Setting of this research is Bishop’s constructive mathematics, the mathematics developed on Intuitionistic logic. If (X, =, 6=, θ) is an anti-ordered set, for a coequality q on X we say that it is strongly regular if it is regular and θ ◦ q ⊆ q ◦ θ holds. In this case, θ ◦ q is a quasi-antiorder relation on X such that the relation Θ = π ◦ θ ◦ π−1 on X/q is the maximal anti-order on X/q.

Reversible cellular automata are seen as microscopic physical models, and their states of macroscopic equilibrium are described using invariant probability measures. Characterizing all the invariant measures of a cellular automaton could be challenging. Nevertheless, we establish a connection between the invariance of Gibbs measures (used in statistical mechanics to describe thermodynamic equil...

Quantum trajectories are Markov processes that describe the time evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they defined as solutions so-called Stochastic Schrödinger Equations, which nonlinear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to study invariant measures trajectories. Particularly, we p...

We exhibit a change of variables that maintains the Mahler measure given polynomial. This method leads to construction highly non-trivial polynomials with and settles some conjectural numerical formulas due Boyd Brunault.

We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are provided, in the direction which enlarges the scope of its application. We formulate a more general version of Noether’s theorem for optimal control problems, wh...