Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.57 (2025), 2nd Issue

The journal Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics. Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. In 2008 the Dipartimento di Matematica e Informatica, the owner of the journal, decided to renew it. The name of the journal however remained unchanged, but the subtitle An International Journal of Mathematics was added. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in. The articles published by Rendiconti dell’Istituto di Matematica dell’Universit`a di Trieste are reviewed/indexed by MathSciNet, Zentralblatt Math, Scopus, OpenStarTs.

In this paper we study autonomous systems whose Lagrangian function is the combination of several homogeneous terms with respect to positions and velocities. We show that, assuming certain relations between the degrees of homogeneity of such terms, the systems considered possess (in addition to energy) a further first integral that provides information about their solutions. A new feature of these results is the use of the theory of nonlocal constants, which finds useful constants using one-parameter perturbed motions.

In this article, we introduce the concept of generalized (α, T)-G-contractive mappings in partial b-metric spaces endowed with a digraph G and obtain a new coincidence point and common fixed point result for a pair of self mappings satisfying such contractive condition. Our main result will extend and unify several known results in the existing literature and also brings some new results as consequences. Finally, we give an application of our main result to obtain a unique solution of an integral equation.

In this paper, we produce explicit examples of mean curvature flow of (2m − 1)-dimensional submanifolds which converge to (2m − 2)-dimensional submanifolds at a finite time. These examples are a special class of hyperspheres in Cm with a U(m)-invariant Kähler metrics. We first discuss the mean curvature flow problem and then investigate the type of singularities for them.