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

  1. 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.

  2. 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.

  3. P. Vellucci, A. M. Bersani, The class of Lucas-Lehmer polynomials. Rend. Mat. Appl. (7) 37 (2016), 43-62.

  4. 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.

  5. P. Vellucci, A simple pointview for Kadec-1/4 theorem in the complex case, Ricerche di Matematica, 64.1 (2015), 87-92.

  6. G. Riccardi, P. Vellucci, E. De Bernardis, Asymptotic expansions of the complete elliptic integrals about unitary modulus, CAIM 5 (2015), 1-12.


Proceedings


  1. 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.

  2. 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.

  3. 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

  1. 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.

  2. 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

  3. 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

  1. L. Mastroeni, P. Vellucci, "Chaos" in energy futures markets: a controversial matter. Tables; Data

  2. 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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