29,032 research outputs found
Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities
In this paper, we prove the local well-posedness in critical Besov spaces for
the compressible Navier-Stokes equations with density dependent viscosities
under the assumption that the initial density is bounded away from zero.Comment: 27page
Inflation with Holographic Dark Energy
We investigate the corrections of the holographic dark energy to inflation
paradigm. We study the evolution of the holographic dark energy in the
inflationary universe in detail, and carry out a model-independent analysis on
the holographic dark energy correction to the primordial scalar power spectrum.
It turns out that the corrections generically make the spectrum redder. To be
consistent with the experimental data, there must be a upper bound on the
reheating temperature. We also discuss the corrections due to different choices
of the infrared cutoff.Comment: 15 pages, 3 figures, v2: references added, a fast-roll discussion
added. v3: typos corrected. v4: final version to appear in NP
Non-adiabatic elimination of auxiliary modes in continuous quantum measurements
When measuring a complex quantum system, we are often interested in only a
few degrees of freedom-the plant, while the rest of them are collected as
auxiliary modes-the bath. The bath can have finite memory (non-Markovian), and
simply ignoring its dynamics, i.e., adiabatically eliminating it, will prevent
us from predicting the true quantum behavior of the plant. We generalize the
technique introduced by Strunz et. al. [Phys. Rev. Lett 82, 1801 (1999)], and
develop a formalism that allows us to eliminate the bath non-adiabatically in
continuous quantum measurements, and obtain a non-Markovian stochastic master
equation for the plant which we focus on. We apply this formalism to three
interesting examples relevant to current experiments.Comment: a revised versio
A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
We show a new Bernstein's inequality which generalizes the results of
Cannone-Planchon, Danchin and Lemari\'{e}-Rieusset. As an application of this
inequality, we prove the global well-posedness of the 2D quasi-geostrophic
equation with the critical and super-critical dissipation for the small initial
data in the critical Besov space, and local well-posedness for the large
initial data.Comment: 18page
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Examining Uncertainty and Misspecification of Attributes in Cognitive Diagnostic Models
In recent years, cognitive diagnostic models (CDMs) have been widely used in educational assessment to provide a diagnostic profile (mastery/non-mastery) analysis for examinees, which gives insights into learning and teaching. However, there is often uncertainty about the specification of the Q-matrix that is required for CDMs, given that it is based on expert judgment. The current study uses a Bayesian approach to examine recovery of Q-matrix elements in the presence of uncertainty about some elements. The first simulation examined the situation where there is complete uncertainty about whether or not an attribute is required, when in fact it is required. The simulation results showed that recovery was generally excellent. However, recovery broke down when other elements of the Q-matrix were misspecified. Further simulations showed that, if one has some information about the attributes for a few items, then recovery improves considerably, but this also depends on how many other elements are misspecified. A second set of simulations examined the situation where uncertain Q-matrix elements were scattered throughout the Q-matrix. Recovery was generally excellent, even when some other elements were misspecified. A third set of simulations showed that using more informative priors did not uniformly improve recovery. An application of the approach to data from TIMSS (2007) suggested some alternative Q-matrices
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