5,241 research outputs found
Increasing stability for the inverse problem for the Schr\"odinger equation
In this article, we study the increasing stability property for the
determination of the potential in the Schr\"odinger equation from partial data.
We shall assume that the inaccessible part of the boundary is flat and
homogeneous boundary condition is prescribed on this part. In contrast to
earlier works, we are able to deal with the case when potentials have some
Sobolev regularity and also need not be compactly supported inside the domain
Towards a quantum-mechanical model for multispecies exclusion statistics
It is shown how to construct many-particle quantum-mechanical spectra of
particles obeying multispecies exclusion statistics, both in one and in two
dimensions. These spectra are derived from the generalized exclusion principle
and yield the same thermodynamic quantities as deduced from Haldane's
multiplicity formula.Comment: 12 pages, REVTE
Recovery of time dependent volatility coefficient by linearization
We study the problem of reconstruction of special special time dependent
local volatility from market prices of options with different strikes at two
expiration times. For a general diffusion process we apply the linearization
technique and we conclude that the option price can be obtained as the sum of
the Black-Scholes formula and of an operator which is linear in
perturbation of volatility. We further simplify the linearized inverse problem
and obtain unique solvability result in basic functional spaces. By using the
Laplace transform in time we simplify the kernels of integral operators for
and we obtain uniqueness and stability results for for volatility under natural
condition of smallness of the spacial interval where one prescribes the
(market) data. We propose a numerical algorithm based on our analysis of the
linearized problem
Trustee Fundraising Dialogue
Summary of a 2009 BC Library Conference session dedicated to exploring what BC public libraries are doing to fundraise, and how library trustees are helping
Quantum liquids of particles with generalized statistics
We propose a phenomenological approach to quantum liquids of particles
obeying generalized statistics of a fermionic type, in the spirit of the Landau
Fermi liquid theory. The approach is developed for fractional exclusion
statistics. We discuss both equilibrium (specific heat, compressibility, and
Pauli spin susceptibility) and nonequilibrium (current and thermal
conductivities, thermopower) properties. Low temperature quantities have the
same temperature dependences as for the Fermi liquid, with the coefficients
depending on the statistics parameter. The novel quantum liquids provide
explicit realization of systems with a non-Fermi liquid Lorentz ratio in two
and more dimensions. Consistency of the theory is verified by deriving the
compressibility and -sum rules.Comment: 14 pages, Revtex, no figures; typos correcte
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