In this paper, we investigate team optimal control of coupled major-minor subsystems with mean-field sharing. In such a model, there is one major subsystem that directly influences the dynamics of n homogeneous minor subsystems; however, the minor subsystems influence the dynamics of the major subsystem and each other only through their mean behaviour (indirectly). In this model, the major and ...

The notion of entanglement quantum states is usually defined with respect to a fixed bipartition. Indeed, global basis change can always map an entangled state separable one. situation however different when considering set states. In this work we define the "absolutely set" states: for any possible choice basis, at least one in entangled. Hence, all bipartitions, i.e. definition subsystems, fe...

Let X,Y be finite sets, r,s,h,??N with s?r,X?Y. By ?Xh we mean the collection of all h-subsets X where each subset occurs ? times. A coloring (partition) is r-regular if element in exactly r subsets color. one-regular color class a perfect matching. We are interested necessary and sufficient conditions under which an can embedded into s-regular ?Yh. Using algebraic techniques involving glueing ...

We consider numerical certification of approximate solutions to a system polynomial equations with more than unknowns by first certifying square subsystem. give several approaches that certifiably select which are the original overdetermined system. These each use different additional information for this certification, such as liaison, Newton-Okounkov bodies, or intersection theory. They may b...

In this paper, we investigate the disturbance attenuation properties of timecontrolled switched systems consisting of several linear time-invariant subsystems by using a dwell time approach incorporated with piecewise Lyapunov functions. First, we show that when all subsystems are Hurwitz stable and achieve a disturbance attenuation level smaller than γ0, then the switched system can achieve an...