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Strategies for overcoming math avoidance in an urban high school.
Typical high school algebra classes contain females, minority males, and white males in somewhat proportionate numbers. In contrast, the usual high school calculus class, three years hence, is but a small percentage of the original total who were in algebra, and they are predominantly white males of average to above-average ability. In a time span of less than two weeks, through three brief educational presentations that included factual information to demystify math study, showed the importance of math to personal goals, and provided panel presenters who would serve as role models, I sought to influence students, especially females and minority males, to commit to study math through calculus. When data collected on a questionnaire from 110 students studying Algebra 1 or geometry was analyzed in terms of two of the most important outcomes of the study--factual knowledge acquired and commitment to study math through calculus--there were no results significant at the.05 level for the experimental group who received the presentations. Regarding five other outcomes: the actual levels of math studied, the ability to match an appropriate amount of math to one\u27s post-high school plans, the choice of counselor over other options for career or educational information, and the choice of any school personnel as opposed to other options for career counseling--the only outcome significant at the.05 level was the selection of school personnel for career counseling. In conclusion, perhaps a greater use of role models whose job it is to stress the importance of math to one\u27s life goals, over a sustained period of time, might be most effective in changing student attitudes toward studying math through calculus
Little-Parks effect in a superconducting loop with magnetic dot
We have studied the nucleation of superconductivity in a mesoscopic Al loop,
enclosing magnetic dot with perpendicular magnetization. The superconducting
phase boundary Tc(B), determined from transport measurements, is asymmetric
with respect to the polarity of an applied magnetic field. The maximum critical
temperature has been found for a finite applied magnetic field, which is
antiparallel to the magnetization of the dot. Theoretical phase boundary shows
a good agreement with the experimental data.Comment: to be published in Phys. Rev. B - Brief Report
Vortex rectification effects in films with periodic asymmetric pinning
We study the transport of vortices excited by an ac current in an Al film
with an array of nanoengineered asymmetric antidots. The vortex response to the
ac current is investigated by detailed measurements of the voltage output as a
function of ac current amplitude, magnetic field and temperature. The
measurements revealed pronounced voltage rectification effects which are mainly
characterized by the two critical depinning forces of the asymmetric potential.
The shape of the net dc voltage as a function of the excitation amplitude
indicates that our vortex ratchet behaves in a way very different from standard
overdamped models. Rather, as demonstrated by the observed output signal, the
repinning force, necessary to stop vortex motion, is considerably smaller than
the depinning force, resembling the behavior of the so-called inertia ratchets.
Calculations based on an underdamped ratchet model provide a very good fit to
the experimental data.Comment: 5 pages, 4 figure
Dynamic programming on bipartite tree decompositions
We revisit a graph width parameter that we dub bipartite treewidth, along
with its associated graph decomposition that we call bipartite tree
decomposition. Bipartite treewidth can be seen as a common generalization of
treewidth and the odd cycle transversal number. Intuitively, a bipartite tree
decomposition is a tree decomposition whose bags induce almost bipartite graphs
and whose adhesions contain at most one vertex from the bipartite part of any
other bag, while the width of such decomposition measures how far the bags are
from being bipartite. Adapted from a tree decomposition originally defined by
Demaine, Hajiaghayi, and Kawarabayashi [SODA 2010] and explicitly defined by
Tazari [Th. Comp. Sci. 2012], bipartite treewidth appears to play a crucial
role for solving problems related to odd-minors, which have recently attracted
considerable attention. As a first step toward a theory for solving these
problems efficiently, the main goal of this paper is to develop dynamic
programming techniques to solve problems on graphs of small bipartite
treewidth. For such graphs, we provide a number of para-NP-completeness
results, FPT-algorithms, and XP-algorithms, as well as several open problems.
In particular, we show that -Subgraph-Cover, Weighted Vertex
Cover/Independent Set, Odd Cycle Transversal, and Maximum Weighted Cut are
parameterized by bipartite treewidth. We provide the following complexity
dichotomy when is a 2-connected graph, for each of -Subgraph-Packing,
-Induced-Packing, -Scattered-Packing, and -Odd-Minor-Packing problem:
if is bipartite, then the problem is para-NP-complete parameterized by
bipartite treewidth while, if is non-bipartite, then it is solvable in
XP-time. We define 1--treewidth by replacing the bipartite graph
class by any class . Most of the technology developed here works for
this more general parameter.Comment: Presented in IPEC 202
Critical temperature oscillations in magnetically coupled superconducting mesoscopic loops
We study the magnetic interaction between two superconducting concentric
mesoscopic Al loops, close to the superconducting/normal phase transition. The
phase boundary is measured resistively for the two-loop structure as well as
for a reference single loop. In both systems Little-Parks oscillations,
periodic in field are observed in the critical temperature Tc versus applied
magnetic field H. In the Fourier spectrum of the Tc(H) oscillations, a weak
'low frequency' response shows up, which can be attributed to the inner loop
supercurrent magnetic coupling to the flux of the outer loop. The amplitude of
this effect can be tuned by varying the applied transport current.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.
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