3,169 research outputs found
Geometric Aspects of the Moduli Space of Riemann Surfaces
This is a survey of our recent results on the geometry of moduli spaces and
Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and
math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller
spaces of Riemann surfaces with very good properties, study their curvatures
and boundary behaviors in great detail. Based on the careful analysis of these
new metrics, we have a good understanding of the Kahler-Einstein metric from
which we prove that the logarithmic cotangent bundle of the moduli space is
stable. Another corolary is a proof of the equivalences of all of the known
classical complete metrics to the new metrics, in particular Yau's conjectures
in the early 80s on the equivalences of the Kahler-Einstein metric to the
Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes
corrrecte
The range of the tangential Cauchy-Riemann system on a CR embedded manifold
We prove that every compact, pseudoconvex, orientable, CR manifold of \C^n,
bounds a complex manifold in the sense. In particular, the
tangential Cauchy-Riemann system has closed range
The Utilization of Heat Exchangers for Energy Conservation in Air Conditioning
This paper investigates the characteristics of heat exchanger (HPHE) as an efficient
coolness recovery unit in air conditioning through experimental studies. It was conducted
under a multiple-nozzle code tester based on the ASHRAE standards. The wind tunnel
was subjected to airflow with considerable variation in its inlet air temperature. Among
the factors being investigated are the air velocity, inlet and outlet air temperatures,
overall efficiency and the number of rows in longitudinal direction. The data obtained
were compared with the results predicted by previous theoretical studies. Good agreement
was observed
The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension
The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has
been the subject of intensive study over the last few decades, following Yau's
solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton
has become one of the most powerful tools in geometric analysis.
We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one
and show that the flow collapses and converges to a unique canonical metric on
its canonical model. Such a canonical is a generalized K\"ahler-Einstein
metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric
classification for K\"aher surfaces with a numerical effective canonical line
bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding
canonical metrics on canonical models of projective varieties of positive
Kodaira dimension
Generalized McKay quivers of rank three
For each finite subgroup G of SL(n, C), we introduce the generalized Cartan
matrix C_{G} in view of McKay correspondence from the fusion rule of its
natural representation. Using group theory, we show that the generalized Cartan
matrices have similar favorable properties such as positive semi-definiteness
as in the classical case of affine Cartan matrices (the case of SL(2,C)). The
complete McKay quivers for SL(3,C) are explicitly described and classified
based on representation theory
Implementing an eleven year through-train model to complete Primary and Secondary Education: creating a platform for accommodating the newest pedagogical practices and technologies in school
In educational transformation, Logos Academy of Hong Kong has started to create space in two aspects: to accommodate for new learning areas, and to use the most updated technologies for learning.
In different Learning Stages, new learning areas like "Family Life Education", "Analytical study of Current Issues", Mind-mapping, MegaSkills and Media Education are introduced. The teachers will design different level- and age-appropriate activities and assignments that encourage the mastery of basic concepts and development of aesthetic appreciation, family life education, character formation, physique building and inquiry/research skills. Moreover, integrated tasks and projects intertwining with different study skills are mounted to enable the children to experiment creative designs and try out increasingly complex investigations.
To facilitate learning and teaching, Logos Academy also creates new platforms to use the newest technologies for pre-lesson use, for lesson use, and for post-lesson use. It is reviewed that with the aid of some updated technologies, our teachers are committed to facilitate change, reflect on current practices, explore further improvements in new learning areas and to use the new technologies effectively - which will in turn enhance the effectiveness of integrated study skills, self-directed learning, team work and social interaction of the students
Some estimates of Wang-Yau quasilocal energy
Given a spacelike 2-surface in a spacetime and a constant future
timelike unit vector in , we derive upper and lower estimates
of Wang-Yau quasilocal energy for a given isometric
embedding of into a flat 3-slice in . The quantity itself depends on the choice of , however the infimum of
over does not. In particular, when lies
in a time symmetric 3-slice in and has nonnegative Brown-York quasilocal
mass \mby(\Sigma), our estimates show that equals \mby (\Sigma). We also study the spatial limit of , where is a large coordinate sphere in a
fixed end of an asymptotically flat initial data set and is
an isometric embeddings of into .
We show that if has future timelike ADM energy-momentum, then
equals the ADM mass
of .Comment: 17 page
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