7,234 research outputs found
Recursion relations for generalized Fresnel coefficients: Casimir force in a planar cavity
We emphasize and demonstrate that, besides using the usual recursion
relations involving successive layers, generalized Fresnel coefficients of a
multilayer can equivalently be calculated using the recursion relations
involving stacks of layers, as introduced some time ago [M. S. Tomas, Phys.
Rev. A 51, 2545 (1995)]. Moreover, since the definition of the generalized
Fresnel coefficients employed does not imply properties of the stacks, these
nonstandard recursion relations can be used to calculate Fresnel coefficients
not only for local systems but also for a general multilayer consisting of
various types (local, nonlocal, inhomogeneous etc.) of layers. Their utility is
illustrated by deriving a few simple algorithms for calculating the
reflectivity of a Bragg mirror and extending the formula for the Casimir force
in a planar cavity to arbitrary media.Comment: 5 pages, 2 figures, slightly expande
NONDETERMINACY AND RECURSION VIA STACKS AND GAMES
The weakest-precondition interpretation of recursive procedures is developed for a language with a combination of unbounded demonic choice and unbounded angelic choice. This compositional formal semantics is proved to be equal to a game-theoretic operational semantics. Two intermediate stages are exploited. One step consists of unfolding the declaration of the recursive procedures. Fixpoint induction is used to prove the validity of this step. The compositional semantics of the unfolded declaration is proved to be equal to a formal semantics of a stack implementation of the recursive procedures. After an introduction to boolean two-person games, this stack semantics is shown to correspond to a game-theoretic operational semantics
Solving Mahjong Solitaire boards with peeking
We first prove that solving Mahjong Solitaire boards with peeking is
NP-complete, even if one only allows isolated stacks of the forms /aab/ and
/abb/. We subsequently show that layouts of isolated stacks of heights one and
two can always be solved with peeking, and that doing so is in P, as well as
finding an optimal algorithm for such layouts without peeking.
Next, we describe a practical algorithm for solving Mahjong Solitaire boards
with peeking, which is simple and fast. The algorithm uses an effective pruning
criterion and a heuristic to find and prioritize critical groups. The ideas of
the algorithm can also be applied to solving Shisen-Sho with peeking.Comment: 10 page
A Mirror Theorem for Toric Stacks
We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X.
This determines the genus-zero Gromov--Witten invariants of X in terms of an
explicit hypergeometric function, called the I-function, that takes values in
the Chen--Ruan orbifold cohomology of X.Comment: 35 pages. v2: key references added. v3: errors corrected; formal
setup changed; proofs simplified, clarified, and shortened; references added.
v4: references updated. v5: references update
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