In this paper we characterize the left Jordan derivations on Banach algebras. Also, it is shown that every bounded linear map $d:mathcal Ato mathcal M$ from a von Neumann algebra $mathcal A$ into a Banach $mathcal A-$module $mathcal M$ with property that $d(p^2)=2pd(p)$ for every projection $p$ in $mathcal A$ is a left Jordan derivation.

Let A be a prime *-algebra. In this paper, we suppose that ? : satisfies ?(A B) = ?(A) B + ?(B) where A*B B*A for all A, A. Then, is an additive *-derivation.

We deene an optimal proof-by-proof embedding of intuitionistic sequent calculus into linear logic and analyse the (purely logical) linearity information thus obtained.

Much of this section was copied and paraphrased from Heath’s Scientific Computing. Anyways. Suppose we are looking for an orthogonal transformation that annihilates desired components of a given vector. Recall that a square real matrix Q is said to be orthogonal if its columns are orthonormal, that is, that Q Q = I. Orthogonal transformations are nice because they preserve Euclidean norms of an...

We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the components of the derivations vanish along arbitrary paths. All such bases are explicitly described. The holonomicity of the normal bases is considered. The res...

The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor algebra over a differentiable manifold are considered.

In this paper we show how the notion of tree dimension can be used in the verification of constrained Horn clauses (CHCs). The dimension of a tree is a numerical measure of its branching complexity and the concept here applies to Horn clause derivation trees. Derivation trees of dimension zero correspond to derivations using linear CHCs, while trees of higher dimension arise from derivations us...