a subgroup x of a group g is said to be an h -subgroup if n_g(x) ∩ x^g ≤ x for each element g belonging to g. in [m. bianchi e. a., on finite soluble groups in which normality is a transitive relation, j. group theory, 3 (2000), 147–156] the authors showed that finite groups in which every subgroup has the h -property are exactly soluble groups in which normality is a transitive relation. here ...

in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

A class of large-scale systems with decentralized information structures such as multi-agent dynamical systems can be represented by a linear system with a generalized frequency variable. In this paper, we propose efficient H2 and H∞ norm computations based on the generalized frequency variable. Specifically, we first derive a way of H2 norm computation from state-space realizations of subsyste...

Two methods are proposed in this paper for fractional system H -norm computation. These methods are extensions to fractional systems of well-known methods for integer systems. The first is based on singular value properties of a linear system and is applied on an academic example. In the second, two extensions of the real bounded lemma derived directly from Lyapunov’s theory are deduced. The fi...

A Hankel operator $\mathbf{H}_\varphi$ on the Hardy space $H^2$ of unit circle with analytic symbol $\varphi$ has minimal norm if $\|\mathbf{H}_\varphi\|=\|\varphi \|_2$ and maximal $\|\mathbf{H}_\varphi\| = \|\varphi\|_\infty$. The both only $|\varphi|$ is constant almost everywhere or, equivalently, a multiple an inner function. We show that norm-attaining norm, then norm. If continuous but n...