66,295 research outputs found
Quantum gravity at a large number of dimensions
We consider the large- limit of Einstein gravity. It is observed that a
consistent leading large- graph limit exists, and that it is built up by a
subclass of planar diagrams. The graphs in the effective field theory extension
of Einstein gravity are investigated in the same context, and it is seen that
an effective field theory extension of the basic Einstein-Hilbert theory will
not upset the latter leading large- graph limit, {\it i.e.}, the same
subclass of planar diagrams will dominate at large- in the effective field
theory. The effective field theory description of large- quantum gravity
limit will be renormalizable, and the resulting theory will thus be completely
well defined up to the Planck scale at GeV. The
expansion in gravity is compared to the successful expansion in
gauge theory (the planar diagram limit), and dissimilarities and parallels of
the two expansions are discussed. We consider the expansion of the effective
field theory terms and we make some remarks on explicit calculations of
-point functions.Comment: 18 pages, 23 figures (75 files), format RevTex4, typos corrected,
references adde
Endomorphisms of graph algebras
We initiate a systematic investigation of endomorphisms of graph C*-algebras
C*(E), extending several known results on endomorphisms of the Cuntz algebras
O_n. Most but not all of this study is focused on endomorphisms which permute
the vertex projections and globally preserve the diagonal MASA D_E of C*(E).
Our results pertain both automorphisms and proper endomorphisms. Firstly, the
Weyl group and the restricted Weyl group of a graph C*-algebra are introduced
and investigated. In particular, criteria of outerness for automorphisms in the
restricted Weyl group are found. We also show that the restriction to the
diagonal MASA of an automorphism which globally preserves both the diagonal and
the core AF-subalgebra eventually commutes with the corresponding one-sided
shift. Secondly, we exhibit several properties of proper endomorphisms,
investigate invertibility of localized endomorphisms both on C*(E) and in
restriction to D_E, and develop a combinatorial approach to analysis of
permutative endomorphisms.Comment: Several improvements in the exposition, to appear in JF
Finite-time synchronization of tunnel diode based chaotic oscillators
This paper addresses the problem of finite-time synchronization of tunnel
diode based chaotic oscillators. After a brief investigation of its chaotic
dynamics, we propose an active adaptive feedback coupling which accomplishes
the synchronization of tunnel diode based chaotic systems with and without the
presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov
stability theories. This feedback coupling could be applied to many other
chaotic systems. A finite horizon can be arbitrarily established by ensuring
that chaos synchronization is achieved at a pre-established time. An advantage
of the proposed feedback coupling is that it is simple and easy to implement.
Both mathematical investigations and numerical simulatioComment: 11 pages, 43 figure
- …