Quasi-measures with image transformations as generalized variables

We introduce an image transformation as a generalization of measurable maps. Structure properties of the image transformation is given. Unique extension of image transformations from solid sets is proven. The multidimensional median and sample median are presented as image transformations, providing a construction suitable for probability theorists.     

Melting curve of MgO from first-principles simulations

First-principles calculations based on density functional theory, both with the local density approximation (LDA) and with generalized gradient corrections (GGA), have been used to simulate solid and liquid MgO in direct coexistence in the range of pressure 0 < or = p < or = 135 GPa. The calculated LDA zero pressure melting temperature is T(LDA)m = 3110 +/- 50 K, in good agreement with the experimental data. The GGA zero pressure melting temperature T(GGA)m = 2575 +/- 100 K is significantly lower than the LDA one, but the difference between the GGA and the LDA is greatly reduced at high pressure. The LDA zero pressure melting slope is dT/dp approximately 100 K/GPa, which is more than 3 times higher than the currently available experimental one from Zerr and Boehler [Nature (London) 371, 506 (1994)]. At the core mantle boundary pressure of 135 GPa MgO melts at Tm = 8140 +/- 150 K.     

Rates of convergence for the laws of large numbers for independent Banach-valued random variables

In this paper, results of Lai, Heyde, and Rohatgi concerning the convergence rates for the laws of large numbers are extended for the case of independent random variables taking values in a separable Banach space.     

A novel regiospecific N to O-methyl transferase activity in the biotransformation of a thebaine derivative with Cunninghamella echinulata NRRL 1384

A novel regiospecific N- to O-methyl transfer reaction has been characterised in the biotransformation of an N-CD3-thebaine derivative with the fungus Cunninghamella echinulata NRRL 1384.     

Phonon Spectroscopy of Oriented hcp Iron

High-pressure phonon spectroscopy was performed on iron in the bcc and hcp phase up to 40 GPa using the nuclear inelastic scattering (NIS) of synchrotron radiation (SR). In hcp iron we observe differences in the density of phonon states for spectra measured with different orientations of the diamond anvil cell (DAC) with respect to the SR beam. These differences are attributed to a preferred orientation of the hexagonal c -axis along the load axis of the DAC. These texture effects are used, in conjunction with theoretical calculations, to extract density of phonon states as seen parallel and perpendicular to the c -axis of hcp iron.     

NEEDING TO USE ALGEBRA

We have completed a Teacher Training Agency (TTA) funded project looking at the teaching and learning of algebra with one mixed-ability year 7 class (11–12 year-olds in the UK). We take Kieran's (quoted in Sutherland, 1997) definition of algebra and see ourselves as developing a'community of practice’ (Lave and Wenger, 1991) in the classroom where the practice is not that of mathematician but of inquirer (Schoenfeld, 1996) into mathematics. The teacher in this community acts as role model for inquirer and metacomments (Bateson, 1972) on the practice of inquiry. In this paper we present evidence for how such metacommenting supports the development of a'community of inquiry’ which leads to the'need’ for algebraic activity. We conclude with a case study, illustrating one student's need for algebra.     

Mathematics teachers learning with video: the role,for the didactician,of a heightened listening

This article addresses two main questions, how do mathematics teachers learn from using video? and, what is the role of the didactician? A common problem is reported in the difficulty of keeping teacher discussion of video away from judgment and evaluation. A review of mathematics education literature revealed four existing models for the use of video with teachers. Drawing on enactivist ideas (Rosch, Concepts: core readings, pp 189–206, 1999), there are reasons why these models are likely to be productive and therefore suggestions for how teachers can learn from video. However, little is known about the role of the didactician in supporting learning. From empirical data, there is evidence that didacticians need to engage in a particular form of attention that I label a ‘heightened listening’ since there are simultaneous foci (on the content of teachers’ contributions and what kind of a comment is being made), in order to establish discussion norms and to support the development of new ways of seeing and acting in the classroom.