Order-sorted algebras and many sorted algebras exist in a long history with many different implementations and applications. A lot of language specifications have been defined in order-sorted algebra frameworks such as the language specifications in K (an order-sorted algebra framework). The biggest problem in a lot of the order-sorted algebra frameworks is that even if they might allow develop...

Built-in equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tools based, for example, on explicit or inductionless induction techniques, and of other formal tools for chec...

The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra. Classical results of Kostant [7] give a fairly complete invarianttheoretic picture of the (co)adjoint representation of g. Let σ ∈ Aut(g) be an involution and g = g0 ⊕ g1 the corresponding Z2-grading. Associated to this decomposition, there is a non-reductive Lie algebra k = g0 ⋉ g...

Let G be a Lie group of dimension n, and let A(G) be the Fourier algebra of G. We show that the anti-diagonal ∆̌G = {(g, g ) ∈ G × G | g ∈ G} is both a set of local smooth synthesis and a set of local weak synthesis of degree at most [ 2 ]+1 for A(G×G). We achieve this by using the concept of the cone property in [14]. For compact G, we give an alternative approach to demonstrate the preceding r...

this study compares and contrasts tense and inherent aspect in english and persian lan-guage from a semantic and syntactic point of view. the aspectual verb system in both english and persian are semantically interpreted alike. however, in persian a group of stative verbs are grammaticalized by the imperfective obligatory morpheme mi-, while in english all sta-tive verbs perfective. furthermore...

We present a novel theoretical model of multiple stages in the acquisition of tense and agreement in Child French. First, we show that tense and agreement inflection follow independent courses of acquisition. Over the three stages of development attested in the data, tense production starts and ends at near-adult levels, but suffers a “dip” in production at the second stage. Agreement develops ...

The number of distinct operations (that is, the range of the variable a) may be infinite, but for our main result (Theorem 2), we shall require every n(a) to be finite—that is, it will concern algebras with finitary operations. The concepts of subalgebra, congruence relation on an algebra, homomorphism of one algebra A onto (or into) another algebra with the same operations, and of the direct u...