Landmarks in Maltese Constitutional History 1849-1974

In a few words - alas, too few to do justice to this subject – the author commemorates, as this beautiful medal is also intended to do, an event which is undoubtedly the greatest one in Malta's modern history: the achievement of independence. In doing so, he begs forgiveness if he seems to overindulge in the use of the first person singular. But, to some extent this is unavoidable given that the events running up to Independence he had the good fortune of being right at the forefront and literally in the thick of it all.peer-reviewe

Doctors and would-be doctors in the law reports

This paper is the St. Luke's Day Oration, delivered by His Honour the Chief Justice to the Malta Branch of the British Medical Association on the 18th October 1973 at the Medical School of the University. Civil cases in which doctors had been involved and which figure out in Maltese Law Reports are described. A case in point shows how a father, sued a doctor for damages arising out of the fact that the son, who was under the professional care of the doctor, allegedly through the doctor's negligence, lost his foot and suffered permanent debilitation. Warrants of seizure and of impediment of departure, as well as a garnishee order, were also issued against the doctor. It was on the basis of the experts' findings themselves that both Courts reached the clear conclusion that there had been negligence on the part of the doctor. Several other cases are reported, one of which for instance involves the doctor`s prescription. The focus here is on the dark side of things that brings out more fully the brighter side, whereby the medical profession in Malta has indeed a very bright record.peer-reviewe

What is the probability that a random integral quadratic form in nn variables has an integral zero?

We show that the density of quadratic forms in $n$ variables over $\mathbb Z_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. When real quadratic forms in $n$ variables are distributed according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we determine explicitly the probability that a random such real quadratic form is isotropic (i.e., indefinite). As a consequence, for each $n$, we determine an exact expression for the probability that a random integral quadratic form in $n$ variables is isotropic (i.e., has a nontrivial zero over $\mathbb Z$), when these integral quadratic forms are chosen according to the GOE distribution. In particular, we find an exact expression for the probability that a random integral quaternary quadratic form has an integral zero; numerically, this probability is approximately $98.3\%$.Comment: 17 pages. This article supercedes arXiv:1311.554

On elliptic curves of prime power conductor over imaginary quadratic fields with class number one

The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number one a result of Serre (1987) and Mestre-Oesterlé (1989), namely that if E is an elliptic curve of prime conductor then either E or a 2-, 3- or 5-isogenous curve has prime discriminant. For four of the nine fields, the theorem holds with no change, while for the remaining five fields the discriminant of a curve with prime conductor is either prime or the square of a prime. The proof is conditional in two ways: first that the curves are modular, so are associated to suitable Bianchi newforms; and second that a certain level-lowering conjecture holds for Bianchi newforms. We also classify all elliptic curves of prime power conductor and non-trivial torsion over each of the nine fields: in the case of 2-torsion, we find that such curves either have CM or with a small finite number of exceptions arise from a family analogous to the Setzer-Neumann family over Q

The proportion of plane cubic curves over Q that everywhere locally have a point

We show that the proportion of plane cubic curves over Qpℚp that have a Qpℚp-rational point is a rational function in pp, where the rational function is independent of pp, and we determine this rational function explicitly. As a consequence, we obtain the density of plane cubic curves over Qℚ that have points everywhere locally; numerically, this density is shown to be ≈97.3%≈97.3%

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent

The right to free interpretation under article 6 of the European Convention on Human Rights

The Council of Europe Colloquy held in Madeira in 1983 on Human Rights of Aliens in Europe brought to the fore various problems, some of them far from small, facing aliens and especially migrant workers in Europe. The present paper seeks to focus on one particular area where the European Convention on Human Rights has afforded them effective protection. This concerns the right to free interpretation in criminal proceedings when the person charged is not, or not sufficiently, conversant with the language used in court. Article 6 paragraph 3(e) of the Convention provides that everyone charged with a criminal offence has the right "to have the free assistance of an interpreter if he cannot understand or speak the language used in court." Obviously, this right is not confined exclusively to aliens since there may be aliens who are sufficiently conversant with the language of the proceedings, and on the other hand, even a national forming part of a linguistic minority may conceivably find himself in need of protection in this regard, though in view of the modern principle of compulsory education, it is not easy to envisage a member of a linguistic minority within a member State not being sufficiently conversant with the national language. [excerpt]peer-reviewe