14,765 research outputs found
Traces in monoidal categories
The main result of this paper is the construction of a trace and a trace
pairing for endomorphisms satisfying suitable conditions in a monoidal
category. This construction is a common generalization of the trace for
endomorphisms of dualizable ob jects in a balanced monoidal category and the
trace of nuclear operators on a locally convex topological vector space with
the approximation property
Relativistic wave and Green's functions for hydrogen--like ions
The \textsc{Greens} library is presented which provides a set of C++
procedures for the computation of the (radial) Coulomb wave and Green's
functions. Both, the nonrelativistic as well as relativistic representations of
these functions are supported by the library. However, while the wave functions
are implemented for all, the bound and free--electron states, the Green's
functions are provided only for bound--state energies ). Apart from the
Coulomb functions, moreover, the implementation of several special functions,
such as the Kummer and Whittaker functions of the first and second kind, as
well as a few utility procedures may help the user with the set--up and
evaluation of matrix elements.Comment: 21 page
Is the minimum value of an option on variance generated by local volatility?
We discuss the possibility of obtaining model-free bounds on volatility
derivatives, given present market data in the form of a calibrated local
volatility model. A counter-example to a wide-spread conjecture is given
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