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Gauge theory in dimension $7$
calibrations elliptic boundary problems on manifolds G2–manifolds
2010/12/31
We first review the notion of a G2–manifold, defined in terms of a principal G2 (“gauge”)
bundle over a 7–dimensional manifold, before discussing their relation to supergravity. In a
second thread, ...
On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields
The Characteristic Polynomial Frobenius Supersingular Abelian
2010/11/1
In this article, we derive the list of the characteristic polynomials of the Frobenius endomorphism of simple supersingular abelian varieties of dimension $1,~2,~3,~4,~5,~6,~7$ over $\mathbb{F}_q$ whe...
Deciding the dimension of effective dimension reduction space for functional and high-dimensional data
effective dimension reduction space high-dimensional data
2010/11/1
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The ...
In this paper we prove the lying over and going down theorems for modules. Finally, we apply the above theorems and prove some results on the dimension of a module and its submodule.
We investigate the relations between a radical submodule N of a module M being a finite intersection of prime submodules of M and the factor module M/N having finite uniform dimension. It is proved th...
New Solutions of the Einstein-Dirac Equation in Dimension n=3
Solutions the Einstein-Dirac Equation Dimension n=3
2000/1/31
The aim of this short note is to announce the existence of a one-parameter family of left-invariant metrics on $S^3$ admitting WK-spinors. This family contains the two non-Einstein Sasakian metrics w...