In [3], Nathan Bowler and the first author introduced a category of algebraic objects called tracts defined notion (weak strong) matroids over tract. part paper, we summarize clarify connections to other which have previously been used in connection with matroid theory. For example, show that both partial fields hyperfields are fuzzy rings, rings tracts, these relations compatible theories. We ...

We find that for various solitonic processes the corresponding canonical moduli space can have a boundary which is accessible in finite time evolution. show such not failure of approach but has physical meaning. In our example, it corresponds to complete annihilation colliding kink and antikink after time. further that, close boundary, solutions an approximate self-similar form.

This is the second of two articles that describe the moduli spaces of pseudoholomorphic, multiply punctured spheres in R .S S/ as defined by a certain natural pair of almost complex structure and symplectic form. The first article in this series described the local structure of the moduli spaces and gave existence theorems. This article describes a stratification of the moduli spaces and gives ...

We define Hilbert–Siegel modular forms and Hecke “operators” acting on them. As with Hilbert modular forms (i.e. with Siegel degree 1), these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert–Siegel forms (i.e. with arbitrary Siegel d...

We define Hilbert-Siegel modular forms and Hecke “operators” acting on them. As with Hilbert modular forms (i.e. with Siegel degree 1), these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert-Siegel forms (i.e. with arbitrary Siegel d...