Future teachers’ competence to plan a lesson: first results of a six-country study on the efficiency of teacher education

The study "Mathematics Teaching in the 21st Century (MT21)" focuses beyond others on the measurement of teachers’ general pedagogical knowledge (GPK). GPK is regarded as a latent construct embedded in a larger theory of teachers’ professional competence. It is laid out how GPK was defined and operationalized. As part of an international comparison GPK was measured with several complex vignettes. In the present paper, the results of future mathematics teachers’ knowledge from four countries (Germany, South Korea, Taiwan, and the US) with very different teacher-education systems are presented. Significant and relevant differences between the four countries as well as between future teachers at the beginning and at the end of teacher education were found. The results are discussed with reference to cultural discourses about teacher education.     

Prediction of losses in the flow through the last stage of low‐pressure steam turbine

In this paper, the numerical modelling of the flow through the low‐pressure steam turbine last stage was presented. On the basis of predicted wet steam flow‐field, the aerodynamic as well as thermodynamic losses were estimated. For calculations of the wet steam steady flow‐field three numerical methods were employed. The first method was a streamline curvature method (SCM). The commercial CFD code (CFX‐TACflow) and an in‐house code, both solving the 3‐D RANS equations, were the next two methods. In the wet steam region, by means of all three methods, the equilibrium flow was modelled. Additionally, the in‐house CFD code was used for modelling of the non‐equilibrium steam condensing flow. In this work, the comparison of the cascade loss coefficient for stator and rotor and selected flow parameters for the stage were presented, compared and discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Conditions for blow-up of solutions of some nonlinear Volterra integral equations

In this paper we give necessary and sufficient conditions for blow-up of solutions for a particular class of nonlinear Volterra equations. We also give some examples.     

Rotation Sets of Billiards with One Obstacle

We investigate the rotation sets of billiards on the m-dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the displacement function, whose averages we consider, measures the change of the position of a point in the universal covering of the torus (that is, in the Euclidean space), in the second case it measures the rotation around the obstacle. A substantial part of the rotation set has usual strong properties of rotation sets.The first author was partially supported by NSF grant DMS 0456748.The second author was partially supported by NSF grant DMS 0456526.The third author was partially supported by NSF grant DMS 0457168.     

On differential properties for bivariate orthogonal polynomials

In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.      

Finite-size scaling in the multiparticle production

The finite-size scalling analysis of the scaled factorial moment data is proposed. This analysis allows to extract the scaling indices of the underlying higher-dimensional scale-invariant multiparticle distributions. Moreover, it exhibits the change of the effective scale involved in the dimensional projection with transverse momentum cuts applied to the data.     

Tritium-labeled abscisic acid

A simple method for the preparation of biologically active abscisic acid (growth inhibiting plant hormone) labeled with tritium is described. The product obtained has a specific radioactivity of 1.12 GBq mmol^–1: the yield is about 60% as compared to the initial amount of the substance used.     

Non-homeomorphic density topologies

In [ANISZCZYK, B.-FRANKIEWICZ, R.: Non homeomorphic density topologies, Bull. Polish Acad. Sci. Math. 34 (1986), 211–213] the authors constructed 2^c non-homeomorphic density topologies tied to the concept of measure. In [WROŃSKI, S.: The number of non-homeomorphic I-density topologies. Institute of Mathematics of Polish Academy of Sciences. Preprint 482, December 1990, XXXIV Semester in Banach Center, Theory of Real Functions] an analogous construction has been given for topologies tied to the concept of category. Here we present a generalization containing both the results mentioned above. This generalization based only on the topological ideas is independent of the concept of measure or category. Communicated by L’ubica Holá     

On Sums of Units

It is shown that if R is a finitely generated integral domain of zero characteristic, then for every n there exist elements of R which are not sums of at most n units. This applies in particular to rings of integers in finite extensions of the rationals. On the other hand there are many infinite algebraic extensions of the rationals in which every integer is a sum of two units.