Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica. La presenza del fulltext è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 864 prodotti

QDD231
Andrà, C.; Brunetto, D.; Pini, A.
 A contribution to understand STEM students' difficulties with mathematics   ABSTRACT Drop out during the first year at university STEM courses is a plague spreading all around the world: it has been estimated that, on average, 40% of freshmen abandon their studies before the end of the first academic year.
Research in Mathematics Education has revealed that mathematics is one of the main causes for drop out: not only the students' mathematical knowledge, but also affective issues such as attitudes towards learning mathematics, views about mathematics itself, as well as emotions determine the students' success or failure in university career. On the one's hand, thus, it is important to develop suitable and reliable means for investigating both cognitive and affective dimensions, and on the other hand it becomes necessary to reflect on the kind of information the researcher can get from these means of investigation. One of the central issues is the private versus public dimension of learning mathematics. This is connected to the public and private nature of telling about one's emotions and views. We understand ``public'' versus ``private'' as identifiable versus anonymous questionnaires and tests, respectively. In this paper, we discuss gains and drawbacks of either approach. In doing so, we also investigate the intertwining of cognitive and affective dimensions in freshmen Engineering students attending a bridge course in mathematics at the beginning of the first semester at the Politecnico di Milano. 
13/11/2018

QDD230
Sabadini, I; Sommen, F.
 Radon type transforms for holomorphic functions in the Lie ball   ABSTRACT In this paper we consider holomorphic functions on the $m$dimensional Lie ball $LB(0,1)$ which admit a square integrable extension on the Lie sphere. We then define orthogonal projections of this set onto suitable subsets of functions defined in lower dimensional spaces to obtain several Radontype transforms. For all these transforms we provide the kernel and an integral representation, besides other properties. In particular, we introduce and study a generalization to the case of the Lie ball of the SzegoRadon transform, and various types of HuaRadon transforms.

10/04/2018

QDD229
Alpay, D.; Colombo, F.; Sabadini, I.
 de Branges spaces and characteristic operator function: the quaternionic case   ABSTRACT This work inserts in the very fruitful study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the socalled $S$spectrum and $S$resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. We also introduce a notion of the characteristic operator function of a bounded linear operator $A$ with finite real part and we address several questions like the study of $J$contractive functions, where $J$ is selfadjoint and unitary, and we also treat the inverse problem namely to characterize which $J$contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in
this framework. Besides other topics, we also consider canonical differential equations in the setting of slice hyperholomorphic functions.
We define the lossless inverse scattering problem in the present setting. We also consider the inverse scattering problem associated to canonical differential equations. These equations provide a convenient unifying framework to discuss a number of
questions pertaining, for example, to inverse scattering, nonlinear partial differential equations and are studied in the last section of this paper.

09/01/2018

QDD228
Bucur, D.; Fragalà, I.; Velichkov, B.; Verzini, G.
 On the honeycomb conjecture for a class of minimal convex partitions   ABSTRACT We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be convex, and the criterion is to minimize either the sum or the maximum among the energies of the cells, the cost being a shape functional F which satisfies a few assumptions. They are: monotonicity under inclusions; homogeneity under dilations; a FaberKrahn inequality for convex hexagons; a convexitytype inequality for the map which associates with every integer n the minimizers of F among convex ngons with given area. In particular, our result allows to obtain the honeycomb conjecture for the Cheeger constant and for the logarithmic capacity (still assuming the cells to be convex). Moreover we show that, in order to get the conjecture also for the first Dirichlet eigenvalue of the Laplacian, it is sufficient to establish some facts about its behaviour among convex pentagons, hexagons, and heptagons with prescribed area.

06/07/2017

QDD227
Terracini, S.; Verzini, G.; Zilio, A.
 Spiraling asymptotic profiles of competitiondiffusion systems   ABSTRACT This paper describes the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reactiondiffusion systems with strongly competitive interactions of Lotka Volterra type, when the matrix of the interspecific competition coefficients is asymmetric and the competition parameter tends to infinity. Unlike the symmetric case, when it is known that the nodal set consists in a locally finite collection of curves meeting with equal angles at a locally finite number of singular points, the asymmetric case shows the emergence of spiraling nodal curves, still meeting at locally isolated points with finite vanishing order. 
06/07/2017

QDD226
Pavani R.
 About a new approach to the characterization of Dstability   ABSTRACT The concept of Dstability is relevant for stable square matrices of any order, especially when they appear in ordinary differential systems modelling physical problems. Indeed, Dstability was treated from different points of view in the last fifty years, but the problem of characterization of a Dstable matrix was solved for low order matrices only (i.e. up to order 4). Here a new approach is proposed within the context of numerical linear algebra. A new necessary and sufficient condition for Dstability is proved and, according to that, an algorithm is implemented by computer algebra. Results show that it is easy and efficient to characterize matrices of order grater than 4. 
12/06/2017

QDD225
Bertacchi D.; Coletti C.F.; Zucca F.
 Global survival of branching random walks and treelike branching random walks   ABSTRACT The local critical parameter $lambda_s$ of continuoustime branching random walks is completely understood and can be computed as a function of the reproduction rates. On the other hand, only for some classes of branching random walks it is known that the global critical parameter $lambda_w$ is a certain function of the reproduction rates, which we denote by $ 1/K_w$. We provide here new sufficient conditions which guarantee that the global critical parameter equals $ 1/K_w$. This result extends previously known results for branching random walks on multigraphs and general branching random walks.
We show that these sufficient conditions are satisfied by periodic treelike branching random walks.
We also discuss the critical parameter and the critical behaviour of continuoustime branching processes in varying environment.
So far, only examples where $lambda_w=1/K_w$ were known; here we
provide an example where $lambda_w>1/K_w$. 
20/03/2017

QDD224
Zucca F.; Bertacchi D.; Rodriguez P.M.
 GaltonWatson processes in varying environment and accessibility percolation   ABSTRACT This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the
generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments of the
offspring distributions. These results are then applied
to branching processes in varying environment with selection where every particle has a realvalued label and labels can only increase along
genealogical lineages;
we obtain analogous conditions for survival or extinction. These last results can be interpreted in terms of
accessibility percolation on GaltonWatson trees, which represents a relevant tool for modeling the evolution of biological populations. 
10/11/2016
