In the title compound, C(21)H(17)FN(4)O(2)S, the planar indole fused-ring [maximum deviation 0.009 (1) Å] makes dihedral angles of 54.75 (9) and 14.90 (9)°, respectively, with the phenyl ring and the dihydro-thia-zolyl ring. The -CH2CH=CH(2) substituent is disordered over two positions in a 0.51 (1):0.49 (1) ratio. An intra-molecular N-H⋯S hydrogen bond generates an S(5) ring motif. The two ind...

In the title compound, C(34)H(26)F(2)N(2)O(2)S, an intra-molecular O-H⋯N hydrogen bond forms an S(5) ring motif. The piperidine ring adopts a chair conformation. The thia-zolidine ring and one of the pyrrolidine rings adopt envolope conformations with methyl-ene C atoms at the flap, whereas the other pyrrolidine ring adopts a half-chair conformation. The fluoro-substituted benzene rings form di...

Classical obstruction theory can be applied to the problem of finding an S-algebra structure, or a commutative S-algebra structure, on a ring spectrum. It is shown that there is no obstruction to upgrading the homotopy unit in the ring spectrum to a strict unit in the S-algebra.

Let S be a ring with identity in which 2 is invertible. In this paper we describe the structure of quaternion R = H(S) generalization Hamilton?s division real quaternions H H(R).

Cycloaddition reaction between C30 and hula-I, 3-diene was studied within the Snimework of AM I (RHF)level. The reaction involving the double bond between two hexagons and a hexagon and a pentagon, as wellas the cycloaddition products followed by disrotatory ogs s electrocyclic ring openings were considered.Thermodynamics parameters and stability energy and innsation state are evaluated in thre...

Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a λ-ring, {λn}n∈N. However, a priori λ (S) can only be computed recursively, by first computing λ(S), . . . , λ(S). In this paper we establish an explicit formula, expressing λ(S) as a linear combination of classes of G-sets.

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

A silicon dual-ring modulator consisting of two serially cascaded rings with embedded PN junctions is driven by a differential signal pair. We show by simulation and experiment that the device has advantages over the single-ring modulator in terms of optical bandwidth, 3-dB modulation bandwidth and bit rate, at the expense of a 1.7-dB increase in the transmission penalty and a twofold increase ...

In the title salt, C(6)H(14)NO(+)·C(7)H(6)NO(4)S(-), the 2-sulfamoylbenzoate anion has two intra-molecular hydrogen bonds, forming a five membered C-H⋯O and a seven-membered N-H⋯O twisted ring with ring motifs S(5) and S(7), respectively, while the 2-methyl-4-oxopentan-2-aminium cation also has a stabilizing intra-molecular N-H⋯O hydrogen bond with a twisted S(6) ring motif. The anions form inv...

In the title compound, C(13)H(9)ClN(2)O(5)S, the N-C bond in the C-SO(2)-NH-C segment has a gauche torsion with respect to the S=O bonds. The conformation between the N-H bond and the ortho-nitro group in the sulfonyl benzene ring is syn, and that between the C=O and the meta-Cl atom in the benzoyl ring is anti. The mol-ecule is twisted at the S-N bond, with a torsion angle of 65.41 (38)°. The ...