Multiple-scale analysis of dynamical systems on the lattice

We propose a new approach to the multiple-scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled equations are of finite order. Our results are applied to the study of multiple-scale reductions of dynamical systems, and in particular to the case of a discrete nonlinear harmonic oscillator.     

On Appell sequences of polynomials of Bernoulli and Euler type

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number theoretical properties. A class of Euler-type polynomials is also presented.     

Lie Symmetries and Weak Transversality

We discuss the notion of weak transversality and clarify its role in the context of Lie group theory with several examples. In particular, we present some new results concerning models of fluid dynamics.     

Convulsant alkaloids from Dioscorea dumetorum

Investigation of the West African medicinal yam $\text{Dioscorea dumetorum}$ Pax has resulted in the isolation and stereostructural elucidation of the previously reported dihydrodioscorine as well as the new alkaloid dumetorine.     

Recursion operators, higher-order symmetries and superintegrability in quantum mechanics

A connection between the theory of superintegrable quantum-mechanical systems, which admit a maximal number of integrals of motion, and the standard Lie group theory is established. It is shown that the flows generated by first- and second-order Lie symmetries of the bidimensional Schrödinger equation can be classified and interpreted as quantum-mechanical operators which commute with integrable or superintegrable Hamiltonians. In this way, all known superintegrable potentials in the plane are naturally obtained and slightly more general integrals of motion are found.     

Integrable maps from Galois differential algebras,Borel transforms and number sequences

A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a given differential equation, in particular symmetries and integrability (see Tempesta, 2010 [40]). Our approach is based on the properties of a suitable Galois differential algebra, that we shall call a Rota algebra. A formulation of the procedure in terms of category theory is proposed. In order to render the lattice dynamics confined, a Borel regularization is also adopted. As a byproduct of the theory, a connection between number sequences and integrability is discussed.     

Beyond the Shannon–Khinchin formulation: The composability axiom and the universal-group entropy

The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann–Gibbs (BG) entropy and could be applicable in thermodynamics, quantum mechanics and information theory. In Khinchin (1957), by extending previous ideas of Shannon (1948) and Shannon and Weaver (1949), Khinchin proposed a characterization of the BG entropy, based on four requirements, nowadays known as the Shannon–Khinchin (SK) axioms.     

Development of reliable analytical tools for evaluating the influence of reductive winemaking on the quality of Lugana wines

This paper presents methods for the definition of important analytical tools, such as the development of sensitive and rapid methods for analysing reduced and oxidised glutathione (GSH and GSSG), hydroxycinnamic acids (HCA), bound thiols (GSH-3MH and Cys-3MH) and free thiols (3MH and 3MHA), and their first application to evaluate the effect of reductive winemaking on the composition of Lugana juices and wines.     

Binary relations, interval structures and join spaces

We study correspondences between interval structures and hyperstructures.     

Structure of the bromination product of 2-ethyl-1,4-benzothiazin-3(4H)-one

2-Ethyl-1,4-benzothiazin-3(4H)-one and bromine react smoothly to give Z-2-(1-bromoethylidine)-2(H)-1,4-benzothiazin-3(4H)-one, which results from a complex bromination-oxidation sequence. The structure of this product was determined by an X-ray study.