16,333 research outputs found
Canonical Height Functions For Monomial Maps
We show that the canonical height function defined by Silverman does not have
the Northcott finiteness property in general. We develop a new canonical height
function for monomial maps. In certain cases, this new canonical height
function has nice properties
On the proper moduli spaces of smoothable K\"ahler-Einstein Fano varieties
In this paper, we investigate the geometry of the orbit space of the closure
of the subscheme parametrizing smooth Fano K\"ahler-Einstein manifolds inside
an appropriate Hilbert scheme. In particular, we prove that being K-semistable
is a Zariski open condition and establish the uniqueness for the
Gromov-Hausdorff limit for a punctured flat family of Fano K\"ahler-Einstein
manifolds. Based on these, we construct a proper scheme parameterizing the
S-equivalent classes of \QQ-Gorenstein smoothable, K-semistable Fano
varieties, and verify various necessary properties to guarantee that it is a
good moduli space.Comment: 41 pages. Final version. Minor change with exposition improved. To
appear in Duke Math.
Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds
In this note, we prove that there is a canonical continuous Hermitian metric
on the CM line bundle over the proper moduli space of
smoothable Kahler-Einstein Fano varieties. The curvature of this metric is the
Weil-Petersson current, which exists as a positive (1,1)-current on
and extends the canonical Weil-Petersson current on the
moduli space parametrizing smooth Kahler-Einstein Fano manifolds .
As a consequence, we show that the CM line bundle is nef and big on
and its restriction on is ample.Comment: 23 pages. Comments are welcom
Evolution of Alfv\'enic fluctuations inside an interplanetary coronal mass ejection and their contributions to local plasma heating: Joint observations from 1.0 AU to 5.4 AU
Directly tracking an interplanetary coronal mass ejection (ICME) by widely
separated spacecrafts is a great challenge. However, such an event could
provide us a good opportunity to study the evolution of embedded Alfv\'enic
fluctuations (AFs) inside ICME and their contributions to local plasma heating
directly. In this study, an ICME observed by Wind at 1.0 au on March 4-6 1998
is tracked to the location of Ulysess at 5.4 au. AFs are commonly found inside
the ICME at 1.0 au, with an occurrence rate of 21.7% and at broadband
frequencies from 4 to 5 Hz. When the ICME
propagates to 5.4 au, the Aflv\'enicity decreases significantly, and AFs are
rare and only found at few localized frequencies with the occurrence rate
decreasing to 3.0%. At the same time, the magnetic field intensity at the
AF-rich region has an extra magnetic dissipation except ICME expansion effect.
The energetics of the ICME at different radial distance is also investigated
here. Under similar magnetic field intensity situations at 1.0 au, the
turbulence cascade rate at the AF-rich region is much larger than the value at
the AF-lack region. Moreover, it can maintain as the decrease of magnetic field
intensity if there is lack of AFs. However, when there exists many AFs, it
reduces significantly as the AFs disappear. The turbulence cascade dissipation
rate within the ICME is inferred to be 1622.3 ,
which satisfies the requirement of local ICME plasma heating rate, 1653.2
. We suggest that AF dissipation is responsible for
extra magnetic dissipation and local plasma heating inside ICME.Comment: 15 pages, 3 figures, 1 tabl
Optimal Bounds on Functions of Quantum States under Quantum Channels
Let be quantum states and be a scalar function such as the trace norm, the fidelity, and the
relative entropy, etc. We determine optimal bounds for for for different class of functions
, where is the set of unitary quantum channels,
the set of mixed unitary channels, the set of unital quantum channels, and the
set of all quantum channels
On-Demand Density-Aware UAV Base Station 3D Placement for Arbitrarily Distributed Users with Guaranteed Data Rates
In this letter, we study the on-demand UAV-BS placement problem for
arbitrarily distributed users. This UAV-BS placement problem is modeled as a
knapsack-like problem, which is NP-complete. We propose a density-aware
placement algorithm to maximize the number of covered users subject to the
constraint of the minimum required data rates per user. Simulations are
conducted to evaluate the performance of the proposed algorithm in a real
environment with different user densities. Our numerical results indicate that
for various user densities our proposed solution can service more users with
guaranteed data rates compared to the existing method, while reducing the
transmit power by 29%.Comment: Accepted by IEEE Wireless Communications Letter
Tunneling states in graphene heterostructures consisting of two different graphene superlattices
We have theoretically investigated the properties of electronic transport in
graphene heterostructures, which are consisted of two different graphene
superlattices with one-dimensional periodic potentials. It is found that such
heterostructures possess an unusual tunneling state occurring inside the
original forbidden gaps, and the electronic conductance is greatly enhanced and
Fano factor is strongly suppressed near the energy of the tunneling state.
Finally we present the matching condition of the impedance of the pseudospin
wave for occuring the tunneling state by using the Bloch-wave expansion method.Comment: 8 pages, 5 figure
Product of two positive contractions
Several characterizations are given for a square matrix that can be written
as the product of two positive (semidefinite) projections. Based on one of
these characterizations, and the theory of alternating projections, a Matlab
program is written to check the condition and construct the two positive
projections whose product equal to the given matrix, if they exist.Comment: 12 page
Numerical Ranges of the product of Operators
We study containment regions of the numerical range of the product of
operators and such that and are line segments. It is
shown that the containment region is equal to the convex hull of elliptical
disks determined by the spectrum of , and conditions on and for the
set equality holding are obtained. The results cover the case when and
are self-adjoint operators extending the previous results on the numerical
range of the product of two orthogonal projections
Modulation of Solar Wind Energy Flux Input on Global Tropical Cyclone Activity
Studies on Sun-climate connection have been carried out for several decades,
and almost all of them focused on the effects of solar total irradiation
energy. As the second major terrestrial energy source from outer space, the
solar wind energy flux exhibits more significant long-term variations. However,
its link to the global climate change is rarely concerned and remain a mystery.
As a fundamental and important aspect of the Earth's weather and climate
system, tropical cyclone activity has been causing more and more attentions.
Here we investigate the possible modulation of the total energy flux input from
the solar wind into the Earth's magnetosphere on the global tropical cyclone
activity during 1963--2012. From a global perspective, the accumulated cyclone
energy increases gradually since 1963 and start to decrease after 1994. Compare
to the previously frequently used parameters, e,g., the sunspot number, the
total solar irradiation, the solar F10.7 irradiation, the tropical sea surface
temperature, and the south oscillation index, the total solar wind energy flux
input exhibits a better correlation with the global tropical cyclone activity.
Furthermore, the tropical cyclones seem to be more intense with higher
geomagnetic activities. A plausible modulation mechanism is thus proposed to
link the terrestrial weather phenomenon to the seemly-unrelated solar wind
energy input.Comment: 18 pages, 4 figure
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