While a low-level, operational definition of a language’s semantics is a straightforward way of specifying the behaviour of programs written in that language, it is not necessarily very suitable for formal activities such as program verification. This is clearly the case with languages such as C, where the language definition is complicated by much tedious detail. However, the work described he...

In [9] Weir introduced control grammars as a model for describing the syntactic structure of natural languages. Informally, a control grammar is a pair {G, C} where G is a context-free grammar whose productions are assigned labels from a finite set of labels II, and C (called the control set) is a set of strings over II. A derivation in a control grammar is similar to that in an ordinary contex...

let $mathfrak{l}$ be the virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. we investigate the structure of the lie triplederivation algebra of $mathfrak{l}$ and $mathfrak{g}$. we provethat they are both isomorphic to $mathfrak{l}$, which provides twoexamples of invariance under triple derivation.

We determine conditions under which a left Jordan derivation defined on an $MA$-semiring $S$ is this semiring and prove when implies the commutativity of $S$.

This article first explains concepts in taxometrics, including the meaning of "taxon" in relation to taxometric procedures. It then mathematically develops the MAXSLOPE procedure of Grove and Meehl which relies on nonlinear regression of one taxometric indicator variable on another. Sufficient conditions for MAXSLOPE's validity are set forth. The relationship between the point of maximum regres...

Let M be a 2-torsion free prime Γ-ring satisfying the condition a α b β c=a β b α c,∀a,b,c∈M and α,β∈Γ, U be an admissible Lie ideal of M and F=(f i ) i∈N be a generalized higher (U,M)-derivation of M with an associated higher (U,M)-derivation D=(d i ) i∈N of M. Then for all n∈N we prove that [Formula: see text]. Mathematics Subject Classification (2010): 13N15; 16W10; 17C50.