36,219 research outputs found
Cosmology with Coupled Gravity and Dark Energy
Dark energy is a fundamental constituent of our universe, its status in the
cosmological field equation should be equivalent to that of gravity. Here we
construct a dark energy and matter gravity coupling (DEMC) model of cosmology
in a way that dark energy and gravity are introduced into the cosmological
field equation in parallel with each other from the beginning. The DEMC
universe possesses a composite symmetry from global Galileo invariance and
local Lorentz invariance. The observed evolution of the universe expansion rate
at redshift z>1 is in tension with the standard LCDM model, but can be well
predicted by the DEMC model from measurements of only nearby epochs. The so far
most precise measured expansion rate at high z is quite a bit slower than the
expectations from LCDM, but remarkably consistent with that from DEMC. It is
hoped that the DEMC scenario can also help to solve other existing challenges
to cosmology: large scale anomalies in CMB maps and large structures up to
about 10^3 Mpc of a quasar group. The DEMC universe is a well defined
mechanical system. From measurements we can quantitatively evaluate its total
rest energy, present absolute radius and expanding speed.Comment: 9 pages, 4 figure
Heliospheric Origin of Gamma-Ray Bursts
Systematic variations of average observational characteristics and
correlation properties between different parameters of gamma-ray bursts (GRBs)
with time from 1991 April to 1994 September are revealed. It is hard to explain
the observed long-term variability by variations of experimental conditions.
The variability of GRB properties with the time scale of months to years,
together with the similarity between GRBs, solar hard X-ray flares and
terrestrial gamma-ray flashes, may indicate an origin of GRBs, at least partly,
within the heliosphere. Large-voltage and high-temperature pinch plasma columns
produced by disruptive electrical discharges in the outer heliosphere can
generate hard X-ray and gamma-ray flashes with energy spectra and spectral
evolution characters consistent with that observed in GRBs.Comment: LaTex, epsfig. 20 pages, 17 figures, replace to correct the
definition of Epk and revise Figs 12-1
Constructing a Robust Universe with Attraction-Repulsion Coupling and Energy Conservation
The discovery of accelerated cosmic expansion implies that, in addition to
the attractive gravity of matter, there exists in our universe some other form
of energy (dark energy or cosmological constant) producing a repulsive force.
The natural interpretation of dark energy is the vacuum energy. However, the
density of vacuum energy expected by the quantum field theory is 120 orders of
magnitude larger than what is allowed by cosmological observations, which is
called the cosmological constant problem and remains one of the most
significant unsolved problems in fundamental physics. Here we show that the
huge discrepancy can be resolved by assuming that our universe is an
attraction-repulsion coupled system with energy conservation, and that the
pre-inflation vacuum is in equilibrium between attraction and repulsion (in
flat Minkowski spacetime, not de Sitter or anti de Sitter). The
attraction-repulsion coupling picture can also easily explain why both kinds of
energy in our universe have similar magnitude today, and avoid singularity
problems in general relativity and cosmology.Comment: 8 pages, 1 figur
Ramsey numbers of paths and graphs of the same order
For graphs and of order , if , then is said to be -good,
where is the minimum size of a color class among all proper
vertex-colorings of with colors. Given , it is shown that is asymptotically -good if
.Comment: 8 pages, 3 figure
Symmetry of Solutions for a Fractional System
We consider the following equations: \begin{equation*}
\left\{\begin{array}{ll} (-\triangle)^{\alpha/2}u(x)=f(v(x)), \\
(-\triangle)^{\beta/2}v(x)=g(u(x)), &x \in R^{n},\\ u,v\geq 0, &x \in R^{n},
\end{array} \right. \end{equation*} for continuous and . Under some natural assumptions on and , by applying the
\emph{method of moving planes} directly to the system, we obtain symmetry on
non-negative solutions without any decay assumption on the solutions at
infinity
On generalization of D'Aurizio-S\'andor trigonometric inequalities with a parameter
In this work, we generalize the D'Aurizio-S\'andor inequalities
(\cite{D'Aurizio,Sandor}) using an elementary approach. In particular, our
approach provides an alternative proof of the D'Aurizio-S\'andor inequalities.
Moreover, as an immediate consequence of the generalized D'Aurizio-S\'andor
inequalities, we establish the D'Aurizio-S\'andor-type inequalities for
hyperbolic functions
Averaging algebras, Schr\"oder numbers, rooted trees and operads
In this paper, we study averaging operators from an algebraic and
combinatorial point of view. We first construct free averaging algebras in
terms of a class of bracketed words called averaging words. We next apply this
construction to obtain one and two variable generating functions for subsets of
averaging words when the averaging operator is taken to be idempotent. When the
averaging algebra has an idempotent generator, the generating function in one
variable is twice the generating function for large Schr\"oder numbers, leading
us to give interpretations of large Schr\"oder numbers in terms of bracketed
words and rooted trees, as well as a recursive formula for these numbers. We
also give a representation of free averaging algebras by unreduced trees and
apply it to give a combinatorial description of the operad of averaging
algebras.Comment: 30 page
Representations of Polynomial Rota-Baxter Algebras
A Rota--Baxter operator is an algebraic abstraction of integration, which is
the typical example of a weight zero Rota-Baxter operator. We show that
studying the modules over the polynomial Rota--Baxter algebra is
equivalent to studying the modules over the Jordan plane, and we generalize the
direct decomposability results for the -modules in [Iy] from
algebraically closed fields of characteristic zero to fields of characteristic
zero. Furthermore, we provide a classification of Rota--Baxter modules up to
isomorphism based on indecomposable -modules
A Pohozaev Identity for the Fractional Hnon System
In this paper, we study the Pohozaev identity associated with a
Hnon-Lane-Emden system involving the fractional Laplacian:
\begin{equation}
\left\{\begin{array}{ll}
(-\triangle)^su=|x|^av^p,&x\in\Omega,
(-\triangle)^sv=|x|^bu^q,&x\in\Omega, u=v=0,&x\in R^n\backslash\Omega,
\end{array}
\right.
\end{equation} in a star-shaped and bounded domain for .
As an application of our identity, we deduce the nonexistence of positive
solutions in the critical and supercritical cases
Improved CMB Map from WMAP Data
The cosmic microwave background (CMB) temperature maps published by the
Wilkinson Microwave Anisotropy Probe (WMAP) team are found to be inconsistent
with the differential time-ordered data (TOD), from which the maps are
reconstructed. The inconsistency indicates that there is a serious problem in
the map making routine of the WMAP team, and it is necessary to reprocess the
WMAP data. We develop a self-consistent software package of map-making and
power spectrum estimation independently of the WMAP team. Our software passes a
variety of tests. New CMB maps are then reconstructed, which are significantly
different from the official WMAP maps. In the new maps, the inconsistency
disappeared, along with the hitherto unexplained high level alignment between
the CMB quadrupole and octopole components detected in released WMAP maps. An
improved CMB cross-power spectrum is then derived from the new maps which
better agrees with that of BOOMRANG. Two important results are hence obtained:
the CMB quadrupole drops to nearly zero, and the power in multiple moment range
between 200 and 675 decreases on average by about 13%, causing the best-fit
cosmological parameters to change considerably, e.g., the total matter density
increases from 0.26 up to 0.32 and the dark energy density decreases from 0.74
down to 0.68. These new parameters match with improved accuracy those of other
independent experiments. Our results indicate that there is still room for
significant revision in the cosmological model parameters.Comment: Submitted to MNRAS. In the revised version (v3) we make foreground
reduction with the same technique WMAP team used and add the results of
reconstructing the sky maps with the WMAP default flagging and our softwar
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