535 research outputs found
Activities and programs for gifted students
The aim of TSG-3 at ICME-12 was to gather educational researchers, research mathematicians, mathematics teachers, teacher educators, designers and other congress participants for the international exchange of ideas related to identifying and nourishing mathematically gifted students..
Equation of state for polymer liquid crystals: theory and experiment
The first part of this paper develops a theory for the free energy of
lyotropic polymer nematic liquid crystals. We use a continuum model with
macroscopic elastic moduli for a polymer nematic phase. By evaluating the
partition function, considering only harmonic fluctuations, we derive an
expression for the free energy of the system. We find that the configurational
entropic part of the free energy enhances the effective repulsive interactions
between the chains. This configurational contribution goes as the fourth root
of the direct interactions. Enhancement originates from the coupling between
bending fluctuations and the compressibility of the nematic array normal to the
average director. In the second part of the paper we use osmotic stress to
measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl
solutions. These measurements cover 5 orders of magnitude in DNA osmotic
pressure. At high osmotic pressures the equation of state, dominated by
exponentially decaying hydration repulsion, is independent of the ionic
strength. At lower pressures the equation of state is dominated by fluctuation
enhanced electrostatic double layer repulsion. The measured equation of state
for DNA fits well with our theory for all salt concentrations. We are able to
extract the strength of the direct electrostatic double layer repulsion. This
is a new and alternative way of measuring effective charge densities along
semiflexible polyelectrolytes.Comment: text + 5 figures. Submitted to PR
Effective interaction between helical bio-molecules
The effective interaction between two parallel strands of helical
bio-molecules, such as deoxyribose nucleic acids (DNA), is calculated using
computer simulations of the "primitive" model of electrolytes. In particular we
study a simple model for B-DNA incorporating explicitly its charge pattern as a
double-helix structure. The effective force and the effective torque exerted
onto the molecules depend on the central distance and on the relative
orientation. The contributions of nonlinear screening by monovalent counterions
to these forces and torques are analyzed and calculated for different salt
concentrations. As a result, we find that the sign of the force depends
sensitively on the relative orientation. For intermolecular distances smaller
than it can be both attractive and repulsive. Furthermore we report a
nonmonotonic behaviour of the effective force for increasing salt
concentration. Both features cannot be described within linear screening
theories. For large distances, on the other hand, the results agree with linear
screening theories provided the charge of the bio-molecules is suitably
renormalized.Comment: 18 pages, 18 figures included in text, 100 bibliog
On the instructional triangle and sources of justification for actions in mathematics teaching
We elaborate on the notion of the instructional triangle, to address the question of how the nature of instructional activity can help justify actions in mathematics teaching. We propose a practical rationality of mathematics teaching composed of norms for the relationships between elements of the instructional system and obligations that a person in the position of the mathematics teacher needs to satisfy. We propose such constructs as articulations of a rationality that can help explain the instructional actions a teacher takes in promoting and recognizing learning, supporting work, and making decisions.The ideas reported in this paper have been developed in part with the support of National Science Foundation grants ESI-0353285 and DRL-0918425 to the authors.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91281/1/On_the_instructional_triangle_PH&DC_May2012.pdf-
Measurement of the Ds lifetime
We report precise measurement of the Ds meson lifetime. The data were taken
by the SELEX experiment (E781) spectrometer using 600 GeV/c Sigma-, pi- and p
beams. The measurement has been done using 918 reconstructed Ds. The lifetime
of the Ds is measured to be 472.5 +- 17.2 +- 6.6 fs, using K*(892)0K+- and phi
pi+- decay modes. The lifetime ratio of Ds to D0 is 1.145+-0.049.Comment: 5 pages, 2 figures submitted to Phys. Lett.
Confirmation of the Double Charm Baryon Xi_cc+ via its Decay to p D+ K-
We observes a signal for the double charm baryon Xi_cc+ in the charged decay
mode Xi_cc+ -> p D+ K- to complement the previously reported decay Xi_cc+ ->
Lambda_c K- pi+ in data from SELEX, the charm hadro-production experiment
(E781) at Fermilab. In this new decay mode we observe an excess of 5.62 events
over an expected background estimated by event mixing to be 1.38+/-0.13 events.
The Poisson probability that a background fluctuation can produce the apparent
signal is less than 6.4E-4. The observed mass of this state is
(3518+/-3)MeV/c^2, consistent with the published result. Averaging the two
results gives a mass of (3518.7+/-1.7)MeV/c^2. The observation of this new weak
decay mode confirms the previous SELEX suggestion that this state is a double
charm baryon. The relative branching ratio Gamma(Xi_cc+ -> pD+K-)/Gamma(Xi_cc+
-> Lambda_c K- pi+) = 0.36+/-0.21.Comment: 11 pages, 6 included eps figures. v2 includes improved statistical
method to determine significance of observation. Submitted to PL
Mathematical talent in Braille code pattern finding and invention
The recognition of patterns and creativity are two characteristics associated with mathematical
talent. In this study, we analyzed these characteristics in a group of 37 mathematically talented
students. The students were asked to find the pattern the Braille code had been built upon and
reinvent it with the aim of making its mathematical language become more functional.
Initially, the students were unable to identify the formation pattern of Braille, but after
experiencing the difficulties that blind people face when reading it, they recognized the
generating element and the regularity. The results were in contrast with those of a control
group, and it is noted that the students with mathematical talent were more effective in using
visualization to identify the regularity of the pattern and their invention proposals were more
sophisticated and used less conventional mathematical content.This research is part of the R+D+I project EDU2015-
69,731-R (Spanish Government/MinEco and ERDF)
First observation of a narrow charm-strange meson DsJ(2632) -> Ds eta and D0 K+
We report the first observation of a charm-strange meson DsJ(2632) at a mass
of 2632.6+/-1.6 MeV/c^2 in data from SELEX, the charm hadro-production
experiment E781 at Fermilab. This state is seen in two decay modes, Ds eta and
D0 K+. In the Ds eta decay mode we observe an excess of 49.3 events with a
significance of 7.2sigma at a mass of 2635.9+/-2.9 MeV/c^2. There is a
corresponding peak of 14 events with a significance of 5.3sigma at 2631.5+/-1.9
MeV/c^2 in the decay mode D0 K+. The decay width of this state is <17 MeV/c^2
at 90% confidence level. The relative branching ratio Gamma(D0K+)/Gamma(Dseta)
is 0.16+/-0.06. The mechanism which keeps this state narrow is unclear. Its
decay pattern is also unusual, being dominated by the Ds eta decay mode.Comment: 5 pages, 3 included eps figures. v2 as accepted for publication by
PR
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