5,638 research outputs found
Towards the Green-Griffiths-Lang conjecture
The Green-Griffiths-Lang conjecture stipulates that for every projective
variety X of general type over C, there exists a proper algebraic subvariety of
X containing all non constant entire curves f : C X. Using the
formalism of directed varieties, we prove here that this assertion holds true
in case X satisfies a strong general type condition that is related to a
certain jet-semistability property of the tangent bundle TX . We then give a
sufficient criterion for the Kobayashi hyperbolicity of an arbitrary directed
variety (X,V). This work is dedicated to the memory of Professor Salah
Baouendi.Comment: version 2 has been expanded and improved (15 pages
Variable frequency microwave (VFM) processing facilities and application in processing thermoplastic matrix composites
Microwave processing of materials is a relatively new technology advancement alternative that provides new approaches for enhancing material properties as well as economic advantages through energy savings and accelerated product development. Factors that hinder the use of microwaves in materials processing are declining, so that prospect for the development of this technology seem to be very promising. The two mechanisms of orientation polarisation and interfacial space charge polarisation, together with dc conductivity, form the basis of high frequency heating. Clearly, advantages in utilising microwave technologies for processing materials include penetration radiation, controlled electric field distribution and selective and volumetric heating. However, the most commonly used facilities for microwave processing materials are of fixed frequency, e.g. 2.45 GHz. This paper presents a state-of-the-art review of microwave technologies, processing methods and industrial applications, using variable frequency microwave (VFM) facilities. This is a new alternative for microwave processing
Effective algebraic degeneracy
We prove that any nonconstant entire holomorphic curve from the complex line
C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary
dimension n (at least 2) must be algebraically degenerate provided X is generic
if its degree d = deg(X) satisfies the effective lower bound: d larger than or
equal to n^{{(n+1)}^{n+5}}
On the cohomology of pseudoeffective line bundles
The goal of this survey is to present various results concerning the
cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and
related properties of their multiplier ideal sheaves. In case the curvature is
strictly positive, the prototype is the well known Nadel vanishing theorem,
which is itself a generalized analytic version of the fundamental
Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested
here in the case where the curvature is merely semipositive in the sense of
currents, and the base manifold is not necessarily projective. In this
situation, one can still obtain interesting information on cohomology, e.g. a
Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a
surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his
PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing
theorem that depends on the concept of numerical dimension of a given
pseudoeffective line bundle. The proof of these results depends in a crucial
way on a general approximation result for closed (1,1)-currents, based on the
use of Bergman kernels, and the related intersection theory of currents.
Another important ingredient is the recent proof by Guan and Zhou of the strong
openness conjecture. As an application, we discuss a structure theorem for
compact K{\"a}hler threefolds without nontrivial subvarieties, following a
joint work with F.Campana and M.Verbitsky. We hope that these notes will serve
as a useful guide to the more detailed and more technical papers in the
literature; in some cases, we provide here substantially simplified proofs and
unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the
Abel Symposium, Trondheim, July 201
Low-momentum ring diagrams of neutron matter at and near the unitary limit
We study neutron matter at and near the unitary limit using a low-momentum
ring diagram approach. By slightly tuning the meson-exchange CD-Bonn potential,
neutron-neutron potentials with various scattering lengths such as
and are constructed. Such potentials are renormalized
with rigorous procedures to give the corresponding -equivalent
low-momentum potentials , with which the low-momentum
particle-particle hole-hole ring diagrams are summed up to all orders, giving
the ground state energy of neutron matter for various scattering lengths.
At the limit of , our calculated ratio of to that of
the non-interacting case is found remarkably close to a constant of 0.44 over a
wide range of Fermi-momenta. This result reveals an universality that is well
consistent with the recent experimental and Monte-Carlo computational study on
low-density cold Fermi gas at the unitary limit. The overall behavior of this
ratio obtained with various scattering lengths is presented and discussed.
Ring-diagram results obtained with and those with -matrix
interactions are compared.Comment: 9 pages, 7 figure
Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles
The construction of sections of bundles with prescribed jet values plays a
fundamental role in problems of algebraic and complex geometry. When the jet
values are prescribed on a positive dimensional subvariety, it is handled by
theorems of Ohsawa-Takegoshi type which give extension of line bundle valued
square-integrable top-degree holomorphic forms from the fiber at the origin of
a family of complex manifolds over the open unit 1-disk when the curvature of
the metric of line bundle is semipositive. We prove here an extension result
when the curvature of the line bundle is only semipositive on each fiber with
negativity on the total space assumed bounded from below and the connection of
the metric locally bounded, if a square-integrable extension is known to be
possible over a double point at the origin. It is a Hensel-lemma-type result
analogous to Artin's application of the generalized implicit function theorem
to the theory of obstruction in deformation theory. The motivation is the need
in the abundance conjecture to construct pluricanonical sections from flatly
twisted pluricanonical sections. We also give here a new approach to the
original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the
punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi
to a simple application of the standard method of constructing holomorphic
functions by solving the d-bar equation with cut-off functions and additional
blowup weight functions
An algebra of deformation quantization for star-exponentials on complex symplectic manifolds
The cotangent bundle to a complex manifold is classically endowed
with the sheaf of \cor-algebras \W[T^*X] of deformation quantization, where
\cor\eqdot \W[\rmptt] is a subfield of \C[[\hbar,\opb{\hbar}]. Here, we
construct a new sheaf of \cor-algebras \TW[T^*X] which contains \W[T^*X]
as a subalgebra and an extra central parameter . We give the symbol calculus
for this algebra and prove that quantized symplectic transformations operate on
it. If is any section of order zero of \W[T^*X], we show that
\exp(t\opb{\hbar} P) is well defined in \TW[T^*X].Comment: Latex file, 24 page
The home team advantage gives football referees something to ruminate about
Observation suggests that referees significantly contribute to the home team advantage in football. The atmosphere created by the home team fans is thought to be the major contributing factor, but the extent of this influence is dependent on the referee. The Decision-Specific Reinvestment Scale was developed to identify those individuals susceptible to disrupted decision making under pressure as a result of their tendency to overinvolve consciousness in decision making (Decision Reinvestment) or as a result of their tendency to ruminate upon poor decisions made in the past (Decision Rumination). We asked qualified referees to make a series of video-based decisions to examine whether the home team advantage effect was associated with a high or low tendency for Decision Reinvestment or Decision Rumination. We showed that referees categorized as high Decision Ruminators disproportionately made decisions in favour of the home team. The tendency to ruminate upon poor decisions may help explain some of the variance in the home team advantage effect shown by different referees. We conclude that aspects of personality should be considered in the development of training programs designed to improve and standardise football refereeing.published_or_final_versio
Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives
Contractor Renormalization (CORE) is a numerical renormalization method for
Hamiltonian systems that has found applications in particle and condensed
matter physics. There have been few studies, however, on further understanding
of what exactly it does and its convergence properties. The current work has
two main objectives. First, we wish to investigate the convergence of the
cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This
is important because the linked cluster expansion used to evaluate this formula
non-perturbatively is not controlled by a small parameter. Here we present a
study of three different blocking schemes which reveals some surprises and in
particular, leads us to suggest a scheme for defining successive terms in the
cluster expansion. Our second goal is to present some new perspectives on CORE
in light of recent developments to make it accessible to more researchers,
including those in Quantum Information Science. We make some comparison to
entanglement-based approaches and discuss how it may be possible to improve or
generalize the method.Comment: Completely revised version accepted by Phy Rev B; 13 pages with added
material on entropy in COR
Classification of the Lie bialgebra structures on the Witt and Virasoro algebras
We prove that all the Lie bialgebra structures on the one sided Witt algebra W1, on the Witt algebra W and on the Virasoro algebra V are triangular coboundary Lie bialgebra structures associated to skew-symmetric solutions r of the classical Yang-Baxter equation of the form r = a ∧ b. In particular, for the one-sided Witt algebra W1 = Der k[t] over an algebraically closed field k of characteristic zero, the Lie bialgebra structures discovered in Michaelis (Adv. Math. 107 (1994) 365-392) and Taft (J. Pure Appl. Algebra 87 (1993) 301-312) are all the Lie bialgebra structures on W1 up to isomorphism. We prove the analogous result for a class of Lie subalgebras of W which includes W1. © 2000 Elsevier Science B.V. All rights reserved
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