Bibliography: Publications of J. L. Doob

Publications of J. L. DoobComment: Compiled by Don Burkholder; Published in at http://dx.doi.org/10.1214/09-AOP466 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Mathematics of Chinese Checkers

Our goal for this project was to expand and improve upon the findings of George I. Bell and Nicholas Fonseca, who have both written papers on optimization in Chinese Checkers. While their work focuses mainly on cooperative games between one, two, and three players, we have considered games for six players. While doing this, we have redefined the playing board in a more intuitive manner, while developing and proving its associated distance formula. As well, we have found the shortest game for six players, and are working to generalize a formula for the number of moves required to finish a six player game as fast as possible. This could further incite research to generalize a lower bound for any number of players

Tracer diffusion in active suspensions

We study the diffusion of a Brownian probe particle of size $R$ in a dilute dispersion of active Brownian particles (ABPs) of size $a$, characteristic swim speed $U_0$, reorientation time $\tau_R$, and mechanical energy $k_s T_s = \zeta_a U_0^2 \tau_R /6$, where $\zeta_a$ is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity $D_P = k_B T/\zeta_P$, where $k_B T$ is the thermal energy of the solvent and $\zeta_P$ is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by $Pe_s = U_0 a /D_P$. The active contribution to the diffusivity scales as $Pe_s^2$ for weak swimming and $Pe_s$ for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale $\tau_R$, the active diffusivity scales as $k_s T_s /\zeta_P$: the probe moves as if it were immersed in a solvent with energy $k_s T_s$ rather than $k_B T$.Comment: 5 pages, 3 figures, submitted for publication. Please contact authors regarding supplemental informatio

Emerging Evidence Regarding the Roles of Emotional, Behavioural, and Cognitive Aspects of Student Engagement in the Online Classroom

There is emerging evidence that suggests emotions as a discrete factor in academic online contexts that significantly contribute to student engagement and higher order learning (Cleveland-Innes & Campbell, 2012; You, 2012, You & Kang, 2014; Zembylas, 2008; Liaw, 2008). Pekrun (2000) and Pekrun, Goetz, Frenzel, Barchfeld, and Perry (2011) developed the control-value theory of achievement emotion that not only showed that emotions represent a discrete category in student engagement, but that there are certain factors such as perceived academic control and self-regulation that function as antecedents of students’ emotional reactions that affect online learning. The aim of the present paper is to review the emerging research evidence of the impact of emotions on students’ engagement in order to understand the distinct role that emotions may play in online learning. The review also proposes strategies and activities that teachers can use in order to enhance students’ positive engagement in online learning. The findings suggest that emotions are significant factors in students’ engagement in online learning while cognitive and behavioural factors function as antecedents of emotions in online contexts. The inclusion of emotional, cognitive and behavioural strategies in online teaching can enhance students’ engagement and learning experience in the online classroom

Reasons for Ethical Misconduct of Counseling Students: What do Faculty Think?

The ethics training of students in the helping professions has been a frequent topic in the literature, yet students still commit ethics violations (Li, Lampe, Trusty, & Lin, 2009). No known research has examined the attributions faculty give for student ethics violations. This qualitative study used a conceptual framework of attribution theory and explored faculty attributions of counseling master’s students’ ethical misconduct. Emergent themes were grouped across two broad domains, attribution themes and prevention themes. Attribution themes include: (a) the person, (b) educational factors, and (d) performance. Prevention themes include (a) education and training, (b) gatekeeping and screening, (c) monitoring, (d) personal growth, and (e) support. Singular data for the ethics training of students in the helping professions is discussed

Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width

One-sided maximal functions and Hp

AbstractLet N be the nontangential maximal function of a function u harmonic in the Euclidean half-space Rn × (0, ∞) and let N− be the nontangential maximal function of its negative part. If u(0, y) = o(y−n) as y → ∞, then ∥N∥p ⩽ cp ∥N−∥p, 0 < p < 1, and more. The basic inequality of the paper (Theor. 2.1) can be used not only to derive such global results but also may be used to study the behavior of u near the boundary. Similar results hold for martingales with continuous sample functions. In addition, Theorem 1.3 contains information about the zeros of u. For example, if u belongs to Hp for some 0 < p < 1, then every thick cone in the half-space must contain a zero of u

Beyond the Checklist: Using Rhetorical Analysis to Evaluate Sources as Social Acts

Rhetorical analysis can transform information literacy instruction. A familiar concept in the study of rhetoric, it illustrates that all messages are deliberate, social acts, constructed by authors to achieve specific purposes and speak to specific audiences. To be effective, authors must make rhetorical choices that suit both the purpose and audience they are addressing. Under the current paradigm of source evaluation, librarians largely ignore the rhetorical nature of messages, focusing instead on the identification of surface features that indicate high-quality information. This can lead to the impression that messages are inert objects, rather than dynamic, social acts. Forms of communication, from personal blogs to television news stories to journal articles, are different in content and style because they allow writers to address different rhetorical situations. By examining the relationships between author, purpose, audience, and context—a process called rhetorical analysis--students can describe and evaluate the actions performed by each message. This forces them to think deeply about why certain features are included or excluded. In this workshop, I will model an interactive lesson that takes a rhetorical approach to evaluation. Attendees will deconstruct a source by conducting a detailed analysis of its intended purpose, intended audience, and author. They will then be asked to examine how a broader context (e.g., academic, political, cultural, economic, etc.) influences the use of — and provides meaning to — credibility cues that signal bias, authority, and accuracy. Once the analysis is complete, attendees will use their understanding to evaluate the source’s rhetorical effectiveness and credibility