Let A be a non-commutative prime ring with involution ∗, of characteristic ≠2(and3), Z as the center and Π mapping Π:A→A such that [Π(x),x]∈Z for all (skew) symmetric elements x∈A. If is non-zero CE-Jordan derivation A, then satisfies s4, standard polynomial degree 4. ∗-derivation s4 or Π(y)=λ(y−y*) y∈A, some λ∈C, extended centroid A. Furthermore, we give an example to demonstrate importance re...

The domain (δ) of a closed ∗-derivation δ in C(K) (K : a compact Hausdorff space) is a generalization of the space C(1)[0,1] of differentiable functions on [0,1]. In this paper, a problem proposed by Jarosz (1985) is studied in the context of derivations instead of C(1)[0,1].

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.

BACKGROUND Pulmonary function testing parameters predict cardiovascular and mortality outcomes. Previously, risk scores were created using the basic metabolic profile and complete blood count, including the Intermountain Risk Score (IMRS). This study sought to develop similar pulmonary-specific risk scores for mortality prediction. METHODS Subjects evaluated by spirometry at 5 Intermountain H...

One important aspect of scienti c data management is metadata management. Metadata is broadly de ned as information about data (e.g., content, source, processing applied, precision). One kind of metadata which needs special attention is the data derivation information, i.e., how data are generated. In our application domain of geographical information systems (GIS) and global change research, w...

BACKGROUND The aim of this study was to derive and validate a risk score for rejection after orthotopic heart transplantation. METHODS AND RESULTS The United Network for Organ Sharing registry was used to identify patients undergoing orthotopic heart transplantation between 1998 and 2008. A total of 14 265 eligible patients were randomly divided into derivation (80%; n=11 412) and validation ...

The task of inverting logical entailment is of central importance to the disciplines of Abductive and Inductive Logic Programming (ALP& ILP). Bottom Generalisation (BG) is a widely applied approach for Inverse Entailment (IE), but is limited to deriving single clauses from a hypothesis space restricted by Plotkin’s notion of C-derivation. Moreover, known practical applications of BG are confine...

Background—The aim of this study was to derive and validate a risk score for rejection after orthotopic heart transplantation. Methods and Results—The United Network for Organ Sharing registry was used to identify patients undergoing orthotopic heart transplantation between 1998 and 2008. A total of 14 265 eligible patients were randomly divided into derivation (80%; n 11 412) and validation (2...