In the title compound, C15H13N3O, the pyrrolyl and phenyl rings make dihedral angles of 58.99 (5) and 34.95 (5)°, respectively, with the central pyrazole ring. In the crystal, weak, pairwise C-H⋯O inter-actions across centers of symmetry form dimers, which are further associated into corrugated sheets running approximately parallel to (100) via weak C-H⋯N inter-actions.

Following the approach introduced by Cavers and Ho, the performance of component-interleaved multidimensional constellations over the Rayleigh fading channel is evaluated analytically. Error probabilities are approximated by the union bound using an exact expression of the pairwise error probability. Simulation results show that this bound can be used effectively as a design criterion for the s...

The regularity lemma of Szemerédi asserts that one can partition every graph into a bounded number of quasi-random bipartite graphs. In some applications however, one would like to have a strong control on how quasi-random these bipartite graphs are. Alon, Fischer, Krivelevich and Szegedy obtained a powerful variant of the regularity lemma, which allows one to have an arbitrary control on this ...

A subgroup $H\leq G$ is said to be almost normal if every conjugate of $H$ commensurable $H$. If normal, there a well-defined quotient space $G/H$. We show that group $G$ has type $F_{n+1}$ and contains an coarse $PD_n$ with $e(G/H)=\infty$, then whenever $G'$ quasi-isometric $G$, it $H'$ Moreover, the spaces $G/H$ $G'/H'$ are quasi-isometric. This generalises theorem Mosher-Sageev-Whyte, who p...

Let H be a finite Hopf algebra with CH,H = C −1 H,H . The duality theorem is shown for H, i.e., (R#H)#H ∗̂ ∼= R ⊗ (H⊗̄H ) as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.

Let H be a finite Hopf algebra with CH,H = C −1 H,H . The duality theorem is shown for H, i.e., (R#H)#H ∗̂ ∼= R ⊗ (H⊗̄H ) as algebras in C. Also, it is proved that the Drinfeld double (D(H), [b]) is a quasi-triangular Hopf algebra in C. 2000 Mathematics subject Classification: 16w30.