55 research outputs found
Smooth free involution of and Smith conjecture for imbeddings of in
This paper establishes an equivalence between existence of free involutions
on and existence of involutions on with fixed point set an
imbedded , then a family of counterexamples of the Smith conjecture for
imbeddings of in are given by known result on . In
addition, this paper also shows that every smooth homotopy complex projective
3-space admits no orientation preserving smooth free involution, which answers
an open problem [Pe]. Moreover, the study of existence problem for smooth
orientation preserving involutions on is completed.Comment: 10 pages, final versio
Analysis of a three-component model phase diagram by Catastrophe Theory: Potentials with two Order Parameters
In this work we classify the singularities obtained from the Gibbs potential
of a lattice gas model with three components, two order parameters and five
control parameters applying the general theorems provided by Catastrophe
Theory. In particular, we clearly establish the existence of Landau potentials
in two variables or, in other words, corank 2 canonical forms that are
associated to the hyperbolic umbilic, D_{+4}, its dual the elliptic umbilic,
D_{-4}, and the parabolic umbilic, D_5, catastrophes. The transversality of the
potential with two order parameters is explicitely shown for each case. Thus we
complete the Catastrophe Theory analysis of the three-component lattice model,
initiated in a previous paper.Comment: 17 pages, 3 EPS figures, Latex file, continuation of Phys. Rev. B57,
13527 (1998) (cond-mat/9707015), submitted to Phys. Rev.
Causal categories: relativistically interacting processes
A symmetric monoidal category naturally arises as the mathematical structure
that organizes physical systems, processes, and composition thereof, both
sequentially and in parallel. This structure admits a purely graphical
calculus. This paper is concerned with the encoding of a fixed causal structure
within a symmetric monoidal category: causal dependencies will correspond to
topological connectedness in the graphical language. We show that correlations,
either classical or quantum, force terminality of the tensor unit. We also show
that well-definedness of the concept of a global state forces the monoidal
product to be only partially defined, which in turn results in a relativistic
covariance theorem. Except for these assumptions, at no stage do we assume
anything more than purely compositional symmetric-monoidal categorical
structure. We cast these two structural results in terms of a mathematical
entity, which we call a `causal category'. We provide methods of constructing
causal categories, and we study the consequences of these methods for the
general framework of categorical quantum mechanics.Comment: 43 pages, lots of figure
Designing the Unexpected : Endlessly Fascinating Interaction for Interactive Installations
This research was supported in part by SSHRC, NSERC, SMART Technologies, AITF, SurfNet and GRAND.We present A Delicate Agreement, an interactive art installation designed to intrigue viewers by offering them an unfolding story that is endlessly fascinating. To achieve this, we set our story in the liminal space of an elevator, and populated this elevator with a set of unique characters. Viewers watch the story unfold through peepholes in the elevator’s doors, where in turn their gaze can trigger changes in the storyline. This storyline’s interactive response was created via a complex adaptive system using simple rules based on Goffman’s performance theory.Postprin
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