Factors of disconnected graphs and polynomials with nonnegative integer coefficients

We investigate the uniqueness of factorisation of possibly disconnected finite graphs with respect to the Cartesian, the strong and the direct product. It is proved that if a graph has $n$ connected components, where $n$ is prime, or $n=1,4,8,9$, and satisfies some additional conditions, it factors uniquely under the given products. If, on the contrary, $n=6$ or 10, all cases of nonunique factorisation are described precisely.Comment: 14 page

mathematische

The well known binary, decimal,..., number systems in the integers admit many generalisations. Here, we investigate whether still every integer could have a finite expansion on a given integer base b, when we choose a digit set that does not contain 0. We prove that such digit sets exist and we provide infinitely many examples for every base b with |b | ≥ 4, and for b = −2. For the special case b = −2, we give a full characterisation of all valid digit sets. Key words: Radix systems 1 Introduction an

Deterministic equation solving over finite fields

It is shown how to solve diagonal forms in many variables over finite fields by means of a deterministic efficient algorithm. Applications to norm equations, quadratic forms, and elliptic curves are given.Thomas Stieltjes Institute for MathematicsUBL - phd migration 201

Unusual Hybrid Closure of Ventricular Septal Defects

A planned combined perventricular and “open heart” surgical closure of multiple ventricular septal defects had to be modified intraoperatively due to a technical fault disabling echocardiographic guidance. Through an atriotomy, device closure of a muscular defect and patch closure of a perimembranous ventricular septal defect were performed. In unusual situations, collaboration of the surgical and interventional team is crucial

"Thunderstruck": Penetrating thoracic injury from lightning strike

Lightning strike victims are rarely presented at an emergency department. Burns are often the primary focus. This case report describes the improvised explosive device like-injury to the thorax due to lightning strike and its treatment, which has not been described prior in (kerauno)medicine. Penetrating injury due to blast from lightning strike is extremely rare. These shrapnel injuries should however be rule

An unusual case of redo tricuspid valve replacement and repair of a previously unidentified anomalous pulmonary venous return in a patient with congenitally corrected transposition of the great arteries

Contains fulltext : 225333.pdf (publisher's version ) (Open Access)Associated cardiovascular malformations in congenitally corrected transposition of the great arteries (CCTGA) should not be missed when a patient requires surgical correction. We present a case of an adult CCTGA patient who required redo surgery for recurrent tricuspid (left atrioventricular) valve regurgitation and previously unidentified partial anomalous pulmonary venous return. Publisher: Abstract available from the publisher