The asymmetric unit of the title compound, 2C23H33NO2S·H2O, contains one organic mol-ecule in a general position and one co-crystallized water mol-ecule on a crystallographic twofold axis. Each water mol-ecule serves as a hydrogen-bond donor to a pair of S=O acceptors on symmetry-related mol-ecules. Thus, each trio of mol-ecules forms one title formula unit. These groupings are further connecte...

We unify a view on three extensions of Process Rewrite Systems (PRS) and compare their expressive power with that of PRS. We show that the class of Petri nets is less expressive up to bisimulation equivalence than the class of PA processes extended with a finite state control unit. Further we show our main result that the reachability problem for PRS extended with a so called weak finite state ...

There are two independent mol-ecules in the asymmetric unit of the title compound, C(19)H(19)NO(4). The indole unit in each mol-ecule is essentially planar, with mean deviations of 0.017 (1) and 0.013 (1) Å and forms dihedral angles of 50.17 (7) and 26.05 (6)° with the phenyl ring. In the crystal, mol-ecules are linked by weak C-H⋯π inter-actions.

The title compound, C16H13NO6, exhibits a biphenyl unit with a dihedral angle between the two aryl rings of 56.01 (5)°. The two ester groups vary slightly from planarity, with ar-yl-ester dihedral angles of 4.57 (5) and 16.73 (5)°. The nitro group is turned from the aromatic unit with an ar-yl-nitro dihedral angle of 48.66 (4)°. In the crystal, mol-ecules are connected by weak C-H⋯O inter-actio...

In the title compound, C(34)H(30)N(2)O(6)·0.5C(4)H(8)O(2), there are two mol-ecules in the asymmetric unit and the structure is stabilized by C-H⋯O inter-actions. The two nonsolvent mol-ecules of the asymmetric unit are linked together by a weak C-H⋯O hydrogen bond. The ethyl acetate mol-ecule is present as a space filler and does not participate in the hydrogen-bonding network.

The title compound, C(11)H(10)O(2), crystallizes with two independent mol-ecules in the asymmetric unit. In one mol-ecule, the dihedral angle between the mean planes of the C-C=C-C group of the diene unit and essentially planar cyclo-hexene ring is 51.07 (9)°, while in the other mol-ecule it is 54.49 (12)°. In the crystal structure, weak inter-molecular C-H⋯O inter-actions link the mol-ecules i...

We first introduce 20 weak forms of continuity, which are closely related to 5 known weak forms of continuity. Then we classify them into 9 groups and give 12 decompositions of continuity. 1. Introduction. Continuity is one of the most important concepts in mathematics. In order to find deep properties of continuity, many weak forms of continuity were introduced in the literature. For instance,...

In this work we define generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures recently proposed in the literature. Moreover, we study some properties of the interior, the closure and other concepts in this new context. Mathematics Subject Classification: Primary 54A05, Secondary 54D10

This paper considers a supply chain where a manufacturer sells its product through a retailer. In such a market, a potential entrant can make a substitute product by imitating the incumbent's product and then sells it to the common market with one of three alternative entry modes: (i) selling through the incumbent's retailer, (ii) selling through another independent retailer, or (iii) selling d...

The ®rst of the title compounds, C31H27NO4S, (V), crystallizes in the monoclinic space group P21/c with two independent molecules in the asymmetric unit, while the second, C23H27Cl2NS, (IX), crystallizes in the orthorhombic space group Pbca with one molecule in the asymmetric unit. In both crystal structures, the 1,3-thiazolidine ring adopts a half-chair conformation. The crystal structures are...