Seno, coseno & Co. Spunti e idee per una didattica della trigonometria

Alcuni capitoli della matematica godono di una brutta reputazione e sono spesso considerati dagli studenti (e non solo) particolarmente aridi, noiosi, astrusi. Il modulo di 10 ore, inserito nell’offerta didattica disciplinare “Didattica dell’analisi e laboratorio” del Tirocinio Formativo Attivo (TFA), classe A049 (Matematica e Fisica), dell’Università degli Studi di Trieste, proponeva di prendere in considerazione, come esempio tra i tanti, quello relativo alla trigonometria.Some chapters of mathematics have a bad reputation and are often considered by students (and not only) especially barren, boring, abstruse. The 10 hour module, included in the course “Didattica dell’analisi e laboratorio” of the Tirocinio Formativo Attivo (a Teacher Training Class offered to obtain the qualification of high school teacher), Class 049 (Mathematics and Physics), at the University of Trieste, proposed taking into account, as an example among many, the one regarding trigonometry

Optimal profiles in a phase-transition model with a saturating flux

It is well known that for the Allen\u2013Cahn equation, the minimizing transition in an infinite cylinder R 7\u3c9R 7\u3c9 is one-dimensional and unique up to a translation in the first variable. We analyze in this paper the existence and symmetry of optimal profiles for transitions in a similar phase-separation model with a saturating flux. This amounts to consider transitions in the space of BV functions as we consider the area integral instead of the Dirichlet energy to penalize the creation of wild interfaces

The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz-Minkowski space

We discuss existence, multiplicity, localisation and stability properties of solutions of the Dirichlet problem associated with the gradient dependent prescribed mean curvature equation in the Lorentz-Minkowski space { 12div( 07u/ 1a1 12| 07u|\ub2)=f(x,u, 07u) in \u2126, u=0 on 02\u2126 . The obtained results display various peculiarities, which are due to the special features of the involved differential operator and have no counterpart for elliptic problems driven by other quasilinear differential operators. This research is also motivated by some recent achievements in the study of prescribed mean curvature graphs in certain Friedmann\u2013Lema\ueetre\u2013Robertson\u2013Walker, as well as Schwarzschild\u2013Reissner\u2013Nordstr\uf6m, spacetimes

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion

Corrigendum to “Some notes on weakly Whyburn spaces” Topology Appl. 128 (2003) 257–262

In our paper [O] the proof of Theorem 2.7 is not correct. In that proof we constructed a space X 7 X and said that it had a subspace Z that was not weakly Whyburn. In fact X 7 X is regular and scattered, hence by Corollary 2.9 [TY] hereditarily weakly Whyburn. Thus the following problem raised in [TY] remains open: are sequential spaces hereditarily weakly Whyburn? We will now describe a Hausdorff counterexample to this problem, hence what remains open is the questions does there exist a sequential Tychonoff (or even regular) space that is not hereditarily weakly Whyburn

On the Dirichlet problem associated with bounded perturbations of positively-(p, q)- homogeneous Hamiltonian systems

The existence of solutions for the Dirichlet problem associated to bounded perturbations of positively-(p; q)-homogeneous Hamiltonian systems is considered both in nonresonant and resonant situations. In order to deal with the resonant case, the existence of a couple of lower and upper solutions is assumed. Both the well-ordered and the non-well-ordered cases are analysed. The proof is based on phase-plane analysis and topological degree theory

Qualitative analysis of a curvature equation modelling MEMS with vertical loads

We investigate existence, multiplicity and qualitative properties of the solutions of the Dirichlet problem for a singularly perturbed prescribed mean curvature equation, which appears in the theory of micro-electro-mechanical systems (MEMS) when the effects of capillarity and vertical forces are taken into account

Existence, regularity and boundary behaviour of bounded variation solutions of a one-dimensional capillarity equation

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Dreißig Jahre Familienplanung in Slowenien

Family planning programmes were introduced in Slovenia 35 years ago. Births were planned more successfully than pregnancies. The prevailing family planning method in the first stage was abortion, later on contraceptive use. Despite a consistent improvement in family planning and a decreased number of abortions, the maternal mortality rate among Slovenian women is still by three to five times higher than elsewhere in the developed world. Maternal mortality among adolescents is by three times higher than among older women, and their infants die more often than those born to older women. This makes adolescent pregnancies the most important risk factor for reproductive health.Programi obiteljskog planiranja uvedeni su u Sloveniju prije 35 godina. Rođenja su se uspješnije planirala od trudnoća. Prevladavajuća metoda planiranja obitelji u prvom je razdoblju bila prekid trudnoće, a kasnije upotreba sredstava za sprječavanje začeća. Usprkos dosljednom poboljšanju planiranja obitelji i smanjenju broja abortusa, smrtnost majki među slovenskim ženama još je uvijek tri do pet puta veća nego drugdje u razvijenom svijetu. Smrtnost adolescentnih majki je tri puta veća nego među starijim ženama, a njihova djeca umiru češće od djece koju rađaju starije žene. Stoga su trudnoće adolescentnih majki najznačajniji čimbenik rizika za reproduktivno zdravlje.Vor 35 Jahren wurden in Slowenien erstmals Programme zur Familienplanung eingeführt. Dabei erwies sich die Geburtenplanung erfolgreicher als die Planung der Zahl der Schwangerschaften. Die vorherrschende Methode der Familienplanung bestand zunächst im Schwangerschaftsabbruch, später in der Einnahme von Empfängnisverhütungsmitteln. Trotz der konsequenten Verbesserung der Familienplanung und der verringerten Zahl von Abtreibungen liegt die Sterblichkeitsrate unter slowenischen Frauen noch immer drei- bis fünfmal über den Durchschnittswerten in anderen Industriestaaten. Die Sterblichkeit von adoleszenten Gebärenden ist dreimal größer als die unter älteren Frauen, auch sterben Säuglinge gebärender Jugendlicher häufiger als die Säuglinge älterer Frauen. Es erweist sich also, daß Schwangerschaften in der Adoleszenz den größten Risikofaktor darstellen, der die Gesunderhaltung der Reproduktionsfähigkeit bei Frauen gefährdet