This paper discusses a relationship between the prime factorizability of a normal full rank n-D (n > 2) polynomial matrix and its reduced minors. Two conjectures regarding the n-D polynomial matrix prime factorization problem are posed, and a partial solution to one of the conjectures is provided. Another related open problem of factorizing an n-D polynomial matrix that is not of normal full ra...

In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fold cover of the sporadic simple group of Rudvalis. In this article we construct a second enhanced vertex operator superalgebra whose full automorphism group is a cyclic cover of the Rudvalis group. This new example is...

Abstract. There is a well-known asymptotic formula, due to W. M. Schmidt (1968) for the number of full-rank integer lattices of index at most V in Z. This set of lattices L can naturally be partitioned with respect to the factor group Z/L. Accordingly, we count the number of full-rank integer lattices L ⊆ Z such that Z/L is cyclic and of order at most V , and deduce that these co-cyclic lattice...

For multiuser systems, several direct blind identification algorithms require that the linear multiple-input multiple-output (MIMO) system have a full rank convolution matrix. This condition requires that the system transfer function be irreducible and column reduced. We show that this restrictive identification condition can be relaxed for some direct blind identification methods to accommodat...

We first develop a reduced-rank minimum mean square error (MMSE) detector for direct-sequence (DS) code division multiple access (CDMA) by forcing the linear MMSE detector to lie in a signal subspace of a reduced dimension. While a reduced-rank MMSE detector has lower complexity, it cannot outperform the full-rank MMSE detector. We then concentrate on the blind reduced-rank MMSE detector which ...

We show that almost surely the rank of the adjacency matrix of the Erdös-Rényi random graph G(n, p) equals the number of non-isolated vertices for any c lnn/n < p < 1/2, where c is an arbitrary positive constant larger than 1/2. In particular the giant component (a.s.) has full rank in this range.

Let $n \in \mathbb{Z}^{+}$ and $X_{n}=\{1,2,\ldots,n\}$ be a finite set. $\mathcal ODCT_{n}$ the order-preserving order-decreasing full contraction mappings on $X_{n}$. It is well known that monoid. In this paper, we have found monoid rank presentation of ODCT_{n}$. particular, proved $n-1$ for $$ \geq 3$.

| Low rank estimators for higher order statistics are considered in this paper. Rank reduction methods ooer a general principle for trading estimator bias for reduced estimator variance. The bias-variance tradeoo is analyzed for low rank estimators of higher order statistics using a tensor product formulation for the moments and cumulants. In general the low rank estimators have a larger bias a...

The following two results are proven: The full automorphism group of any non-projective hyperkähler manifold M is almost abelian of rank at most maximum of ρ(M) − 1 and 1. Any groups of automorphisms of nullentropy of a projective hyperkähler manifold M is almost abelian of rank at most ρ(M) − 2. A few applications for K3 surfaces are also given.

We discuss computational procedures based on descriptor state-space realizations to compute proper range space bases of rational matrices. The main computation is the orthogonal reduction of the system matrix pencil to a special Kronecker-like form, which allows to extract a full column rank factor, whose columns form a proper rational basis of the range space. The computation of several types ...