Some problems on algebraic groups over global fields like the congruence subgroup problem involve the determination of topological central extensions of the adelic group which, in turn, leads naturally to the study of topological central extensions of p-adic Lie groups by finite groups like the group of roots of unity in the p-adic field. Moreover, central extensions of semisimple p-adic Lie gr...

Abstract Low-rank matrix recovery problem is difficult due to its non-convex properties and it usually solved using convex relaxation approaches. In this paper, we formulate the low-rank exactly novel Ky Fan 2- k -norm-based models. A general difference of functions algorithm (DCA) developed solve these proximal point (PPA) framework proposed sub-problems within DCA, which allows us handle larg...

Rivcst [5] defines the notion of a decision list as a representation for Boolean functions. He shows that k-decision lists, a generalization of k-CNF and k-DNF formulas, are learnable for constant k in the PAC (or distribution-free) learning model [&,3]. Ehrenfcucht and Haussler [l] define the notion of the rank of a decision tree, and prove that decision trees of constant rank are also learnab...

It is proved that over every countable field K there is a nil algebra R such that the algebra obtained from R by extending the field K contains noncommutative free subalgebras of arbitrarily high rank. It is also shown that over every countable field K there is an algebra R without noncommutative free subalgebras of rank two such that the algebra obtained from R by extending the field K contain...

Equidistant codes over vector spaces are considered. For k-dimensional subspaces over a large vector space the largest code is always a sunflower. We present several simple constructions for such codeswhichmight produce the largest non-sunflower codes. A novel construction, based on the Plücker embedding, for 1-intersecting codes of k-dimensional subspaces over Fq , n ≥ k+1 2  , where the cod...

For a positive integer k, the rank-k numerical range Λk(A) of an operator A acting on a Hilbert space H of dimension at least k is the set of scalars λ such that PAP = λP for some rank k orthogonal projection P . In this paper, a close connection between low rank perturbation of an operator A and Λk(A) is established. In particular, for 1 ≤ r < k it is shown that Λk(A) ⊆ Λk−r(A + F ) for any op...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

The problem of estimating the k frequency moment Fk for any nonnegative k, over a data stream by looking at the items exactly once as they arrive, was considered in a seminal paper by Alon, Matias and Szegedy [1, 2]. The space complexity of their algorithm is Õ(n1− 1 k ). For k > 2, their technique does not apply to data streams with arbitrary insertions and deletions. In this paper, we present...