7,194 research outputs found
On an Approximation Theorem of Kupka and Smale
Simplified and generalized geometrical proof of Kupka and Smale approximation theorem concerning differential equations defined on closed, compact, infinitely differentiable manifol
Trajectories in a space with a spherically symmetric dislocation
We consider a new type of defect in the scope of linear elasticity theory,
using geometrical methods. This defect is produced by a spherically symmetric
dislocation, or ball dislocation. We derive the induced metric as well as the
affine connections and curvature tensors. Since the induced metric is
discontinuous, one can expect ambiguity coming from these quantities, due to
products between delta functions or its derivatives, plaguing a description of
ball dislocations based on the Geometric Theory of Defects. However, exactly as
in the previous case of cylindric defect, one can obtain some well-defined
physical predictions of the induced geometry. In particular, we explore some
properties of test particle trajectories around the defect and show that these
trajectories are curved but can not be circular orbits.Comment: 11 pages, 3 figure
Spontaneous centralization of control in a network of company ownerships
We introduce a model for the adaptive evolution of a network of company
ownerships. In a recent work it has been shown that the empirical global
network of corporate control is marked by a central, tightly connected "core"
made of a small number of large companies which control a significant part of
the global economy. Here we show how a simple, adaptive "rich get richer"
dynamics can account for this characteristic, which incorporates the increased
buying power of more influential companies, and in turn results in even higher
control. We conclude that this kind of centralized structure can emerge without
it being an explicit goal of these companies, or as a result of a
well-organized strategy.Comment: 5 Pages, 7 figure
Eisenstein Series and String Thresholds
We investigate the relevance of Eisenstein series for representing certain
-invariant string theory amplitudes which receive corrections from BPS
states only. may stand for any of the mapping class, T-duality and
U-duality groups , or respectively.
Using -invariant mass formulae, we construct invariant modular functions
on the symmetric space of non-compact type, with the
maximal compact subgroup of , that generalize the standard
non-holomorphic Eisenstein series arising in harmonic analysis on the
fundamental domain of the Poincar\'e upper half-plane. Comparing the
asymptotics and eigenvalues of the Eisenstein series under second order
differential operators with quantities arising in one- and -loop string
amplitudes, we obtain a manifestly T-duality invariant representation of the
latter, conjecture their non-perturbative U-duality invariant extension, and
analyze the resulting non-perturbative effects. This includes the and
couplings in toroidal compactifications of M-theory to any
dimension and respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms
renumbered, plus minor corrections; v3: relation (1.7) to math Eis series
clarified, eq (3.3) and minor typos corrected, final version to appear in
Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde
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