there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

ABSTRACT: In this paper, a complete construction of quaternary complex Hadamard matrices of order 2 n is obtained using the method of Sylvester construction and Williamson construction. Williamson construction has been generalized to obtain any kind of Hadamard matrices (Complex or Real Numbers). Non-equivalent family of Hadamard Matrices can be obtained using the Generalized Williamson constru...

The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space. We show that any other query in the algebra which expresses transitive closure needs exponential space. This proves that in general the powerset is an intractable operator for implementing xpoint queries.

From the assumption that there is a measurable cardinal κ with o(κ) = κ, we produce a model in which for all x ⊆ אω, HODx does not contain the powerset of אω. We also prove that this assertion requires large cardinals.

Functors which are determined, up to natural isomorphism, by their values on objects, are called DVO (Defined by Values on Objects). We focus on the collection of polynomial functors on a category of sets (classes), and we give a characterization theorem of the DVO functors over such collection of functors. Moreover, we show that the (κ-bounded) powerset functor is not DVO.

It is known that implications in powerset-based closure systems correspond to Horn approximations in propositional logic frameworks. Here we focus on the problem of implications between injective partial orders. We set up the definitions that allow one to apply standard constructions of implications, and formally characterize the propositional theory obtained. We describe also some experimental...

Church’s Problem, stated fifty years ago, asks for a finitestate machine that realizes the transformation of an infinite sequence α into an infinite sequence β such that a requirement on (α, β), expressed in monadic second-order logic, is satisfied. We explain how three fundamental techniques of automata theory play together in a solution of Church’s Problem: Determinization (starting from the ...

The inversion method proposed by Glück and Kawabe uses grammar programs as intermediate results that comprise sequences of operations (data generation, matching, etc.). The determinization method used in the inversion method fails for a grammar program of which the collection of item sets causes a conflict even if there exists a deterministic program equivalent to the grammar program. In this p...

A principle is proposed that organizes verbs in the lexicon according to their meaning and the number of arguments they require. This principle, which we call the Paradigmatic Structure, acts as a filter for the permanent lexicon, letting all verb stems into the lexicon but only some morphological derivatives. The effects of the Paradigmatic Structure are observed in blocking, in which some but...