826 research outputs found
The Minimal Length of a Lagrangian Cobordism between Legendrians
To investigate the rigidity and flexibility of Lagrangian cobordisms between
Legendrian submanifolds, we investigate the minimal length of such a cobordism,
which is a -dimensional measurement of the non-cylindrical portion of the
cobordism. Our primary tool is a set of real-valued capacities for a Legendrian
submanifold, which are derived from a filtered version of Legendrian Contact
Homology. Relationships between capacities of Legendrians at the ends of a
Lagrangian cobordism yield lower bounds on the length of the cobordism. We
apply the capacities to Lagrangian cobordisms realizing vertical dilations
(which may be arbitrarily short) and contractions (whose lengths are bounded
below). We also study the interaction between length and the linking of
multiple cobordisms as well as the lengths of cobordisms derived from
non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee
comments. More general statement in Proposition 3.3 and some reorganization
at the end of Section
A Hardy inequality in twisted waveguides
We show that twisting of an infinite straight three-dimensional tube with
non-circular cross-section gives rise to a Hardy-type inequality for the
associated Dirichlet Laplacian. As an application we prove certain stability of
the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes.
Namely, it is known that any local bending, no matter how small, generates
eigenvalues below the essential spectrum of the Laplacian in the tubes with
arbitrary cross-sections rotated along a reference curve in an appropriate way.
In the present paper we show that for any other rotation some critical strength
of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page
Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight
twisted tube of a non-circular cross section. It is shown that a local
perturbation which consists of "slowing down" the twisting in the mean gives
rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page
Dark energy domination in the Virgocentric flow
The standard \LambdaCDM cosmological model implies that all celestial bodies
are embedded in a perfectly uniform dark energy background, represented by
Einstein's cosmological constant, and experience its repulsive antigravity
action. Can dark energy have strong dynamical effects on small cosmic scales as
well as globally? Continuing our efforts to clarify this question, we focus now
on the Virgo Cluster and the flow of expansion around it. We interpret the
Hubble diagram, from a new database of velocities and distances of galaxies in
the cluster and its environment, using a nonlinear analytical model which
incorporates the antigravity force in terms of Newtonian mechanics. The key
parameter is the zero-gravity radius, the distance at which gravity and
antigravity are in balance. Our conclusions are: 1. The interplay between the
gravity of the cluster and the antigravity of the dark energy background
determines the kinematical structure of the system and controls its evolution.
2. The gravity dominates the quasi-stationary bound cluster, while the
antigravity controls the Virgocentric flow, bringing order and regularity to
the flow, which reaches linearity and the global Hubble rate at distances \ga
15 Mpc. 3. The cluster and the flow form a system similar to the Local Group
and its outflow. In the velocity-distance diagram, the cluster-flow structure
reproduces the group-flow structure with a scaling factor of about 10; the
zero-gravity radius for the cluster system is also 10 times larger. The phase
and dynamical similarity of the systems on the scales of 1-30 Mpc suggests that
a two-component pattern may be universal for groups and clusters: a
quasi-stationary bound central component and an expanding outflow around it,
due to the nonlinear gravity-antigravity interplay with the dark energy
dominating in the flow component.Comment: 7 pages, 2 figures, Astronomy and Astrophysics (accepted
The observed infall of galaxies towards the Virgo cluster
We examine the velocity field of galaxies around the Virgo cluster induced by
its overdensity. A sample of 1792 galaxies with distances from the Tip of the
Red Giant Branch, the Cepheid luminosity, the SNIa luminosity, the surface
brightness fluctuation method, and the Tully-Fisher relation has been used to
study the velocity-distance relation in the Virgocentric coordinates. Attention
was paid to some observational biases affected the Hubble flow around Virgo.
We estimate the radius of the zero-velocity surface for the Virgo cluster to
be within (5.0 - 7.5) Mpc corresponding to (17 - 26)^\circ at the mean cluster
distance of 17.0 Mpc. In the case of spherical symmetry with cosmological
parameter \Omega_m=0.24 and the age of the Universe T_0= 13.7 Gyr, it yields
the total mass of the Virgo cluster to be within M_T=(2.7 - 8.9) * 10^{14}
M_\sun in reasonable agreement with the existing virial mass estimates for the
cluster.Comment: 22 pages, 11 figures, 2 tables. Accepted for publication in MNRA
Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
We prove general comparison theorems for eigenvalues of perturbed Schrodinger
operators that allow proof of Lieb--Thirring bounds for suitable non-free
Schrodinger operators and Jacobi matrices.Comment: 11 page
Binary Models for Marginal Independence
Log-linear models are a classical tool for the analysis of contingency
tables. In particular, the subclass of graphical log-linear models provides a
general framework for modelling conditional independences. However, with the
exception of special structures, marginal independence hypotheses cannot be
accommodated by these traditional models. Focusing on binary variables, we
present a model class that provides a framework for modelling marginal
independences in contingency tables. The approach taken is graphical and draws
on analogies to multivariate Gaussian models for marginal independence. For the
graphical model representation we use bi-directed graphs, which are in the
tradition of path diagrams. We show how the models can be parameterized in a
simple fashion, and how maximum likelihood estimation can be performed using a
version of the Iterated Conditional Fitting algorithm. Finally we consider
combining these models with symmetry restrictions
Dark energy and key physical parameters of clusters of galaxies
We study physics of clusters of galaxies embedded in the cosmic dark energy
background. Under the assumption that dark energy is described by the
cosmological constant, we show that the dynamical effects of dark energy are
strong in clusters like the Virgo cluster. Specifically, the key physical
parameters of the dark mater halos in clusters are determined by dark energy:
1) the halo cut-off radius is practically, if not exactly, equal to the
zero-gravity radius at which the dark matter gravity is balanced by the dark
energy antigravity; 2) the halo averaged density is equal to two densities of
dark energy; 3) the halo edge (cut-off) density is the dark energy density with
a numerical factor of the unity order slightly depending on the halo profile.
The cluster gravitational potential well in which the particles of the dark
halo (as well as galaxies and intracluster plasma) move is strongly affected by
dark energy: the maximum of the potential is located at the zero-gravity radius
of the cluster.Comment: 8 pages, 1 figur
Stein structures: existence and flexibility
This survey on the topology of Stein manifolds is an extract from our recent
joint book. It is compiled from two short lecture series given by the first
author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred
Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure
Exploring control-value motivational profiles of mathematics anxiety, self-concept, and interest in adolescents
In this study, we identified multidimensional profiles in students’ math anxiety, math self-concept, and math interest using data from a large generalizable sample of 16,547 9th grade students in the United States who participated in the National Study of Learning Mindsets. We also analyzed the extent that students’ profile memberships are associated with related measures such as prior mathematics achievement, academic stress, and challenge-seeking behavior. Five multidimensional profiles were identified: two profiles which demonstrated relatively high levels of interest and self-concept, along with low math anxiety, in line with the tenets of the control-value theory of academic emotions (C-VTAE); two profiles which demonstrated relatively low levels of interest and self-concept, and high levels of math anxiety (again in accordance with C-VTAE); and one profile, comprising more than 37% of the total sample, which demonstrated medium levels of interest, high levels of self-concept, and medium levels of anxiety. All five profiles varied significantly from one another in their association with the distal variables of challenge seeking behavior, prior mathematics achievement, and academic stress. This study contributes to the literature on math anxiety, self-concept, and interest by identifying and validating student profiles that mainly align with the control-value theory of academic emotions in a large, generalizable sample
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