Matrix Riemann-Hilbert problems and factorization on Riemann surfaces

The Wiener-Hopf factorization of 2×2 matrix functions and its close relation to scalar Riemann-Hilbert problems on Riemann surfaces is investigated. A family of function classes denoted C(Q₁,Q₂) is defined. To each class C(Q₁,Q₂) a Riemann surface Σ is associated, so that the factorization of the elements of C(Q₁,Q₂) is reduced to solving a scalar Riemann-Hilbert problem on Σ. For the solution of this problem, a notion of Σ-factorization is introduced and a factorization theorem is presented. An example of the factorization of a function belonging to the group of exponentials of rational functions is studied. This example may be seen as typical of applications of the results of this paper to finite-dimensional integrable systems.     

On Reform Movement and the Limits of Mathematical Discourse

In this article, I take a critical look at some popular ideas about teaching mathematics, which are forcefully promoted worldwide by the reform movement. The issue in focus is the nature and limits of mathematical discourse. Whereas knowing mathematics is conceptualized as an ability to participate in this discourse, special attention is given to meta-discursive rules that regulate participation and are therefore a central, if only implicit, object of learning. Following the theoretical analysis illustrated with empirical examples, the question arises of how far one may go in renegotiating and relaxing the rules of mathematical discourse before seriously affecting its learnability.     

Rheological properties of PDMS/clay nanocomposites and their sensitivity to microstructure

The effect of microstructure on the rheology of clay/polymer nanocomposites is investigated using dispersions of organically treated clay in nearly Newtonian poly(dimethylsiloxane). Degree of dispersion and floc size are altered by using two different dispersion procedures and by changing the shear history. The scaling for dynamic moduli of attractive colloids applies, except for a possible relaxation mechanism at very low frequencies. The time to reach the crossover at a given frequency is found to be extremely sensitive to the dispersion procedure used. Hydrodynamic and elastic components of the steady state stress, on the other hand, evolve in a very similar fashion for the different systems. Although the relaxation times of the elastic stress components change drastically with flow-induced changes in structure, the dispersion process hardly has an effect at all. Intermittent start-up flows in the forward and reverse directions show that anisotropy persists long after the flow has been arrested, even at shear rates where no large reversible flocs are present. The degree of dispersion only had a limited effect on the anisotropy. Finally, the effect of shear on structure recovery has been studied. Very low shear rates are found to increase the rate of recovery, even for small strains.     

New isomeric 2‐ortho‐(meta‐ and para‐) chloro‐(bromo and nitro‐)benzylthio‐6‐aminouracils

Ten new ortho, meta and para substituted derivatives of 2‐benzylthio‐6‐aminouracils have been prepared. Electron Impact (EI) induced mass spectral fragmentation of these compounds was investigated. Fragmentation pathways are proposed on the basis of accurate mass and metastable transition measurements. The correlation between the intensities of the M⁺‐ and the selected fragment ions of these compounds is discussed. The data obtained create the basis for dinstinguishing isomers. The ¹H and ¹³C NMR spectra of these compounds were assigned unambiguously using a combination of heteronuclear (HETCOR) spectra the chemical shifts. The data derived from these spectra can be used to differentiate the isomers.     

On optimal zero-preserving corrections for inconsistent linear systems

This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose objective function is a sum of fractional functions. A branch-and-bound algorithm for solving this nonconvex program is proposed, based on suitably overestimating the denominator function for computing lower bounds. Computational experience is presented to demonstrate the efficacy of this approach.     

Addendum to: Comparison between different types of abstract integrals in riesz spaces

In [3] we did not give explicitly the definition of measurability for realvalued functions, with respect to finitely additive measures with values in a Dedekind complete Riesz space. We note that, in [3], all involved functions are intended to be measurable. We now report the definition of measurability, which we gave in [2] (Definition 3.2).