1,268 research outputs found
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Performance-Based Pay for Teachers
CRS ReportCRSTeachersPerformancePay01.pdf: 10899 downloads, before Oct. 1, 2020
Generalized Legendre transformations and symmetries of the WDVV equations
The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would
expect from an integrable system, has many symmetries, both continuous and
discrete. One class - the so-called Legendre transformations - were introduced
by Dubrovin. They are a discrete set of symmetries between the stronger concept
of a Frobenius manifold, and are generated by certain flat vector fields. In
this paper this construction is generalized to the case where the vector field
(called here the Legendre field) is non-flat but satisfies a certain set of
defining equations. One application of this more general theory is to generate
the induced symmetry between almost-dual Frobenius manifolds whose underlying
Frobenius manifolds are related by a Legendre transformation. This also
provides a map between rational and trigonometric solutions of the WDVV
equations.Comment: 23 page
Entanglement requirements for implementing bipartite unitary operations
We prove, using a new method based on map-state duality, lower bounds on
entanglement resources needed to deterministically implement a bipartite
unitary using separable (SEP) operations, which include LOCC (local operations
and classical communication) as a particular case. It is known that the Schmidt
rank of an entangled pure state resource cannot be less than the Schmidt rank
of the unitary. We prove that if these ranks are equal the resource must be
uniformly (maximally) entangled: equal nonzero Schmidt coefficients. Higher
rank resources can have less entanglement: we have found numerical examples of
Schmidt rank 2 unitaries which can be deterministically implemented, by either
SEP or LOCC, using an entangled resource of two qutrits with less than one ebit
of entanglement.Comment: 7 pages Revte
Detection of the gravitomagnetic clock effect
The essence of the gravitomagnetic clock effect is properly defined showing
that its origin is in the topology of world lines with closed space
projections. It is shown that, in weak field approximation and for a
spherically symmetric central body, the loss of synchrony between two clocks
counter-rotating along a circular geodesic is proportional to the angular
momentum of the source of the gravitational field. Numerical estimates are
presented for objects within the solar system. The less unfavorable situation
is found around Jupiter.Comment: 14 pages; Latex. To be published on Classical and Quantum Gravit
Incentives to Encourage Landowners’ Management for New England Cottontail Rabbit Habitat in New York’s Eastern Hudson Valley
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Class Size Reduction Program: Background and Status
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