In this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. Several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. Then we investigate for a ring $R$, when any fi...

Many classical works from 18th and 19th centuries are sonata forms, exhibiting a piece-level tonal path through an exposition, a development and a recapitulation and involving two thematic zones as well as other elements. The computational music analysis of scores with such a largescale structure is a challenge for the MIR community and should gather different analysis techniques. We propose fi...

This paper contains a critical review of the claim that evaluative conditioning (EC) represents a theoretically distinct form of classical conditioning. A review of the evidence suggests that: (i) while it is claimed that EC can occur without awareness, EC studies have either adopted inappropriate statistical comparisons to demonstrate this or have failed to use the control conditions necessary...

We use a factorisation technique and representations of canonical transformations to construct globally valid closed form expressions without singularities of semi-classical wave functions for arbitrary smooth local potentials over a one-dimensional position space.

De Moivre gave a simple closed form expression for the mean absolute deviation of the binomial distribution. Later authors showed that similar closed form expressions hold for many of the other classical families. We review the history of these identities and extend them to obtain summation formulas for the expectations of all polynomials orthogonal to the constants.

• To propose a direct and “elementary” proof of the main result of [3], nameley that the semi-classical spectrum near a global minimum of the classical Hamiltonian determines the whole semi-classical Birkhoff normal form (denoted the BNF) in the non-resonant case. I believe however that the method used in [3] (trace formulas) are more general and can be applied to any non degenerate non resonan...