9,366 research outputs found
On a class of -constacyclic codes over
Let be a finite field of cardinality ,
which is a finite chain ring, and be a positive integer
satisfying . For any , an explicit representation for all distinct
-constacyclic codes over of length is given, and
the dual code for each of these codes is determined. For the case of
and , all self-dual -constacyclic codes over of
odd length are provided
F\"orster resonance energy transfer, absorption and emission spectra in multichromophoric systems: I. Cumulant expansions
We study the F\"orster resonant energy transfer (FRET) rate in
multichromophoric systems. The multichromophoric FRET rate is determined by the
overlap integral of the donor's emission and acceptor's absorption spectra,
which are obtained via 2nd-order cumulant expansion techniques developed in
this work. We calculate the spectra and multichromophoric FRET rate for both
localized and delocalized systems. (i) The role of the initial entanglement
between the donor and its bath is found to be crucial in both the emission
spectrum and the multichromophoric FRET rate. (ii) The absorption spectra
obtained by the cumulant expansion method are quite close to the exact one for
both localized and delocalized systems, even when the system-bath coupling is
far from the perturbative regime. (iii) For the emission spectra, the cumulant
expansion can give very good results for the localized system, but fail to
obtain reliable spectra of the high excitations of a delocalized system, when
the system-bath coupling is large and the thermal energy is small. (iv) Even
though, the multichromophoric FRET rate is good enough since it is determined
by the overlap integral of the spectra.Comment: 14 pages, 7 figure
Perelman's collapsing theorem for 3-manifolds
We will simplify the earlier proofs of Perelman's collapsing theorem of
3-manifolds given by Shioya-Yamaguchi and Morgan-Tian.
Among other things, we use Perelman's semi-convex analysis of distance
functions to construct the desired local Seifert fibration structure on
collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the
last step of Perelman's proof of Thurston's Geometrization Conjecture on the
classification of 3-manifolds.
Our proof of Perelman's collapsing theorem is almost self-contained. We
believe that our proof of this collapsing theorem is accessible to non-experts
and advanced graduate students.Comment: v1: 5 pictures v2: 2 pictures added v3: 9 pictures total v4: added
one more graph, This final version was refereed and accepted for publication
in "The Journal of Geometric Analysis
On Quantum de Rham Cohomology Theory
We define quantum exterior product wedge_h and quantum exterior differential
d_h on Poisson manifolds (of which symplectic manifolds are an important class
of examples). Quantum de Rham cohomology, which is a deformation quantization
of de Rham cohomology, is defined as the cohomology of d_h. We also define
quantum Dolbeault cohomology. A version of quantum integral on symplectic
manifolds is considered and the correspoding quantum Stokes theorem is proved.
We also derive quantum hard Lefschetz theorem. By replacing d by d_h and wedge
by wedge_h in the usual definitions, we define many quantum analogues of
important objects in differential geometry, e.g. quantum curvature. The quantum
characteristic classes are then studied along the lines of classical Chern-Weil
theory. Quantum equivariant de Rham cohomology is defined in the similar
fashion.Comment: 8 pages, AMSLaTe
Identification of Two Frobenius Manifolds In Mirror Symmetry
We identify two Frobenius manifolds obtained from two different differential
Gerstenhaber-Batalin-Vilkovisky algebras on a compact Kaehler manifold. One is
constructed on the Dolbeault cohomology, and the other on the de Rham
cohomology. Our result can be considered as a generalization of the
identification of the Dolbeault cohomology ring with the complexified de Rham
cohomology ring on a Kaehler manifold.Comment: 12 pages, AMS LaTe
Degenerate Chern-Weil Theory and Equivariant Cohomology
We develop a Chern-Weil theory for compact Lie group action whose generic
stabilizers are finite in the framework of equivariant cohomology. This
provides a method of changing an equivariant closed form within its
cohomological class to a form more suitable to yield localization results. This
work is motivated by our work on reproving wall crossing formulas in
Seiberg-Witten theory, where the Lie group is the circle. As applications, we
derive two localization formulas of Kalkman type for G = SU(2) or SO(3)-actions
on compact manifolds with boundary. One of the formulas is then used to yield a
very simple proof of a localization formula due to Jeffrey-Kirwan in the case
of G = SU(2) or SO(3).Comment: 23 pages, AMSLaTe
Frobenius Manifold Structure on Dolbeault Cohomology and Mirror Symmetry
We construct a differential Gerstenhaber-Batalin-Vilkovisky algebra from
Dolbeault complex of any close Kaehler manifold, and a Frobenius manifold
structure on Dolbeault cohomology.Comment: 10 pages, AMS LaTe
On quasi-isomorphic DGBV algebras
One of the methods to obtain Frobenius manifold structures is via DGBV
(differential Gerstenhaber-Batalin-Vilkovisky) algebra construction. An
important problem is how to identify Frobenius manifold structures constructed
from two different DGBV algebras. For DGBV algebras with suitable conditions,
we show the functorial property of a construction of deformations of the
multiplicative structures of their cohomology. In particular, we show that
quasi-isomorphic DGBV algebras yield identifiable Frobenius manifold
structures.Comment: 16 pages, AMS-LaTe
On Quantum de Rham Cohomology
We define quantum exterior product wedge_h and quantum exterior differential
d_h on Poisson manifolds, of which symplectic manifolds are an important class
of examples. Quantum de Rham cohomology is defined as the cohomology of d_h. We
also define quantum Dolbeault cohomology. Quantum hard Lefschetz theorem is
proved. We also define a version of quantum integral, and prove the quantum
Stokes theorem. By the trick of replacing d by d_h and wedge by wedge_h in the
usual definitions, we define many quantum analogues of important objects in
differential geometry, e.g. quantum curvature. The quantum characteristic
classes are then studied along the lines of classical Chern-Weil theory, i.e.,
they can be represented by expressions of quantum curvature. Quantum
equivariant de Rham cohomology is defined in a similar fashion. Calculations
are done for some examples, which show that quantum de Rham cohomology is
different from the quantum cohomology defined using pseudo-holomorphic curves.Comment: 36 pages, AMS LaTe
DGBV Algebras and Mirror Symmetry
We describe some recent development on the theory of formal Frobenius
manifolds via a construction from differential Gerstenhaber-Batalin-Vilkovisk
(DGBV) algebras and formulate a version of mirror symmetry conjecture: the
extended deformation problems of the complex structure and the Poisson
structure are described by two DGBV algebras; mirror symmetry is interpreted in
term of the invariance of the formal Frobenius manifold structures under
quasi-isomorphism.Comment: 11 pages, to appear in Proceedings of ICCM9
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