When a covariance matrix with a Toeplitz structure is written as the sum of a singular one and a positive scalar multiple of the identity, the singular summand corresponds to the covariance of a purely deterministic component of a time-series whereas the identity corresponds to white noise—this is the Carathéodory-Fejér-Pisarenko (CFP) decomposition. In the present paper we study multivariable ...

Controlled K-theory is used to show that algebraic K-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized by the rational projective space of the group.

B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-alg...

The function bk(n) is defined as the number of partitions of n that contain no summand divisible by k. In this paper we study the 2-divisibility of b5(n) and the 2and 3-divisibility of b13(n). In particular, we give exact criteria for the parity of b5(2n) and b13(2n).

We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer satisfying 1 ≤ i ≤ (dim q)/2). If the degree of each closed point on Q is divisible by 2 and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-i...

Abstract Let R be a ring and let M an -module with $$S={\text {End}}_R(M)$$ S = End R ( M ) . The module is called quasi-dual Baer if for every fully invari...

This paper discusses the problem of whether it is possible to annihilate elements of local cohomology modules by elements of arbitrarily small order under a fixed valuation. We first discuss the general problem and its relationship to the Direct Summand Conjecture, and next present two concrete examples where annihilators with small order are shown to exist. We then prove a more general theorem...