscillations of the Korteweg-de Vries Equation on a Bounded Domain and their Stability
It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem
uuxuxxx 0 \u3c x \u3c 1, t \u3e 0, (*)
It is shown that if the boundary forcing is periodic with small amplitude, then the small amplitude solution of (*) becomes eventually time-periodic. Viewing (*) (without the initial condition ) as an infinite-dimensional dynamical system in the Hilbert space , we also demonstrate that for a given periodic boundary forcing with small amplitude, the system (*) admits a (locally) unique limit cycle, or forced oscillation, which is locally exponentially stable. A list of open problems are included for the interested readers to conduct further investigations
RESEARCH ON THE REFORM OF UNIVERSITY MANAGEMENT SYSTEM FROM THE PERSPECTIVE OF EDUCATIONAL PSYCHOLOGY AND UNIVERSITY GOVERNANCE
A hepatitis E outbreak by genotype 4 virus in Shandong province, China
AbstractHepatitis E vaccine was available in China in 2012, but the priority population for immunization is not clear. In 2013, a hepatitis E outbreak occurred in a company of Shandong province, China where most employees moved from other provinces and dined at the company’s cafeteria. A total of fourteen (19%, 14/73) case-patients were identified, and three of them had symptomatic infection with one death. The proportion of symptomatic infection was much higher among those aged ⩾50years than those aged <50years (2/2 vs. 1/12, P=0.03), and higher in males than females (3/8 vs. 0/6, P=0.21). Food in the company’s cafeteria might be the possible source of the outbreak. The findings from this outbreak investigation indicate that individuals aged ⩾50years, particularly males, might be the population of top priority for hepatitis E vaccination in China
Contact non-squeezing at large scale via generating functions
Using SFT techniques, Eliashberg, Kim and Polterovich (2006) proved that if
for some integer then there is no contact
squeezing in of the prequantization of the ball of
radius into the prequantization of the ball of radius . This result
was extended to the case of balls of radius and with by Chiu (2017) and the first author (2016), using
respectively microlocal sheaves and SFT. In the present article we recover this
general contact non-squeezing theorem using generating functions, a classical
method based on finite dimensional Morse theory. More precisely, we develop an
equivariant version, with respect to a certain action of a finite cyclic group,
of the generating function homology for domains of
defined by the second author (2011). A key role in the construction is played
by translated chains of contactomorphisms, a generalization of translated
points.Comment: 32 page
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