Narrow Results

It is proved that the language family generated by Boolean grammars is effectively closed under injective gsm mappings and inverse gsm mappings (where gsm stands for a generalized sequential machine). The same results hold for conjunctive grammars, unambiguous Boolean grammars and unambiguous conjunctive grammars.

This paper establishes an analogue of Greibach’s hardest language theorem (“The hardest context-free language”, SIAM J. Comp., 1973, http://dx.doi.org/10.1137/0202025) for the classical family of LL($k$) languages. The first result is that there is a language $L_0$ defined by an LL(1) grammar in the Greibach normal form, to which every language $L$ defined by an LL(1) grammar in the Greibach normal form can be reduced by a homomorphism, that is, $w\mathrm{ \in }L$ if and only if $h(w)\mathrm{ \in }{L}_0$. Then it is shown that this statement does not hold for the full class of LL($k$) languages. The other hardest language theorem is then established in the following form: there is a language $L_0$ defined by an LL(1) grammar in the Greibach normal form, such that, for every language $L$ defined by an LL($k$) grammar, with $k\ge 1$, there exists a homomorphism $h$, for which $w\mathrm{ \in }L$ if and only if $h(w\$)$$\mathrm{ \in }$$L_0$, where $\$$ is a new symbol. The results lead to two robust language families: the closures of the languages defined by LL(1) grammars in the Greibach normal form under inverse homomorphisms and under inverse finite transductions.

Let X be a compact metric space and A be a unital simple C*-algebra with TR(A)=0. Suppose that ϕ : C(X) → A is a unital monomorphism. We study the problem when ϕ can be approximated by homomorphisms with finite-dimensional range. We give a K-theoretical necessary and sufficient condition for ϕ being approximated by homomorphisms with finite-dimensional range.

In this paper we introduce a new concept "unrelated pairs". Using this concept, we study a relation between homomorphisms and direct summands of a finitely generated module.

This paper surveys, and in some cases generalizes, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined.

Let $L$ and $K$ be two Lie algebras over a commutative ring with identity. In this paper, under some conditions on $L$ and $K$, it is proved that every triple homomorphism from $L$ onto $K$ is the sum of a homomorphism and an antihomomorphism from $L$ into $K$. We also show that a finite-dimensional Lie algebra $L$ over an algebraically closed field of characteristic zero is nilpotent of class at most $2$ if and only if the sum of every homomorphism and every antihomomorphism on $L$ is a triple homomorphism.

The purpose of this paper is to describe the nearness homomorphisms and the canonical nearness epimorphism of the nearness groups and to investigate their basic properties. It is also to form the substructure to give the nearness isomorphism theorems of the nearness groups.

The concept and properties of cubic sets were first introduced and investigated by Jun et al. in 2011. In this paper, we first introduce the concept of cubic sets in UP-subalgebras and consider the UP-ideals of a UP-algebra. Relationships between the cubic UP-subalgebras and the cubic UP-ideals of a UP-algebra are investigated. In addition, the homomorphic images and the inverse images of the cubic UP-subalgebras and the cubic UP-ideals are also studied. Related properties of UP -algebras and their UP-ideals are explored and discussed. Finally, the Cartesian product of cubic UP-algebras are investigated.

We review Discrete-Event system Specification (DEVS) in the context of Model-based Systems Engineering (MBSE) and discuss an application of DEVS methodology to MBSE. We outline support for an envisioned MBSE development cycle of DEVS top-to-bottom MBSE capability and offer an example of mapping UML activity diagrams into executable activity-based DEVS models. We close with conclusions and future research directions.

In 1958 E. Marczewski introduced a general notion of independence, which contained as special cases the majority of independence notions used in various branches of mathematics. A non-empty set I of the carrier A of an algebra is called M-independent if equality of two term operations f and g of the algebra on any finite system of different elements of I implies f = g in A. There are several interesting results on this notion of independence. However the important scheme of M-independence is not wide enough to cover stochastic independence, independence in projective spaces and some others. This is why some notions weaker than the M-independence have been developed. The notion of independence with respect to a family Q of mappings (defined on subsets of A) into A, Q-independence for short, is a common way of defining almost all known notions of independences. There exists an interesting Galois correspondence between families Q of mappings and families of Q-independent sets. In our article after a brief survey of these topics we will mainly concentrate on a few easily formulated and interesting results.