3,148 research outputs found
The unavoidable arrangements of pseudocircles
It is known that cyclic arrangements are the only {\em unavoidable} simple
arrangements of pseudolines: for each fixed , every sufficiently large
simple arrangement of pseudolines has a cyclic subarrangement of size . In
the same spirit, we show that there are three unavoidable arrangements of
pseudocircles
On the number of unknot diagrams
Let be a knot diagram, and let denote the set of diagrams
that can be obtained from by crossing exchanges. If has crossings,
then consists of diagrams. A folklore argument shows that
at least one of these diagrams is unknot, from which it follows that
every diagram has finite unknotting number. It is easy to see that this
argument can be used to show that actually has more than one
unknot diagram, but it cannot yield more than unknot diagrams. We improve
this linear bound to a superpolynomial bound, by showing that at least
of the diagrams in are unknot. We also show
that either all the diagrams in are unknot, or there is a
diagram in that is a diagram of the trefoil knot
The number radial coherent states for the generalized MICZ-Kepler problem
We study the radial part of the MICZ-Kepler problem in an algebraic way by
using the Lie algebra. We obtain the energy spectrum and the
eigenfunctions of this problem from the theory of unitary
representations and the tilting transformation to the stationary Schr\"odinger
equation. We construct the physical Perelomov number coherent states for this
problem and compute some expectation values. Also, we obtain the time evolution
of these coherent states
Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime
We study a relativistic quantum particle in cosmic string spacetime in the
presence of a uniform magnetic field and a Coulomb-type scalar potential. It is
shown that the radial part of this problem possesses the symmetry. We
obtain the energy spectrum and eigenfunctions of this problem by using two
algebraic methods: the Schr\"odinger factorization and the tilting
transformation. Finally, we give the explicit form of the relativistic coherent
states for this problem.Comment: 21 page
TxPI-u: A Resource for Personality Identification of Undergraduates
Resources such as labeled corpora are necessary to train automatic models
within the natural language processing (NLP) field. Historically, a large
number of resources regarding a broad number of problems are available mostly
in English. One of such problems is known as Personality Identification where
based on a psychological model (e.g. The Big Five Model), the goal is to find
the traits of a subject's personality given, for instance, a text written by
the same subject. In this paper we introduce a new corpus in Spanish called
Texts for Personality Identification (TxPI). This corpus will help to develop
models to automatically assign a personality trait to an author of a text
document. Our corpus, TxPI-u, contains information of 416 Mexican undergraduate
students with some demographics information such as, age, gender, and the
academic program they are enrolled. Finally, as an additional contribution, we
present a set of baselines to provide a comparison scheme for further research
Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
We introduce two generalizations of the Jaynes-Cummings (JC) model for two
modes of oscillation. The first model is formed by two Jaynes-Cummings
interactions, while the second model is written as a simultaneous
Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of
its properties and obtain the energy spectrum and eigenfunctions of these
models by using the tilting transformation and the Perelomov number coherent
states of the two-dimensional harmonic oscillator. Moreover, as physical
applications, we connect these new models with two important and novelty
problems: The relativistic non-degenerate parametric amplifier and the
relativistic problem of two coupled oscillators.Comment: 16 page
Approach to Stokes Parameters and the Theory of Light Polarization
We introduce an alternative approach to the polarization theory of light.
This is based on a set of quantum operators, constructed from two independent
bosons, being three of them the Lie algebra generators, and the other
one, the Casimir operator of this algebra. By taking the expectation value of
these generators in a two-mode coherent state, their classical limit is
obtained. We use these classical quantities to define the new Stokes-like
parameters. We show that the light polarization ellipse can be written in terms
of the Stokes-like parameters. Also, we write these parameters in terms of
other two quantities, and show that they define a one-sheet (Poincar\'e
hyperboloid) of a two-sheet hyperboloid. Our study is restricted to the case of
a monochromatic plane electromagnetic wave which propagates along the axis
solution for the Dunkl oscillator in two dimensions and its coherent states
We study the Dunkl oscillator in two dimensions by the algebraic
method. We apply the Schr\"odinger factorization to the radial Hamiltonian of
the Dunkl oscillator to find the Lie algebra generators. The energy
spectrum is found by using the theory of unitary irreducible representations.
By solving analytically the Schr\"odinger equation, we construct the Sturmian
basis for the unitary irreducible representations of the Lie algebra.
We construct the Perelomov radial coherent states for this problem
and compute their time evolution.Comment: 14 page
Non-Hermitian inverted Harmonic Oscillator-Type Hamiltonians Generated from Supersymmetry with Reflections
By modifying and generalizing known supersymmetric models we are able to find
four different sets of one-dimensional Hamiltonians for the inverted harmonic
oscillator. The first set of Hamiltonians is derived by extending the
supersymmetric quantum mechanics with reflections to non-Hermitian
supercharges. The second set is obtained by generalizing the supersymmetric
quantum mechanics valid for non-Hermitian supercharges with the Dunkl
derivative instead of . Also, by changing the derivative
by the Dunkl derivative in the creation and annihilation-type
operators of the standard inverted Harmonic oscillator
, we generate the third
set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a
parameter of the supersymmetric two-body Calogero-type model to take imaginary
values. The eigensolutions of definite parity for each set of Hamiltonians are
given
An algebraic approach to a charged particle in an uniform magnetic field
We study the problem of a charged particle in a uniform magnetic field with
two different gauges, known as Landau and symmetric gauges. By using a
similarity transformation in terms of the displacement operator we show that,
for the Landau gauge, the eigenfunctions for this problem are the harmonic
oscillator number coherent states. In the symmetric gauge, we calculate the
Perelomov number coherent states for this problem in cylindrical
coordinates in a closed form. Finally, we show that these Perelomov number
coherent states are related to the harmonic oscillator number coherent states
by the contraction of the group to the Heisenberg-Weyl group.Comment: 11 page
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