1,353 research outputs found
Harnack inequality and regularity for degenerate quasilinear elliptic equations
We prove Harnack inequality and local regularity results for weak solutions
of a quasilinear degenerate equation in divergence form under natural growth
conditions. The degeneracy is given by a suitable power of a strong
weight. Regularity results are achieved under minimal assumptions on the
coefficients and, as an application, we prove local estimates
for solutions of a degenerate equation in non divergence form
K-means Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman\u2019s Unifying Approach
Research in Science Education has shown that often students need to learn how to identify differences and similarities between descriptive and explicative models.
The development and use of explicative skills in the field of thermal science has always been a difficult objective to reach. A way to develop analogical reasoning is to use in Science Education unifying conceptual frameworks.
In this paper we describe a 20-hour workshop focused on Feynman\u2019s Unifying Approach and the two-level system. We measure its efficacy in helping undergraduate chemical engineering students explain phenomena by applying an explanatory model. Contexts involve systems for which a process is activated by thermally overcoming a well-defined potential barrier. A questionnaire containing six open-ended questions was administered to the students before instruction. A second one, similar but focused on different physical content was administered after instruction. Responses were analysed using k-means Cluster Analysis and students\u2019 inferred lines of reasoning about the analysed phenomena were studied. We conclude that students reasoning lines seem to have clearly evolved to explicative ones and it is reasonable to think that the Feynman Unifying Approach has favoured this change
Prospective elementary teachers\u2019 perceptions of the processes of modeling: A case study
In this paper we discuss a study on the approaches to modeling of students of the 4-year elementary school teacher program at the University of Palermo, Italy. The answers to a specially designed questionnaire are analyzed on the basis of an a priori analysis made using a general scheme of reference on the epistemology of mathematics and physics. The study is performed by using quantitative data analysis methods, i.e. factorial analysis of the correspondences and implicative analysis. A qualitative analysis of key words and terms used by students during interviews is also used to examine some aspects that emerged from the quantitative analysis. The students have been classified on the basis of their different epistemological approaches to knowledge construction, and implications between different conceptual strategies used to answer the questionnaire have been highlighted. The study\u2019s conclusions are consistent with previous research, but the use of quantitative data analysis allowed us to classify the students into three \u201cprofiles\u201d related to different epistemological approaches to knowledge construction, and to show the implications of the different conceptual strategies used to answer the questionnaire, giving an estimation of the classification or implication \u201cstrength.\u201d Some hints on how a course for elementary school physics and mathematics education can be planned to orient the future teachers to the construction of models of explanation are reported
A New Approach to Investigate Students\u2019 Behavior by Using Cluster Analysis as an Unsupervised Methodology in the Field of Education
The problem of taking a set of data and separating it into subgroups where the ele- ments of each subgroup are more similar to each other than they are to elements not in the subgroup has been extensively studied through the statistical method of cluster analysis. In this paper we want to discuss the application of this method to the field of education: particularly, we want to present the use of cluster analysis to separate students into groups that can be recognized and characterized by common traits in their answers to a questionnaire, without any prior knowledge of what form those groups would take (unsupervised classification). We start from a detailed study of the data processing needed by cluster analysis. Then two methods commonly used in cluster analysis are before described only from a theoretical point a view and after in the Section 4 through an example of application to data coming from an open-ended questionnaire administered to a sample of university students. In particular we de- scribe and criticize the variables and parameters used to show the results of the clus- ter analysis methods
Lifetimes of b-flavoured hadrons
I discuss the heavy quark expansion for the inclusive widths of heavy-light
hadrons, which predicts quite well the experimental ratios of B_q meson
lifetimes. As for , current determinations of
contribution to do not allow to explain the small measured
value of . As a final topic, I discuss the
implications of the measurement of the B_c lifetime.Comment: LaTex, 4 pages, 1 figure. Talk given at the "U.K. Phenomenology
Workshop on Heavy Flavours and CP violation" Durham, 17-22 Sep. 2000 (Mixing
and Lifetimes Working Group
Hierarchical Model for the Evolution of Cloud Complexes
The structure of cloud complexes appears to be well described by a "tree
structure" representation when the image is partitioned into "clouds". In this
representation, the parent-child relationships are assigned according to
containment. Based on this picture, a hierarchical model for the evolution of
Cloud Complexes, including star formation, is constructed, that follows the
mass evolution of each sub-structure by computing its mass exchange
(evaporation or condensation) with its parent and children, which depends on
the radiation density at the interphase. For the set of parameters used as a
reference model, the system produces IMFs with a maximum at too high mass (~2
M_sun) and the characteristic times for evolution seem too long. We show that
these properties can be improved by adjusting model parameters. However, the
emphasis here is to illustrate some general properties of this nonlinear model
for the star formation process. Notwithstanding the simplifications involved,
the model reveals an essential feature that will likely remain if additional
physical processes are included. That is: the detailed behavior of the system
is very sensitive to variations on the initial and external conditions,
suggesting that a "universal" IMF is very unlikely. When an ensemble of IMFs
corresponding to a variety of initial or external conditions is examined, the
slope of the IMF at high masses shows variations comparable to the range
derived from observational data. (Abridged)Comment: Latex, 29 pages, 13 figures, accepted for publication in Ap
Liquid Structure of a Water-in-Salt Electrolyte with a Remarkably Asymmetric Anion
Water-in-salt systems, i.e., super-concentrated aqueous electrolytes, such as lithium bis(trifluoromethanesulfonyl)imide (21 mol/kgwater), have been recently discovered to exhibit unexpectedly large electrochemical windows and high lithium transference numbers, thus paving the way to safe and sustainable charge storage devices. The peculiar transport features in these electrolytes are influenced by their intrinsically nanoseparated morphology, stemming from the anion hydrophobic nature and manifesting as nanosegregation between anions and water domains. The underlying mechanism behind this structure-dynamics correlation is, however, still a matter of strong debate. Here, we enhance the apolar nature of the anions, exploring the properties of the aqueous electrolytes of lithium salts with a strongly asymmetric anion, namely, (trifluoromethylsulfonyl)(nonafluorobutylsulfonyl) imide. Using a synergy of experimental and computational tools, we detect a remarkable level of structural heterogeneity at a mesoscopic level between anion-rich and water-rich domains. Such a ubiquitous sponge-like, bicontinuous morphology develops across the whole concentration range, evolving from large fluorinated globules at high dilution to a percolating fluorous matrix intercalated by water nanowires at super-concentrated regimes. Even at extremely concentrated conditions, a large population of fully hydrated lithium ions, with no anion coordination, is detected. One can then derive that the concomitant coexistence of (i) a mesoscopically segregated structure and (ii) fully hydrated lithium clusters disentangled from anion coordination enables the peculiar lithium diffusion features that characterize water-in-salt systems
On the Rapid Collapse and Evolution of Molecular Clouds
Stars generally form faster than the ambipolar diffusion time, suggesting
that several processes short circuit the delay and promote a rapid collapse.
These processes are considered here, including turbulence compression in the
outer parts of giant molecular cloud (GMC) cores and GMC envelopes, GMC core
formation in an initially supercritical state, and compression-induced
triggering in dispersing GMC envelopes. The classical issues related to star
formation timescales are addressed: high molecular fractions, low efficiencies,
long consumption times for CO and HCN, rapid GMC core disruption and the lack
of a stable core, long absolute but short relative timescales with accelerated
star formation, and the slow motions of protostars. We consider stimuli to
collapse from changes in the density dependence of the ionization fraction, the
cosmic ray ionization rate, and various dust properties at densities above
~10^5 cm^{-3}. We favor the standard model of subcritical GMC envelops and
suggest they would be long lived if not for disruption by rapid star formation
in GMC cores. The lifecycle of GMCs is illustrated by a spiral arm section in
the Hubble Heritage image of M51, showing GMC formation, star formation, GMC
disruption with lingering triggered star formation, and envelope dispersal.
There is no delay between spiral arm dustlanes and star formation; the
classical notion results from heavy extinction in the dust lane and triggered
star formation during cloud dispersal. Differences in the IMF for the different
modes of star formation are considered.Comment: 46 pages, 5 figures, scheduled for ApJ 668, October 20, 200
M87, Globular Clusters, and Galactic Winds: Issues in Giant Galaxy Formation
New VRI photometry is presented for the globular clusters in the innermost
140'' of the M87 halo. The results are used to discuss several issues
concerning the formation and evolution of globular cluster systems in
supergiant ellipticals like M87. (1) we find no significant change in the
globular cluster luminosity function (GCLF) with galactocentric radius, for
cluster masses M < 10^5 solar masses, indicating that the main effects of
dynamical evolution may be only on lower-mass clusters. (2) Within the core
radius (1') of the globular cluster system, the metallicity distribution is
uniform, but at larger radii the mean metallicity declines steadily as Z ~
r^-0.9. (3) The various options for explaining the existence of high specific
frequency galaxies like M87 are evaluated, and scaling laws for the GCSs in
these galaxies are given. Interpretations involving secondary evolution
(formation of many globular clusters during mergers, intergalactic globular
clusters, etc.) are unlikely to be the primary explanation for high-S_N
galaxies. (4) We suggest that central-supergiant E galaxies may have formed in
an exceptionally turbulent or high-density environment in which an early,
powerful galactic wind drove out a high fraction of the protogalactic gas, thus
artificially boosting the specificComment: 67 pages, 17 figures. To appear in Astronomical Journal, in press for
May 1998. Preprints also available from W.Harris; send e-mail request to
[email protected]
Embolization in Pediatric Patients: A Comprehensive Review of Indications, Procedures, and Clinical Outcomes
Embolization in pediatric patients encompasses a large spectrum of indications, ranging from the elective treatment of congenital diseases of the cardiovascular system to the urgent management of acute hemorrhagic conditions. In particular, the endovascular treatment of central and peripheral vascular malformations and hypervascular tumors represents a wide chapter for both congenital and acquired situations. Thanks to the progressive availability of low-profile endovascular devices and new embolic materials, the mini-invasive approach has gradually overtaken surgery. In this review, the main embolization procedures will be illustrated and discussed, with a focus on clinical indications and expected outcomes. The most recent mini-invasive techniques will be described, with hints on the cutting-edge devices and embolic materials
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