We consider the clause{based version of the general model of semantic derivations proposed by Kraj cek. Resolution refutation proof is a special deterministic version of fanin-2 clause{based derivation. We prove the following combinatorial lower bound on the length of such derivations. Let F be a k-partite hypergraph, with at most b points in each part such that no point belongs to more than d ...

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.

let  be a banach algebra and  a derivation. in this paper, it is proved, under certain conditions, that , where  is the jacobson radical of . moreover, we prove that if  is unital and  is a continuous derivation, then , where  denotes the set of all primitive ideals such that  is commutative,  denotes the set of all maximal (modular) ideals such that  is commutative, and  is the set of all non-...

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...

Here, we investigate symmetric bi-derivations and their generalizations on L? 0 (G)*. For k ? N, show that if B:L?0(G)*x L?0(G)* is asymmetric bi-derivation such [B(m,m),mk] Z(L?0(G)*) for all m (G)*, then B the zero map. Furthermore, characterize generalized biderivations group algebras. We also prove any Jordan 0(G)* a bi-derivation.

We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions f...

In this paper we prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let A(X) be a standard operator algebra on X and let L(X) be an algebra of all bounded linear operators on X. Suppose we have a linear mapping D : A(X) → L(X) satisfying the relation D(Am+n) = D(Am)An + AmD(An) for all A ∈ A(X) and some fixed integers m ≥ 1, ...

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.