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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...
Linear Bandits in High Dimension and Recommendation Systems
Services automation browsing space
2015/8/21
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 ...
High-Dimensional Centrally-Symmetric Polytopes With Neighborliness Proportional to Dimension
Centrosymmetric Polytopes Neighborly Polytopes
2015/8/21
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
Variational problems linear growth dimension 1
2015/4/3
Variational problems with linear growth in dimension 1.
Commmuting exponentials in dimension at most 3
Matrix exponential Property L Rings and Algebras
2011/9/2
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...
On the representation dimension of artin algebras
dimension of artin algebras Representation Theory
2011/8/31
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...
Effective dimension of finite semigroups
dimension of finite semigroups Group Theory Representation Theory
2011/8/29
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...
On a Conjecture on the weak global dimension of Gaussian rings
Gaussian rings weak dimension content non-noetherian rings
2011/8/24
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...
Essential dimension of simple algebras in positive characteristic
Essential dimension simple algebras positive characteristic
2011/2/24
Let p be a prime integer, 1 ≤ s ≤ r integers, F a field of characteristic p.
On the essential dimension of unipotent algebraic groups
essential dimension unipotent algebraic groups
2011/1/21
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...
Fractional Harmonic Maps into Manifolds in odd dimension n>1
Harmonic maps nonlinear elliptic PDE’s regularity of solutions
2011/1/21
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...
Equivalent Semigroup Properties for Curvature-Dimension Condition
Curvature-dimension condition gradient inequality Harnack inequality
2011/2/28
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...
Numerical Resolution near t = 0 of NonlinearEvolution Equations in the Presence of Corner Singularities in Space Dimension 1
Numerical Resolution Nonlinear Evolution Equations
2010/11/23
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...