3,902 research outputs found
Proper Mergings of Stars and Chains are Counted by Sums of Antidiagonals in Certain Convolution Arrays -- The Details
A proper merging of two disjoint quasi-ordered sets and is a
quasi-order on the union of and such that the restriction to or
yields the original quasi-order again and such that no elements of and
are identified. In this article, we determine the number of proper mergings in
the case where is a star (i.e. an antichain with a smallest element
adjoined), and is a chain. We show that the lattice of proper mergings of
an -antichain and an -chain, previously investigated by the author, is a
quotient lattice of the lattice of proper mergings of an -star and an
-chain, and we determine the number of proper mergings of an -star and an
-chain by counting the number of congruence classes and by determining their
cardinalities. Additionally, we compute the number of Galois connections
between certain modified Boolean lattices and chains.Comment: 27 pages, 7 figures, 1 table. Jonathan Farley has solved Problem
4.18; added Section 4.4 to describe his solutio
Power operations in orbifold Tate K-theory
We formulate the axioms of an orbifold theory with power operations. We
define orbifold Tate K-theory, by adjusting Devoto's definition of the
equivariant theory, and proceed to construct its power operations. We calculate
the resulting symmetric powers, exterior powers and Hecke operators and put our
work into context with orbifold loop spaces, level structures on the Tate curve
and generalized Moonshine.Comment: This paper formulates part of the material of math/0701565 (Stringy
power operations in Tate K-theory) for general orbifolds, and discusses some
additional topic
Orbifold genera, product formulas and power operations
We generalize the definition of orbifold elliptic genus, and introduce
orbifold genera of chromatic level h, using h-tuples rather than pairs of
commuting elements. We show that our genera are in fact orbifold invariants,
and we prove integrality results for them. If the genus arises from an
H-infinity-map into the Morava-Lubin-Tate theory E_h, then we give a formula
expressing the orbifold genus of the symmetric powers of a stably almost
complex manifold M in terms of the genus of M itself. Our formula is the
p-typical analogue of the Dijkgraaf-Moore-Verlinde-Verlinde formula for the
orbifold elliptic genus. It depends only on h and not on the genus.Comment: 36 pages, PhD thesis, revised versio
Towards Collaborative Conceptual Exploration
In domains with high knowledge distribution a natural objective is to create
principle foundations for collaborative interactive learning environments. We
present a first mathematical characterization of a collaborative learning
group, a consortium, based on closure systems of attribute sets and the
well-known attribute exploration algorithm from formal concept analysis. To
this end, we introduce (weak) local experts for subdomains of a given knowledge
domain. These entities are able to refute and potentially accept a given
(implicational) query for some closure system that is a restriction of the
whole domain. On this we build up a consortial expert and show first insights
about the ability of such an expert to answer queries. Furthermore, we depict
techniques on how to cope with falsely accepted implications and on combining
counterexamples. Using notions from combinatorial design theory we further
expand those insights as far as providing first results on the decidability
problem if a given consortium is able to explore some target domain.
Applications in conceptual knowledge acquisition as well as in collaborative
interactive ontology learning are at hand.Comment: 15 pages, 2 figure
Representation and character theory in 2-categories
We define the character of a group representation in a 2-category C. For
linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory
defined on pairs of commuting elements of the group. We discuss some examples
and prove a formula for the character of the induced representation.Comment: 34 pages, revised version, to appear in Advances in Mathematic
Veterinary treatment in organic husbandry
The organic farming regulations put emphasis on the preservation of animal health by prophylaxis in the agriculture. The No 5 of the regulation EC 1804/99 (EC organic regulation) Appendix I B defines the veterinary treatments in organic animal husbandry. The veterinarian can use any medicine, which is effective for the indication and the animal species. If possible, effective homeopathics, phytotherapeutics or the like should have priority.
Problems of implementing the EC organic regulation into the daily farm practice arise mostly from the doubling of the withdrawal period and the restriction of the numbers of treatments. The strict ban on prophylactic treatments is not mentioned any longer in the new regulation 834/2007, which shall apply as from 1st January 2009.
Clarification of the guidelines for animal treatments in organic farming seems to be useful for farmers, veterinarians and boards of control
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