1,354 research outputs found
Topological noetherianity for cubic polynomials
Let be the space of complex cubic polynomials in
infinitely many variables. We show that this space is
-noetherian, meaning that any
-stable Zariski closed subset is cut out by finitely many
orbits of equations. Our method relies on a careful analysis of an invariant of
cubics introduced here called q-rank. This result is motivated by recent work
in representation stability, especially the theory of twisted commutative
algebras. It is also connected to certain stability problems in commutative
algebra, such as Stillman's conjecture.Comment: 13 page
Das Gottesdienstverständnis der russlanddeutschen Freikirchen im Kontext einer Migrationskultur in Deutschland
Ganzevoort, R.R. [Promotor]Visser, P. [Promotor
Linear equations over multiplicative groups, recurrences, and mixing I
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135647/1/plms1045.pd
Cluster algebras of type
In this paper we study cluster algebras \myAA of type . We solve
the recurrence relations among the cluster variables (which form a T--system of
type ). We solve the recurrence relations among the coefficients of
\myAA (which form a Y--system of type ). In \myAA there is a
natural notion of positivity. We find linear bases \BB of \myAA such that
positive linear combinations of elements of \BB coincide with the cone of
positive elements. We call these bases \emph{atomic bases} of \myAA. These
are the analogue of the "canonical bases" found by Sherman and Zelevinsky in
type . Every atomic basis consists of cluster monomials together
with extra elements. We provide explicit expressions for the elements of such
bases in every cluster. We prove that the elements of \BB are parameterized
by \ZZ^3 via their --vectors in every cluster. We prove that the
denominator vector map in every acyclic seed of \myAA restricts to a
bijection between \BB and \ZZ^3. In particular this gives an explicit
algorithm to determine the "virtual" canonical decomposition of every element
of the root lattice of type . We find explicit recurrence relations
to express every element of \myAA as linear combinations of elements of
\BB.Comment: Latex, 40 pages; Published online in Algebras and Representation
Theory, springer, 201
Quantum finite automata and linear context-free languages: a decidable problem
We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable whether or not they have a nonempty intersection. This extends a result of Blondel et al. which can be interpreted as solving the problem with the free monoid in place of the family of linear context-free languages. Š 2013 Springer-Verlag
Effects of tillage systems and crop rotations on soil water conservation, seedling establishment and crop production of a thin Black soil at Indian Head
Non-Peer ReviewedThe long term sustainability of agriculture for much of western Canada is dependent on the development of economically viable crop production systems that alleviate wind and water erosion. The systems required must be capable of making full use of the benefits of surface residues and standing stubble. A study was initiated in 1986 at Indian Head to examine the interactions of tillage systems and crop rotations on soil water conservation, soil characteristics, seedling establishment, crop production, plant diseases, weed populations, and production economics. Three four year rotations were then superimposed on the three tillage systems. Spring soil water under stubble conditions was significantly greater for the zero and minimum tillage than conventional tillage system for the 0-60 and 0-120 cm soil layer. Under fallow conditions, soil water conserved was similar for all three tillage systems. Seedling establishment, as measured by the number of plants emerged per meter square was similar for all crops and tillage
systems. Plant development in spring wheat, as measured by Haun stage was not affected by tillage system. This implies that the perceived differences in soil temperature at seeding depth between the various tillage systems did not significantly delay plant emergence under zero and minimum tillage. Tillage system had a significant effect on grain production. Zero and minimum tillage out-yielded conventional tillage by 22 % for flax, 20 % for spring wheat on stubble and 8 % for field peas. There was no difference between tillage systems for winter wheat
On the generalized Davenport constant and the Noether number
Known results on the generalized Davenport constant related to zero-sum
sequences over a finite abelian group are extended to the generalized Noether
number related to the rings of polynomial invariants of an arbitrary finite
group. An improved general upper bound is given on the degrees of polynomial
invariants of a non-cyclic finite group which cut out the zero vector.Comment: 14 page
Invariants and separating morphisms for algebraic group actions
The first part of this paper is a refinement of Winkelmannâs work on invariant rings and quotients of algebraic group actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient X//G given by the possibly not finitely generated ring of invariants is âalmostâ an algebraic variety, and that the quotient morphism Ď: X â X//G has a number of nice properties. One of the main difficulties comes from the fact that the quotient morphism is not necessarily surjective. These general results are then refined for actions of the additive group Ga, where we can say much more. We get a rather explicit description of the so-called plinth variety and of the separating variety, which measures how much orbits are separated by invariants. The most complete results are obtained for representations. We also give a complete and detailed analysis of Robertsâ famous example of a an action of Ga on 7-dimensional affine space with a non-finitely generated ring of invariants
Semi-invariants of symmetric quivers of finite type
Let be a symmetric quiver, where is a finite
quiver without oriented cycles and is a contravariant involution on
. The involution allows us to define a nondegenerate bilinear
form on a representation $V$ of $Q$. We shall call the representation
orthogonal if is symmetric and symplectic if is skew-symmetric.
Moreover we can define an action of products of classical groups on the space
of orthogonal representations and on the space of symplectic representations.
For symmetric quivers of finite type, we prove that the rings of
semi-invariants for this action are spanned by the semi-invariants of
determinantal type and, in the case when matrix defining is
skew-symmetric, by the Pfaffians
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