Practitioner's Research: A Study in Changing Preservice Teachers’ Conceptions About Mathematics and Mathematics Teaching and Learning

Educators involved in the current reform movement in mathematics education recommend that students be actively involved in constructing their own knowledge and developing powerful mathematical concepts. This study suggests how ideas based on constructivist learning theory can be put into practice in a preservice mathematics education class.     

Stability of Gorenstein categories

We show that an iteration of the procedure used to define theGorenstein projective modules over a commutative ring R yieldsexactly the Gorenstein projective modules. Specifically, givenan exact sequence of Gorenstein projective R-modules

such that the complexes Hom_R(G, H) and Hom_R(H,G) are exact for each Gorenstein projective R-module H, themodule Coker() is Gorensteinprojective. The proof of this result hinges upon our analysisof Gorenstein subcategories of abelian categories.     

ALM models based on second order stochastic dominance

Computational Management Science - We propose asset and liability management models in which the risk of underfunding is modelled based on the concept of stochastic dominance. Investment decisions...     

On the generalized Bohnenblust–Hille inequality for real scalars

In this paper we obtain new lower and upper estimates for the sharp constants in the generalized Bohnenblust–Hille inequality introduced in Albuquerque et al. (J Funct Anal 266:3726–3740, 2014). We apply these results to find optimal constants in the generalized Bohnenblust–Hille inequality and also to recover the optimal constants of the mixed \(\left( \ell _{1},\ell _{2}\right) \)-Littlewood inequalities recently obtained in Pellegrino (J Number Theory 160:11–18, 2016) and Pellegrino and Teixeira (Commun Contemp Math, to appear).     

Cutting sequences, regular polygons, and the Veech group

We describe the cutting sequences associated to geodesic flow on regular polygons, in terms of a combinatorial process called derivation. This work is an extension of some of the ideas and results in Smillie and Ulcigrai’s recent paper, where the analysis was made for the regular octagon. It turns out that the main structural properties of the octagon generalize in a natural way.     

On the Newton-Kantorovich method inK-normed spaces

Nondifferentiable operator equations in spaces equipped with aK-norm — map taking values in the cone of an ordered Banach space — are studied. The majorant method is used to derive the convergence of a modified sequence of Newton-Kantorovich approximations.     

Markov interest rate models

A general procedure for creating Markovian interest rate models is presented. The models created by this procedure automatically fit within the HJM framework and fit the initial term structure exactly. Therefore they are arbitrage free. Because the models created by this procedure have only one state variable per factor, twoand even three-factor models can be computed efficiently, without resorting to Monte Carlo techniques. This computational efficiency makes calibration of the new models to market prices straightforward. Extended Hull- White, extended CIR, Black-Karasinski, Jamshidian's Brownian path independent models, and Flesaker and Hughston's rational log normal models are one-state variable models which fit naturally within this theoretical framework. The ‘separable’ n-factor models of Cheyette and Li, Ritchken, and Sankarasubramanian - which require n(n + 3)/2 state variables - are degenerate members of the new class of models with n(n + 3)/2 factors. The procedure is used to create a new class of one-factor models, the ‘β-η models.’ These models can match the implied volatility smiles of swaptions and caplets, and thus enable one to eliminate smile error. The β-η models are also exactly solvable in that their transition densities can be written explicitly. For these models accurate - but not exact - formulas are presented for caplet and swaption prices, and it is indicated how these closed form expressions can be used to efficiently calibrate the models to market prices.     

First‐principles calculations of Mössbauer hyperfine parameters for solids and large molecules

Electronic structure calculations based on density functional theory were performed for solids and large molecules. The solids were represented by clusters of 60–100 atoms embedded in the potential of the external crystal. Magnetic moments and Mössbauer hyperfine parameters were derived.     

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion.