In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.

the present paper, through the linguistic analysis of mulla sadra's philosophical views, has shown that a single linguistic model can be applied to the analysis of all his philosophical views. to this end, based on two linguistic theories regarding the semantic structure of derivation, it is illustrated that mulla sadra’s philosophical views conform to the linguistic model of semantic simp...

sarhaddi balochi dialect, a language variety of western (rakhshani) balochi, employs derivation through affixation as one of its word formation processes. the purpose of this article is to present a synchronic description of the way(s) different derivational affixes function in making complex words in sarhaddi balochi as spoken in granchin[1] district located about 35kms to the southeast of kha...

In this paper, we describe the derivations of complex n-dimensional naturally graded filiform Leibniz algebras NGF1, NGF2, and NGF3. We show that the dimension of the derivation algebras of NGF1 and NGF2 equals n+1 and n+2, respectively, while the dimension of the derivation algebra of NGF3 is equal to 2n−1. The second part of the paper deals with the description of the derivations of complex n...

Multicomponent Tree Adjoining Grammars (MCTAG) is a formalism that has been shown to be useful for many natural language applications. The definition of MCTAG however is problematic since it refers to the process of the derivation itself: a simultaneity constraint must be respected concerning the way the members of the elementary tree sets are added. This way of characterizing MCTAG does not al...

Existence of data allows use solution methods for differential equations that would otherwise be inapplicable. The process this is formalized by using derivation matrices reduce the time necessary and solving equations. Derivation are formulated applying numerical in matrix notation, like finite difference schemes. In work, a novel formulation developed based on Lagrange polynomials with specia...

we show that  higher derivations on a hilbert$c^{*}-$module associated with the cauchy functional equation satisfying generalized hyers--ulam stability.

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...