91,438 research outputs found
Least Generalizations and Greatest Specializations of Sets of Clauses
The main operations in Inductive Logic Programming (ILP) are generalization
and specialization, which only make sense in a generality order. In ILP, the
three most important generality orders are subsumption, implication and
implication relative to background knowledge. The two languages used most often
are languages of clauses and languages of only Horn clauses. This gives a total
of six different ordered languages. In this paper, we give a systematic
treatment of the existence or non-existence of least generalizations and
greatest specializations of finite sets of clauses in each of these six ordered
sets. We survey results already obtained by others and also contribute some
answers of our own. Our main new results are, firstly, the existence of a
computable least generalization under implication of every finite set of
clauses containing at least one non-tautologous function-free clause (among
other, not necessarily function-free clauses). Secondly, we show that such a
least generalization need not exist under relative implication, not even if
both the set that is to be generalized and the background knowledge are
function-free. Thirdly, we give a complete discussion of existence and
non-existence of greatest specializations in each of the six ordered languages.Comment: See http://www.jair.org/ for any accompanying file
A design study for an optimal non-linear receiver/demodulator Final report
Design study for optimal nonlinear receiver demodulato
Haar expectations of ratios of random characteristic polynomials
We compute Haar ensemble averages of ratios of random characteristic
polynomials for the classical Lie groups K = O(N), SO(N), and USp(N). To that
end, we start from the Clifford-Weyl algebera in its canonical realization on
the complex of holomorphic differential forms for a C-vector space V. From it
we construct the Fock representation of an orthosymplectic Lie superalgebra osp
associated to V. Particular attention is paid to defining Howe's oscillator
semigroup and the representation that partially exponentiates the Lie algebra
representation of sp in osp. In the process, by pushing the semigroup
representation to its boundary and arguing by continuity, we provide a
construction of the Shale-Weil-Segal representation of the metaplectic group.
To deal with a product of n ratios of characteristic polynomials, we let V =
C^n \otimes C^N where C^N is equipped with its standard K-representation, and
focus on the subspace of K-equivariant forms. By Howe duality, this is a
highest-weight irreducible representation of the centralizer g of Lie(K) in
osp. We identify the K-Haar expectation of n ratios with the character of this
g-representation, which we show to be uniquely determined by analyticity, Weyl
group invariance, certain weight constraints and a system of differential
equations coming from the Laplace-Casimir invariants of g. We find an explicit
solution to the problem posed by all these conditions. In this way we prove
that the said Haar expectations are expressed by a Weyl-type character formula
for all integers N \ge 1. This completes earlier work by Conrey, Farmer, and
Zirnbauer for the case of U(N).Comment: LaTeX, 70 pages, Complex Analysis and its Synergies (2016) 2:
Perfluoro (Imidoylamidine) diamidines
Perfluoroether triazine elastomers having improved properties are prepared from oligomeric imidoylamidines that were in turn, prepared by the process of: (1) reacting a perfluorodinitrile with liquid ammonia to yield a perfluorodiamidine, (2) isolating the perfluorodiamidine, (3) reacting the isolated diamidine with a perfluorodinitrile to yield a perfluoro(imidoylamidine) dinitrile, and then repeating the steps to sequentially grow an oligomer of desired molecular size. The isolated amidine and nitrile intermediates are also disclosed. The elastomers can be fashioned into seals, gaskets, and sealing components and the like
Process for preparing perfluorotriazine elastomers and precursors thereof
Perfluoroether triazine elastomers having improved properties and utility in seals, gaskets, sealing components and the like are prepared from oligomeric imidoylamidines that have, in turn, been prepared by the process of (1) reacting a perfluorodinitrile with liquid ammonia to yield a perfluorodiamidine, (2) isolating the perfluorodiamidine, (3) reacting the isolated diamidine with a perfluorodinitrile to yield a perfluoror(imidoylamidine) dinitrile, and then repeating step (1), (2), and (3) to sequentially grow an oligomer of desired molecular size. The isolated amidine and nitrile intermediates are also described
Intruders in the Dust: Air-Driven Granular Size Separation
Using MRI and high-speed video we investigate the motion of a large intruder
particle inside a vertically shaken bed of smaller particles. We find a
pronounced, non-monotonic density dependence, with both light and heavy
intruders moving faster than those whose density is approximately that of the
granular bed. For light intruders, we furthermore observe either rising or
sinking behavior, depending on intruder starting height, boundary condition and
interstitial gas pressure. We map out the phase boundary delineating the rising
and sinking regimes. A simple model can account for much of the observed
behavior and show how the two regimes are connected by considering pressure
gradients across the granular bed during a shaking cycle.Comment: 5 pages, 4 figure
Formation and kinetics of transient metastable states in mixtures under coupled phase ordering and chemical demixing
We present theory and simulation of simultaneous chemical demixing and phase
ordering in a polymer-liquid crystal mixture in conditions where isotropic-
isotropic phase separation is metastable with respect to isotropic-nematic
phase transition. It is found that mesophase formation proceeds by a transient
metastable phase that surround the ordered phase, and whose lifetime is a
function of the ratio of diffusional to orientational mobilities. It is shown
that kinetic phase ordering in polymer-mesogen mixtures is analogous to kinetic
crystallization in polymer solutions.Comment: 17 pages, 5 figures accepted for publication in EP
The classification of traveling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion
Under the traveling wave transformation, Camassa-Holm equation with
dispersion is reduced to an integrable ODE whose general solution can be
obtained using the trick of one-parameter group. Furthermore combining complete
discrimination system for polynomial, the classifications of all single
traveling wave solutions to the Camassa-Holm equation with dispersion is
obtained. In particular, an affine subspace structure in the set of the
solutions of the reduced ODE is obtained. More general, an implicit linear
structure in Camassa-Holm equation with dispersion is found. According to the
linear structure, we obtain the superposition of multi-solutions to
Camassa-Holm equation with dispersion
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