For linear Hamiltonian systems, the reconstruction of the Poisson bracket from a given energy function and an Hamiltonian flow leads to simple quantization rules. They can also be used in the infinite dimensional case. From this point of view, we consider the examples of oscillators, free electro-magnetic fields and vibrating strings.

Digitally based courses and their online delivery are rapidly expanding access to learning opportunities (Duffy and Kirkley 2004; NRC 2000; Visser and Visser-Valfrey 2008). It is important to ask however: access to what kind of learning opportunities? Weigel (2000) argues that most current attempts to create online learning environments suffer from a "port the classroom to the Web" model. Resea...

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This work reports on some useful applications of the tile model to the speciication and execution of CCS-like process calculi. This activity is part of our ongoing research on the relation between tile logic and rewriting logic. 1 Overview Tile Logic 1;2 is a framework for modular descriptions of the dynamic evolution of concurrent systems, extending rewriting logic 3;4 (in the non-conditional ...

I don't think I have much to teach this audience about string theory as such. What I will do, that I hope is useful, is discuss a few phenomena that have come up in my recent work which are in some way connected to fundamental issues regarding the realization of symmetry in quantum mechanics. My strong impression is that the fundamental symmetry of string theory, or whatever string theory is ev...

Let p be an odd prime. When n ≥ 3, we show that each tensor factor of form E ⊗ Γ in H∗ (Z, n;Zp) is an A∞-infinity bialgebra with nontrivial structure. We give explicit formulas for the structure maps and the quadratic relations among them. Thus E⊗Γ is a naturally occurring example of an A∞-bialgebra whose internal structure is well-understood.

We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg [1]. By means of a partial regularity theorem (proved elsewhere), it turns out that we are able to show the existence of a suitable weak solution to the Navier-Stokes equations with a singular set of positive one dimensional Hausdorff measure.

The purpose of this note is to point out some very elementary examples of special Lagrangian tori in certain Calabi-Yau manifolds that occur as hypersurfaces in complex projective space. All of these are constructed as real slices of smooth hypersurfaces defined over the reals. This method of constructing special Lagrangian submanifolds is, of course, well known. What does not appear to be in t...

Our main contribution is a formal deenition of what could be called a T-notion of innnity, for set theories T extending ZF. Around this deenition we organize some old and new notions of innnity; we also indicate some easy independence proofs.