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RESEARCH
INTERESTS
This page contains a summary of my activity of study/research
carried out in the PhD period.
My research interests, developed during the whole course of
doctorate, are: orthogonal polynomials, non-integer bases, Riesz
bases and frames. These researches were finalised to some areas of
mathematical modeling, pure and applied mathematics: models of
intracellular enzymatic interactions; signal reconstruction;
Robotics (hyper-redundant manipulators); infinite nested square
roots; pi-formulas.
The topics of basis expansions in Mathematics are the main
directions of my research activity: Kadec's 1/4-theorem,
Ingham-type inequalities for Exponential and Sinc Bases, with
applications to sampling clock jitter and nonuniform sampling;
non-integer bases with applications to mathematical models in
Robotics (a model of a robot finger, a hyper-redundant manipulator
analogous in morphology to robotic tentacles); the Lucas-Lehmer
polynomials, a class of orthogonal polynomials related to the
Chebyshev polynomials of the first and second kind, which allows
us to obtain some results on nested square roots of 2 and
pi-formulas.
Many papers of my research activity belong to different research
areas such as: collective decision-making and mathematical models
of biological systems.
A more comprehensive report of my activity of study and research
can be found here.
Articles in
refereed journals
L. Pareschi, P.
Vellucci, M. Zanella, Kinetic models of collective
decision-making in the presence of equality bias, Physica A:
Statistical Mechanics and its Applications, 467 (2017), 201 –
217.
A. C. Lai, P.
Loreti, P. Vellucci, A Fibonacci control system with application
to hyper-redundant manipulators. Math Control Signal. 28.2
(2016), 1-32.
P. Vellucci, A.
M. Bersani, The class of Lucas-Lehmer polynomials. Rend. Mat.
Appl. (7) 37 (2016), 43-62.
P. Vellucci, A.
M. Bersani, Orthogonal polynomials and Riesz bases applied to the
solution of Love’s equation. Mathematics and Mechanics of
Complex Systems 4.1 (2016). 55-66.
P. Vellucci, A
simple pointview for Kadec-1/4 theorem in the complex case,
Ricerche di Matematica, 64.1 (2015), 87-92.
G. Riccardi, P.
Vellucci, E. De Bernardis, Asymptotic expansions of the complete
elliptic integrals about unitary modulus, CAIM 5 (2015), 1-12.
Proceedings
P. Loreti, P.
Vellucci, A Mathematical Model for Signal's Energy at the Output
of an Ideal DAC, Proceedings of 13-th International Conference on
Informatics in Control, Automation and Robotics, (2016), 347-352.
A. Avantaggiati,
P. Loreti, P. Vellucci. An explicit bound for stability of Sinc
Bases. Proceedings of 12-th International Conference on
Informatics in Control, Automation and Robotics, (2015), 473-480.
A. C. Lai, P.
Loreti, P. Vellucci. A model for robotic hand based on Fibonacci
sequence, Proceedings of 11-th International Conference on
Informatics in Control, Automation and Robotics, (2014), 577-587.
Abstracts and
Talks
A.M. Bersani, A.
Borri, A. Milanesi, P. Vellucci, Tihonov approach for
multidimensional systems in bio-informatics, XIII congresso SIMAI
13-16/09/2016, Politecnico di Milano, 184-187.
P. Vellucci,
A.M. Bersani, Nested square roots of 2 and Gray code,
Computationally Assisted Mathematical Discovery and Experimental
Mathematics 12-15/05/2016, London, Ontario, Canada;
https://acmes.org/talks.html
P. Vellucci,
A.M. Bersani, Time Scale Separation, Normal Modes and
Quasi-Steady State Approximations in Enzyme Kinetics, XII
congresso SIMAI 07-10/07/2014, Taormina (ME).
Data Downloads
L.
Mastroeni, P. Vellucci, "Chaos" in energy futures
markets: a controversial matter. Tables;
Data
L.
Mastroeni, P. Vellucci, How reliable are the results on
"Butterfly Effect” and "Chaos" in Financial
and Commodity Futures Markets? Tables
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