7,640 research outputs found
Topological modular forms and conformal nets
We describe the role conformal nets, a mathematical model for conformal field
theory, could play in a geometric definition of the generalized cohomology
theory TMF of topological modular forms. Inspired by work of Segal and
Stolz-Teichner, we speculate that bundles of boundary conditions for the net of
free fermions will be the basic underlying objects representing TMF-cohomology
classes. String structures, which are the fundamental orientations for
TMF-cohomology, can be encoded by defects between free fermions, and we
construct the bundle of fermionic boundary conditions for the TMF-Euler class
of a string vector bundle. We conjecture that the free fermion net exhibits an
algebraic periodicity corresponding to the 576-fold cohomological periodicity
of TMF; using a homotopy-theoretic invariant of invertible conformal nets, we
establish a lower bound of 24 on this periodicity of the free fermions
Conformal nets I: coordinate-free nets
We describe a coordinate-free perspective on conformal nets, as functors from
intervals to von Neumann algebras. We discuss an operation of fusion of
intervals and observe that a conformal net takes a fused interval to the fiber
product of von Neumann algebras. Though coordinate-free nets do not a priori
have vacuum sectors, we show that there is a vacuum sector canonically
associated to any circle equipped with a conformal structure. This is the first
in a series of papers constructing a 3-category of conformal nets, defects,
sectors, and intertwiners.Comment: Updated to published versio
Conformal nets II: conformal blocks
Conformal nets provide a mathematical formalism for conformal field theory.
Associated to a conformal net with finite index, we give a construction of the
`bundle of conformal blocks', a representation of the mapping class groupoid of
closed topological surfaces into the category of finite-dimensional projective
Hilbert spaces. We also construct infinite-dimensional spaces of conformal
blocks for topological surfaces with smooth boundary. We prove that the
conformal blocks satisfy a factorization formula for gluing surfaces along
circles, and an analogous formula for gluing surfaces along intervals. We use
this interval factorization property to give a new proof of the modularity of
the category of representations of a conformal net.Comment: Updated to published versio
Quasi-complete intersection homomorphisms
Extending a notion defined for surjective maps by Blanco, Majadas, and
Rodicio, we introduce and study a class of homomorphisms of commutative
noetherian rings, which strictly contains the class of locally complete
intersection homomorphisms, while sharing many of its remarkable properties.Comment: Final version, to appear in the special issue of Pure and Applied
Mathematics Quarterly dedicated to Andrey Todorov. The material in the first
four sections has been reorganized and slightly expande
Torque Ripple Minimization in a Switched Reluctance Drive by Neuro-Fuzzy Compensation
Simple power electronic drive circuit and fault tolerance of converter are
specific advantages of SRM drives, but excessive torque ripple has limited its
use to special applications. It is well known that controlling the current
shape adequately can minimize the torque ripple. This paper presents a new
method for shaping the motor currents to minimize the torque ripple, using a
neuro-fuzzy compensator. In the proposed method, a compensating signal is added
to the output of a PI controller, in a current-regulated speed control loop.
Numerical results are presented in this paper, with an analysis of the effects
of changing the form of the membership function of the neuro-fuzzy compensator.Comment: To be published in IEEE Trans. on Magnetics, 200
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