7,645 research outputs found
Refined intersection products and limiting linear subspaces of hypersurfaces
Let be a hypersurface of degree in and be the scheme
of 's contained in . If is generic, then will have the
expected dimension (or empty) and its class in the Chow ring of is
given by the top Chern class of the vector bundle , where is the
universal subbundle on the Grassmannian . When we deform a generic
into a degenerate , the dimension of can jump. In this case,
there is a subscheme of with the expected dimension which
consists of limiting 's in with respect to a general
deformation. The simplest example is the well-known case of lines in a
generic cubic surface. If we degenerate the surface into the union of a plane
and a quadric, then there are infinitely many lines in the union. Which
lines are the limiting ones and how many of them are in the plane and how many
of them are in the quadric? The goal of this paper is to study in
general.Comment: AmS-Tex, 26 page
Residual Intersections and Some Applications
We give a new residual intersection decomposition for the refined
intersection products of Fulton-MacPherson. Our formula refines the celebrated
residual intersection formula of Fulton, Kleiman, Laksov, and MacPherson. The
new decomposition is more likely to be compatible with the canonical
decomposition of the intersection products and each term in the decomposition
thus has simple geometric meaning. Our study is motivated by its applications
to some geometric problems. In particular, we use the decomposition to find the
distribution of limiting linear subspaces in degenerations of hypersurfaces. A
family of identities for characteristic classes of vector bundles is also
obtained as another consequence. This paper will appear in Duke Math. Jour.Comment: 23 pages, Ams-Tex Version 2.
Chern classes and degenerations of hypersurfaces and their lines
We study limiting lines on degenerations of generic hypersurfaces in .Comment: 18 pages, AmS-Tex V2.
Global performance of multireference density functional theory for low-lying states in -shell nuclei
We present a comprehensive study of low-lying states in even-even Ne, Mg, Si,
S, Ar isotopes with the multireference density functional theory (MR-DFT) based
on a relativistic point-coupling energy density functional (EDF). Beyond
mean-field (BMF) effects are taken into account by configuration mixing of both
particle-number and angular-momentum projected axially deformed states with
generator coordinate method (GCM). Global performance of the MR-DFT for the
properties of both ground state and of the first states is examined,
in comparison with previous studies based on nonrelativistic EDFs and available
data. Our results indicate that an EDF parameterized at the BMF level is
demanded to achieve a quantitative description
Mixing Time of Random Walk on Poisson Geometry Small World
This paper focuses on the problem of modeling for small world effect on
complex networks. Let's consider the supercritical Poisson continuous
percolation on -dimensional torus with volume . By adding "long
edges (short cuts)" randomly to the largest percolation cluster, we obtain a
random graph . In the present paper, we first prove that the
diameter of grows at most polynomially fast in and we
call it the Poisson Geometry Small World. Secondly, we prove that the random
walk on possesses the rapid mixing property, namely, the random
walk mixes in time at most polynomially large in .Comment: 23 page
Existence of Positive Solutions for a class of Quasilinear Schr\"{o}dinger Equations of Choquard type
In this paper, we study the following quasilinear Schr\"{o}dinger equation of
Choquard type where ,\ ,
and is a Riesz
potential. Under appropriate assumptions on , we establish the existence
of positive solutions
On The Modified Newman-Watts Small World and Its Random Walk
It is well known that adding "long edges (shortcuts)" to a regularly
constructed graph will make the resulted model a small world. Recently,
\cite{W} indicated that, among all long edges, those edges with length
proportional to the diameter of the regularly constructed graph may play the
key role. In this paper, we modify the original Newman-Watts small world by
adding only long special edges to the -dimensional lattice torus (with size
) according to \cite{W}, and show that the diameter of the modified model
and the mixing time of random walk on it grow polynomially fast in .Comment: 17 pages. arXiv admin note: substantial text overlap with
arXiv:1703.0825
On a Lower Bound for the Time Constant of First-Passage Percolation
We consider the Bernoulli first-passage percolation on . That is, the edge passage time is taken independently to be 1 with
probability and 0 otherwise. Let be the time constant. We
prove in this paper that for all by using Russo's
formula.Comment: 7 page
Uniqueness of the critical probability for percolation in the two dimensional Sierpinski carpet lattice
We prove that the critical probability for the Sierpinski carpet lattice in
two dimensions is uniquely determined. The transition is sharp. This extends
the Kumagai's result to the original Sierpinski carpet lattice.Comment: 22pages; typos added(erased pre-finel comments
On The Time Constant for Last Passage Percolation on Complete Graph
This paper focuses on the time constant for last passage percolation on
complete graph. Let be the complete graph on vertex set
, and i.i.d. sequence be the passage
times of edges. Denote by the largest passage time among all
self-avoiding paths from 1 to . First, it is proved that converges
to constant , where is called the time constant and coincides with
the essential supremum of . Second, when , it is proved that
the deviation probability decays as fast as
, and as a corollary, an upper bound for the variance of
is obtained. Finally, when , lower and upper bounds for
are given.Comment: 12 pages, 1 figur
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