First principles calculations are performed to investigate the structural and electronic properties of small IrGen (n = 1–20) clusters. Cage-like configurations where iridium atom is encapsulated inside a germanium cage predicted be favored for n ≥ 12. Doping Ir enhances stability corresponding frame. Our results highlight great IrGe13 which presents high-symmetry cage-like geometry peculiar st...

The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T.Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E....

A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular, decidability of the problem whether a given language is recognisable by some unambiguous automaton is open. Moreover, there are no known upper bounds on the descript...

The energy and time variables of the elementary classical dynami-cal systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivari-ant. Although it has no effect at classical level, the lack of equivariance makes the Galilei actio...

We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure preserving ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar l...