This paper suggests a new method for interpreting D-Tree Grammar (DTG) derivations that is inspired by ideas from the categorial area. The standard treatment of DTG interpretation is based on the derivation tree (a record of the steps made during the derivation) and requires that the derivation process be constrained in ways that would not otherwise be required. The new method suggested is base...

Let A and B be commutative rings such that B is an A-algebra. We define ΩB/A to be the B-module of regular differentials over A. By definition, this B-module ΩB/A is a unique B-module which has the following property. For a B-module M we denote by DerA(B,M ) the set of all A-derivations (an A-homomorphism φ:B → M is called an A-derivation if φ(xy) = xφ(y) + yφ(x) and φ(x) = 0 for any x ∈ A ). T...

Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove th...

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.

We give a purely syntactic proof of the completeness of classical tense display logic Kt: the sequent X ` Y is provable in Kt ii the formula (X ` Y) is a theorem of minimal tense logic Kt. Along the way we show how to relate Kracht's structural rule for seriality to Wansing's one. Finally we observe a trivial way to obtain the same system using diierent primitives.

We derive the Σ-D relation of Galactic supernova remnants of shell-type separately at adiabatic-phase and at radiative-phase through two sets of different formulas, considering the different physical processes of shell-type remnants at both stages. Also statistics on Galactic shell-type remnants about 57 was made. Then we do some comparison with other results obtained before. It shows that all ...

In this paper we prove the following result. Let R be a 6−torsion free semiprime ∗−ring and let D : R → R be an additive mapping satisfying the relation D(xyx) = D(x)y∗x∗ + xD(y)x∗ + xyD(x), for all pairs x, y ∈ R. In this case D is a Jordan ∗−derivation. Mathematics Subject Classification: 16W10, 39B05

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert C∗-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert C∗-module M over a C∗-algebra A as a oneparameter group of unitaries on M and prove that if α : R → U(M) is a dynamical system, where U(M) denotes the set of all unitary operator on M, th...