Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

BACKGROUND AND PURPOSE Procedure-related neurological complications are common after endovascular treatment of unruptured intracranial aneurysms. We aimed to develop a score to quantify individual patient risk. METHODS We retrospectively analyzed consecutive patients who underwent endovascular treatment for unruptured intracranial aneurysms between January 2012 and September 2015. After exclu...

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 ...

OBJECTIVE To derive and validate a clinical prediction rule of acute congestive heart failure obtainable in the emergency care setting. DESIGN Derivation of the score was performed on a retrospective 927 patients cohort admitted to our Emergency Department for dyspnea. The prediction model was externally validated on an independent 206-patient prospective cohort. INTERVENTIONS AND MEASURES ...

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...

To make full use of the polarization information electromagnetic waves for polarimetric sensor array, we derive orthogonality expression state based on Poincaré sphere (PS) representation. The ellipticity angle and orientation ellipse are used to describe point surface sphere. derivation shows that two points characterize a pair orthogonal states distributed in opposite positions. Compared with...

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...

We take the Gauss’ linking integral of two curves as a starting point to discuss the connection between the equation of continuity and the inhomogeneous Maxwell equations. Gauss’ formula has been discussed before, as being derivable from the line integral of a magnetic field generated by a steady current flowing through a loop. We argue that a purely geometrical result such as Gauss’ formula ca...

In previous works, ratios among four-point scattering amplitudes at the leading order in the high-energy limit were derived for the bosonic open string theory. The derivation was based on Ward identities derived from the decoupling of zero-norm states and was purely algebraic. The only assumption of the derivation was that the momentum polarization can be approximated by the longitudinal polari...