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 $6\AA$ 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

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.

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-

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