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Essential dimension is a numerical invariant of an algebraic group G introduced by J. Buhler and the second author to study the complexity of G-torsors over a eld K. It has since been studied by se...
A large number of online services provide automated recommendations to help users to navigate through a large collection of items. New items (products, videos, songs, advertisements) are suggested on ...
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in R n . It has recently been shown that properties of the centrosymmetric polytope P = AC are of interest for ...
Variational problems with linear growth in dimension 1.
Abstract: Let A,B be two square complex matrices of dimension at most 3. We show that the following conditions are equivalent i) There exists a finite subset U included in {2,3,4,...} such that for ev...
Abstract: The representation dimension of an artin algebra as introduced by M.Auslander in his Queen Mary Notes is the minimal possible global dimension of the endomorphism ring of a generator-cogener...
Abstract: In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general...
Abstract: Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is 0,1 or \infty. In this paper, we prove their conjecture in all cases except when R is a non-reduced local Gau...
Let p be a prime integer, 1s ≤ r integers, F a field of characteristic p.
We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field k which is finitely generated over a perfect field, a s...
In this paper we consider critical points of the following nonlocal energy Ln(u) = Z IRn |(−)n/4u(x)|2dx , (1) where u: Hn/2(IRn) → N N ⊂ IRm is a compact k dimensional smooth manifold w...
Some equivalent gradient and Harnack inequalities of a diffusion semigroup are presented for the curvature-dimension condition of the associated generator. As ap-plications, the first eigenvalue, the ...
We classify 4-dimensional austere submanifolds in Euclidean space ruled by 2-planes. The algebraic possibilities for second fundamental forms of an austere 4-fold M were classified by Bryant, falling...
We consider the graph together with the arbitrary partition of its vertex set into n subsets (n-partitioned graph). On the set of $n$-partitioned graphs distinguished up to isomorphism we define the b...
The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the...

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