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 $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ 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 $\Lambda_b$, current determinations of ${\cal O}(m_b^{-3})$ contribution to $\tau(\Lambda_b)$ do not allow to explain the small measured value of $\tau(\Lambda_b)/\tau(B_d)$. 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