12,154 research outputs found
A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
We describe a new polynomial time quantum algorithm that uses the quantum
fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian
operator, and that can be applied in cases (commonly found in ab initio physics
and chemistry problems) for which all known classical algorithms require
exponential time. Applications of the algorithm to specific problems are
considered, and we find that classically intractable and interesting problems
from atomic physics may be solved with between 50 and 100 quantum bits.Comment: 10 page
Expressiveness and Robustness of First-Price Position Auctions
Since economic mechanisms are often applied to very different instances of
the same problem, it is desirable to identify mechanisms that work well in a
wide range of circumstances. We pursue this goal for a position auction setting
and specifically seek mechanisms that guarantee good outcomes under both
complete and incomplete information. A variant of the generalized first-price
mechanism with multi-dimensional bids turns out to be the only standard
mechanism able to achieve this goal, even when types are one-dimensional. The
fact that expressiveness beyond the type space is both necessary and sufficient
for this kind of robustness provides an interesting counterpoint to previous
work on position auctions that has highlighted the benefits of simplicity. From
a technical perspective our results are interesting because they establish
equilibrium existence for a multi-dimensional bid space, where standard
techniques break down. The structure of the equilibrium bids moreover provides
an intuitive explanation for why first-price payments may be able to support
equilibria in a wider range of circumstances than second-price payments
Why Underfiling by States Can and Should be Used to Enforce Environmental Regulations
“Overfiling” occurs when the federal government files an environmental enforcement action in situations where the state environmental enforcement agency has not sufficiently prosecuted a violator of a federal environmental statute. A recent case from the Tenth Circuit appears to support the idea of overfiling under the Resource Conservation and Recovery Act, and other courts have upheld overfiling actions under the Clean Water Act and the Clean Air Act. This Note argues that the practice of “underfiling,” a process in which states file environmental enforcement actions even after the federal government has already overfiled, is also supported by these federal court decisions. This Note also suggests that states may intervene under Rule 24 of the Federal Rules of Civil Procedure in federal environmental enforcement actions in order to seek additional relief from violators of environmental statutes
Commutator Leavitt path algebras
For any field K and directed graph E, we completely describe the elements of
the Leavitt path algebra L_K(E) which lie in the commutator subspace
[L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras
L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt
path algebras have the additional (unusual) property that all their Lie ideals
are (ring-theoretic) ideals, and construct examples of such rings with various
ideal structures.Comment: 24 page
Intellectual Growth For Undergraduate Students: Evaluation Results From An Undergraduate Research Conference
We describe the development and evaluation of the university-wide, weeklong undergraduate research conference at the University of New Hampshire. Despite increases nationally in the number of undergraduate research conferences (URC), there has been little research examining the social and educational impact of these events on student presenters. We describe the development and evaluation of the university-wide, weeklong URC at the University of New Hampshire. A survey administered to URC participants over a four year period revealed that research culminating in a presentation at the URC was one of the more influential events students experienced during their undergraduate years and students realized a high level of satisfaction from presenting at the URC
Quantum interferometric optical lithography:towards arbitrary two-dimensional patterns
As demonstrated by Boto et al. [Phys. Rev. Lett. 85, 2733 (2000)], quantum
lithography offers an increase in resolution below the diffraction limit. Here,
we generalize this procedure in order to create patterns in one and two
dimensions. This renders quantum lithography a potentially useful tool in
nanotechnology.Comment: 9 pages, 5 figures Revte
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