Search results for "Variant"
showing 10 items of 1267 documents
A knot without tritangent planes
1991
We show, with computations aided by a computer, that the (3,2)-curve on some standard torus (which topologically is the trefoil knot) has no tritangent planes, thus answering in the negative a conjecture of M. H. Freedman.
On closures of discrete sets
2018
The depth of a topological space $X$ ($g(X)$) is defined as the supremum of the cardinalities of closures of discrete subsets of $X$. Solving a problem of Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the supremum of the cardinalities of the free sequences in $X$.
Topological lower bounds on the distance between area preserving diffeomorphisms
2000
Area preserving diffeomorphisms of the 2-disk which are Identity near the boundary form a group which can be equipped, using theL2-norm on its Lie algebra, with a right invariant metric. In this paper we give a lower bound on the distance between diffeomorphisms which is invariant under area preserving changes of coordinates and which improves the lower bound induced by the Calabi invariant. In the case of renormalizable and infinitely renormalizable maps, our estimate can be improved and computed.
Central polynomials and matrix invariants
1996
LetK be a field, charK=0 andM n (K) the algebra ofn×n matrices overK. If λ=(λ1,…,λ m ) andμ=(μ 1,…,μ m ) are partitions ofn 2 let $$\begin{gathered} F^{\lambda ,\mu } = \sum\limits_{\sigma ,\tau \in S_n 2} {\left( {\operatorname{sgn} \sigma \tau } \right)x_\sigma (1) \cdot \cdot \cdot x_\sigma (\lambda _1 )^{y_\tau } (1)^{ \cdot \cdot \cdot } y_\tau (\mu _1 )^{x\sigma } (\lambda _1 + 1)} \hfill \\ \cdot \cdot \cdot x_\sigma (\lambda _1 + \lambda _2 )^{y_\tau } (\mu _1 ^{ + 1} )^{ \cdot \cdot \cdot y_\tau } (\mu _1 + \mu _2 ) \hfill \\ \cdot \cdot \cdot x_\sigma (\lambda _1 + \cdot \cdot \cdot + \lambda _{\mu - 1} ^{ + 1} ) \hfill \\ \cdot \cdot \cdot x_\sigma (n^2 )^{y_\tau } (\mu _1 ^{ + \…
On the exponential growth of graded Capelli polynomials
2013
In a free superalgebra over a field of characteristic zero we consider the graded Capelli polynomials Cap M+1[Y,X] and Cap L+1[Z,X] alternating on M+1 even variables and L+1 odd variables, respectively. Here we compute the superexponent of the variety of superalgebras determinated by Cap M+1[Y,X] and Cap L+1[Z,X]. An essential tool in our computation is the generalized-six-square theorem proved in [3].
On the Efficiency of Affine Invariant Multivariate Rank Tests
1998
AbstractIn this paper the asymptotic Pitman efficiencies of the affine invariant multivariate analogues of the rank tests based on the generalized median of Oja are considered. Formulae for asymptotic relative efficiencies are found and, under multivariate normal and multivariatetdistributions, relative efficiencies with respect to Hotelling'sT2test are calculated.
The exact bounds for the degree of commutativity of a p-group of maximal class, I
2002
Abstract The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant of these groups is the ‘degree of commutativity.’ Recently (1995) Fernandez-Alcober proved a best possible inequality for the degree of commutativity in terms of the order of the group. Recent computations for primes up to 43 show that sharper results can be obtained when an additional invariant is considered. A series of conjectures about this for all primes have been recorded in [A. Vera-Lopez et al., preprint]. In this paper, we prove two of these conjectures.
Approximated overlap error for the evaluation of feature descriptors on 3D scenes
2013
This paper presents a new framework to evaluate feature descriptors on 3D datasets. The proposed method employs the approximated overlap error in order to conform with the reference planar evaluation case of the Oxford dataset based on the overlap error. The method takes into account not only the keypoint centre but also the feature shape and it does not require complex data setups, depth maps or an accurate camera calibration. Only a ground-truth fundamental matrix should be computed, so that the dataset can be freely extended by adding further images. The proposed approach is robust to false positives occurring in the evaluation process, which do not introduce any relevant changes in the …
Homology of pseudodifferential operators on manifolds with fibered cusps
2003
The Hochschild homology of the algebra of pseudodifferential operators on a manifold with fibered cusps, introduced by Mazzeo and Melrose, is studied and computed using the approach of Brylinski and Getzler. One of the main technical tools is a new convergence criterion for tri-filtered half-plane spectral sequences. Using trace-like functionals that generate the 0 0 -dimensional Hochschild cohomology groups, the index of a fully elliptic fibered cusp operator is expressed as the sum of a local contribution of Atiyah-Singer type and a global term on the boundary. We announce a result relating this boundary term to the adiabatic limit of the eta invariant in a particular case.
A modeling study suggesting how a reduction in the context-dependent input on CA1 pyramidal neurons could generate schizophrenic behavior.
2011
The neural mechanisms underlying schizophrenic behavior are unknown and very difficult to investigate experimentally, although a few experimental and modeling studies suggested possible causes for some of the typical psychotic symptoms related to this disease. The brain region most involved in these processes seems to be the hippocampus, because of its critical role in establishing memories for objects or events in the context in which they occur. In particular, a hypofunction of the N-methyl-D-aspartate (NMDA) component of the synaptic input on the distal dendrites of CA1 pyramidal neurons has been suggested to play an important role for the emergence of schizophrenic behavior. Modeling st…