2,473 research outputs found
Holographic Algorithm with Matchgates Is Universal for Planar CSP Over Boolean Domain
We prove a complexity classification theorem that classifies all counting
constraint satisfaction problems (CSP) over Boolean variables into exactly
three categories: (1) Polynomial-time tractable; (2) P-hard for general
instances, but solvable in polynomial-time over planar graphs; and (3)
P-hard over planar graphs. The classification applies to all sets of local,
not necessarily symmetric, constraint functions on Boolean variables that take
complex values. It is shown that Valiant's holographic algorithm with
matchgates is a universal strategy for all problems in category (2).Comment: 94 page
Classification of 3-dimensional integrable scalar discrete equations
We classify all integrable 3-dimensional scalar discrete quasilinear
equations Q=0 on an elementary cubic cell of the 3-dimensional lattice. An
equation Q=0 is called integrable if it may be consistently imposed on all
3-dimensional elementary faces of the 4-dimensional lattice.
Under the natural requirement of invariance of the equation under the action
of the complete group of symmetries of the cube we prove that the only
nontrivial (non-linearizable) integrable equation from this class is the
well-known dBKP-system. (Version 2: A small correction in Table 1 (p.7) for n=2
has been made.) (Version 3: A few small corrections: one more reference added,
the main statement stated more explicitly.)Comment: 20 p. LaTeX + 1 EPS figur
Perturbative Analysis of Spectral Singularities and Their Optical Realizations
We develop a perturbative method of computing spectral singularities of a
Schreodinger operator defined by a general complex potential that vanishes
outside a closed interval. These can be realized as zero-width resonances in
optical gain media and correspond to a lasing effect that occurs at the
threshold gain. Their time-reversed copies yield coherent perfect absorption of
light that is also known as an antilaser. We use our general results to
establish the exactness of the n-th order perturbation theory for an arbitrary
complex potential consisting of n delta-functions, obtain an exact expression
for the transfer matrix of these potentials, and examine spectral singularities
of complex barrier potentials of arbitrary shape. In the context of optical
spectral singularities, these correspond to inhomogeneous gain media.Comment: 13 pages, 2 figures, one table, a reference added, typos correcte
Method And Device To Elongate A Solder Joint
A method and device to elongate a solder joint are provided. The method begins by forming an elongator on a first substrate. The elongator comprises an expander and an encapsulant to encapsulate the expander. A solder joint is formed to connect the first substrate to a second substrate. Thereafter, the encapsulant is softened to release the expander from a compressed state to elongate the solder joint. The device to elongate a solder joint comprises a substrate having an elongator formed on it. The elongator includes an expander in a compressed state and an encapsulant to encapsulate the expander.Agency For Science, Technology And ResearchNational Univeristy Of SingaporeGeorgia Tech Research Corporatio
Matrix Lie groups as 3-dimensional almost contact B-metric manifolds
The object of investigation are Lie groups considered as almost contact
B-metric manifolds of the lowest dimension three. It is established a
correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev
classification of the studied manifolds and the explicit matrix representation
of Lie groups. Some known Lie groups are equiped with almost contact B-metric
structure of different types
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