A third grader's way of thinking about linear function tables

This paper is inscribed within the research effort to produce evidence regarding primary school students’ learning of algebra. Given the results obtained so far in the research community, we are convinced that young elementary school students can successfully learn algebra. Moreover, children this young can make use of different representational systems, including function tables, algebraic notation, and graphs in the Cartesian coordinate grid. In our research, we introduce algebra from a functional perspective. A functional perspective moves away from the mere symbolic manipulation of equations and focuses on relationships between variables. In investigating the processes of teaching and learning algebra at this age, we are interested in identifying meaningful teaching situations. Within each type of teaching situation, we focus on what kind of knowledge students produce, what are the main obstacles they find in their learning, as well as the intermediate states of knowledge between what they know and the target knowledge for the teaching situation. In this paper, we present a case study focusing on the approach adopted by a third grade student, Marisa, when she was producing the formula for a linear function while she was working with the information of a problem displayed in a function table containing pairs of inputs-outputs. We will frame the analysis and discussion on Marisa's approach in terms of the concept of theorem-in action (Vergnaud, 1982) and we will contrast it with the scalar and functional approaches introduced by Vergnaud (1988) in his Theory of Multiplicative Fields. The approach adopted by Marisa turns out to have both scalar and functional aspects to it, providing us with new ways of thinking of children's potential responses to functions.     

On the determination of226Ra in soils and uranium ores by direct gamma-ray spectrometry

The evaluation of the source term in facilities related to the first stages of nuclear fuel involves the determination of radium concentration, as well as those from other radionuclides members of the uranium series. These activities are often required within a short time period, making impossible the use of radiochemical methods or the gamma-ray spectrometry of radium daughters. In those situations it can be very convenient to determine the²²⁶Ra activity by means of its 186 keV gamma-ray line. For this purpose it is necessary to estimate the interference due to²³⁵U, also present in natural samples. This method has been applied successfully to several soil samples from an old uranium factory in Southern Spain.     

The dirac equation in 5-dimensional Wesson gravity

Using the Ma interpretation of 5D Wesson gravity, we construct the corresponding Weyl equation in a quasistatic spherically symmetric gravitational background in order to look at the mass term predicted by the theory. We find that the value of this mass depends strongly on the boundary conditions selected for theg55. As an example we calculate its value at the surface of the earth.     

On necessary conditions for infinite-dimensional extremum problems

In this paper, we carry on the analysis (introduced in [4] and developed in [2,7]) of optimality conditions for extremum problems having infinite-dimensional image, in the case of unilateral constraints. This is done by associating to the feasible set a special multifunction. It turns out that the classic Lagrangian multiplier functions can be factorized into a constant term and a variable one; the former is the gradient of a separating hyperplane as introduced in [4,5]; the latter plays the role of selector of the above multifunction. Finally, the need of enlarging the class of Lagrangian multiplier functions is discussed.     

Electrochemical synthesis and optical analysis of poly[(2,2′-dithienyl)-5,5′-diylvinylene]

The electrochemical synthesis of poly[(2,2′-dithienyl)-5,5′-diylvinylene tetrafluoroborate] (PDTE/BF₄) has been accomplished and provides coppery-black free-standing films with a room-temperature four-probe conductivity as high as 15 (Ω cm)^?1. The conductivity and morphology of the films were found to be strongly dependent on synthetic conditions. The oxidized form of PDTE is not air stable, as evidenced by a rapid, three order of magnitude drop in the conductivity. Optoelectrochemical experiments demonstrate that bipolarons are the main charge-carrying species in conductive PDTE and allow their evolution to be followed as a function of oxidation.     

The structure of27Al

Gamma decay modes and spin assignments of levels in²⁷Al have been investigated by proton-γ-ray angular correlation measurements in the²⁴Mg(α, pγ) reaction at 14.2, 15 and 15.6 MeV bombarding energy and byγ-ray angular distribution measurements on the E_p=1820, 2114, 2293 and 2574 keV resonances of the²⁶Mg(p, γ) reaction. Unique spin assignments were obtained as follows: I=3/2 for the 5827 keV state, I=5/2 for the 6115, 6465, 6765, 7577, 7721, 8097, 8136, 8324 keV states, I=7/2 for the 5433, 6533, 7413, 8037, 8442, 8586 keV states, I=9/2 for the 5418, 6512, 6713, 7997 keV states, I=11/2 for the 5500, 6948, 7400, 8396 keV states. The level scheme and electromagnetic properties of levels are compared with the results of shell model calculations which use the complete configuration space of the 0d_5/2-1s_1/2-0d_3/2 shell and the unifieds-d shell Hamiltonian. The agreement is good to excellent and extends into the region of high level density above 7 MeV excitation energy. The total B(M1↑) below 8.5 MeV excitation energy is evaluated, using published resonance fluorescence and (e, e′) data, and quenching relative to the free-nucleon predictions is reexamined. Evidence in favour of a prolate ground state deformation of²⁷Al and implications of this work for the astrophysically interesting²⁶Al(p, γ) reaction are discussed.