We study the concept of stabilization with internal loop for infinite-dimensional discrete timevarying systems in the framework of nest algebra. We originally give a parametrization of all stabilizing controllers with internal loop, and it covers the parametrization of canonical or dual canonical controllers with internal loop obtained before. We show that, in practical application, the control...

Suppose that λ = μ and μ is singular. We consider two aspects of the square property on subsets of λ. First, we have results which show e.g. that for א0 < κ = cf(κ) < μ, the equality cf([μ],⊆) = μ is a sufficient condition for the set of elements of λ whose cofinality is ≤ κ, to be split into the union of μ sets with squares. Secondly, we introduce a certain weak version of the square property ...

The discovery of the Θ resonance opens the possibility of forming exotic Θ hypernuclei, which, like in the case of negative strangeness, could provide complementary information on the structure and properties of the pentaquark to that obtained from elementary reactions. In Ref. 2, a schematic model for quark-pair interaction with nucleons was used to describe the Θ, which suggested that Θ hyper...

A singular masa A in a II1 factor N is defined by the property that any unitary w ∈ N for which A = wAw∗ must lie in A. A strongly singular masa A is one that satisfies the inequality ‖EA − EwAw∗‖∞,2 ≥ ‖w − EA(w)‖2 for all unitaries w ∈ N , where EA is the conditional expectation of N onto A, and ‖ · ‖∞,2 is defined for bounded maps φ : N → N by sup{‖φ(x)‖2 : x ∈ N, ‖x‖ ≤ 1}. Strong singularity...

This paper describes a system called SELP for studying strong equivalence in answer set logic programming. The basic function of the system is to check if two given ground disjunctive logic programs are equivalent, and if not, return a counter-example. This allows us to investigate some interesting properties of strong equivalence, such as a complete characterization for a rule to be strongly e...

In this paper, we propose an alternative notion, called weak forgetting, of forgetting a set of predicates in a first-order theory. One important feature of this new notion is that the result of weak forgetting is always first-order expressible. In contrast, this is not the case for the traditional notion of forgetting, called strong forgetting, introduced by Lin and Reiter. As a consequence, t...

The main aim of this paper is to obtain compositive cone factorizations from non-compositive ones by itereration. This is possible if and only if certain colimits of (possibly large) chains exist. In particular, we show that (strong-epi, mono) factorizations of cones exist if and only if joint coequalizers and colimits of chains of regular epimorphisms exist.

In this paper, we study the problem of factoring an RSA modulus N = pq in polynomial time, when p is a weak prime, that is, p can be expressed as ap = u0 + M1u1 + . . . + Mkuk for some k integers M1, . . . ,Mk and k+2 suitably small parameters a, u0, . . . uk. We further compute a lower bound for the set of weak moduli, that is, moduli made of at least one weak prime, in the interval [2, 2] and...

We calculate the negative integer moments of the (regularized) characteristic polynomials of N × N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as N → ∞. The results agree nontrivially with a recent conjecture of Berry & Keating motivated by techniques developed in the theory of singularity-dominated strong fluctuations. This is the first example where nontrivi...

The Coalitional Manipulation problem has been studied extensively in the literature for many voting rules. However, most studies have focused on the complete information setting, wherein the manipulators know the votes of the non-manipulators. While this assumption is reasonable for purposes of showing intractability, it is unrealistic for algorithmic considerations. In most real-world scenario...