Teacher Rationales for Scoring Students' Problem Solving Work

This article presents the scores teachers assigned to samples of actual students' problem-solving work and the rationales teachers provided for these scores. These rationales may reflect teachers' values relative to aspects of mathematical problem solving. It may be that when teachers can express rationales for scoring students' work, they are able to justify their evaluation of what students can “know and do” in mathematics.     

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.     

Segments and Hilbert schemes of points

Using results obtained from a study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to a degreverse term order (as, for example, the degrevlex order) in the Hilbert scheme of points in Pⁿ. In this context, we look into the properties of several types of “segment” ideals that we define and compare. This study also leads us to focus on the connections between the shape of generators of Borel ideals and the related Hilbert polynomial, thus providing an algorithm for computing all saturated Borel ideals with a given Hilbert polynomial.     

Quantifying Democracy of Wavelet Bases in Lorentz Spaces

We study the efficiency of the greedy algorithm for wavelet bases in Lorentz spaces in order to give the near best approximation. The result is used to give sharp inclusions for the approximation spaces in terms of discrete Lorentz sequence spaces.     

Insertion of Continuous Real Functions on Spaces,Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root

We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.     

Solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Lévy market

We study an integro-differential parabolic problem modeling a process with jumps arising in financial mathematics. Under suitable conditions, we prove the existence of weak solutions to a more general integro-differential equation by using the Schaefer’s fixed point theorem and generalize the result to unbounded domains.     

Optimization of Optimal Power Flow Problems

Optimal power flow problems arise in the context of the optimization and secure exploitation of electrical power in alternating current (AC) networks. This optimization problem evaluates the flow on each line and to ensure that they are under line thermal limits. To improve the reliability of the power supply, a secure network is necessary, i.e., it has to be able to cope with some contingencies. Nowadays high performance solution methods, that are based on nonlinear programming algorithms, search for an optimal state while considering certain contingencies. According to the number of contingencies the problem size increases linearly. As the base case can already be large-scaled, the optimization time computation increases quickly. Parallelization seems to be a good way to solve quickly this kind of problem. This paper considers the minimization of an objective function and at least two constraints at each node. This optimization problem is solved by IPOPT, an interior point method, coupled with ADOL-C, an algorithmic differentiation tool, and MA27, a linear solver. Several results on employed parallelizing strategies will be discussed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sulle equazioni di una curva monomiale proiettiva

Riassunto Si dà una costruzione di un insieme minimale di generatori omogenei per l'ideale di una curva monomiale proiettiva e una limitazione per il grado delle equazioni che la definiscono.

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Summary A construction of a minimal system of homogeneous generators for the ideal of a monomial projective curve and a degree bound for its defining equations are given.

     

Optimal Control of an Evolution Problem Involving Time-Dependent Maximal Monotone Operators

Journal of Optimization Theory and Applications - We consider a control problem in a finite-dimensional setting, which consists in finding a minimizer for a standard functional defined by way of...