A subgroup H is said to be weakly c∗-normal in a group G if there exists a subnormal subgroup K of G such that HK = G and H ∩ K is s-quasinormally embedded in G. We give some results which generalize some authors’ results.

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.

We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random and v unit vector. In particular, we establish that with high probability, outlier can be distinguished at all times t>1+N−1∕3+ε, any ε>0. The this natural process combines elements non-Hermitian analysis, illustrates some aspects intrinsic instability (even weakly) matrices.

Let Qd denote the hypercube of dimension d. Given d ≥ m, a spanning subgraph G of Qd is said to be (Qd, Qm)-saturated if it does not contain Qm as a subgraph but adding any edge of E(Qd) \E(G) creates a copy of Qm in G. Answering a question of Johnson and Pinto [27], we show that for every fixed m ≥ 2 the minimum number of edges in a (Qd, Qm)-saturated graph is Θ(2 d). We also study weak satura...

Let M⊂B(H) be a von Neumann algebra acting on the (separable) Hilbert space H. We first prove that M is finite if and only if, for every x∈M all vectors ξ,η∈H, coefficient function u↦⟨uxu∗ξ|η⟩ weakly almost periodic topological group UM of unitaries in (equipped with weak operator topology). The main device unique invariant mean C∗-algebra WAP(UM) functions UM. Next, we direct sum diffuse, abel...

In title compound, [Cu(C(8)H(7)O(2))(2)(C(6)H(6)N(4))(2)], the Cu(II) atom (site symmetry ) is coordinated by two N,N'-bidentate 2,2'-biimidazole ligands and two weakly bonded 4-methyl-benzoate anions, resulting in a strongly elongated trans-CuO(2)N(4) octa-hedral geometry. In the crystal, adjacent mol-ecules are linked via pairs of N-H⋯O hydrogen bonds into chains propagating in [010].

We consider the deformed Gaussian Ensemble Hn = Mn + H (0) n in which H (0) n is a diagonal Hermitian matrix and Mn is the Gaussian Unitary Ensemble (GUE) random matrix. Assuming that the Normalized Counting Measure of H (0) n (both non-random and random) converges weakly to a measure N (0) with a bounded support we prove universality of the local eigenvalue statistics in the bulk of the limiti...

The molecules of 3-tert-butyl-5-[(4-methoxybenzyl)amino]-1-phenyl-1H-pyrazole, C21H25N3O, are linked into simple C9 chains by a single C-H...N hydrogen bond. 5-[(Benzotriazol-1-ylmethyl)(4-methoxybenzyl)amino]-3-tert-butyl-1-phenyl-1H-pyrazole, C28H30N6O, crystallizes with Z' = 2 in the space group P2(1)/c. The molecules are weakly linked into centrosymmetric tetramolecular aggregates by a comb...