Positive loop-closed automata: a decidable class of hybrid systems

AbstractThe model-checking problem for real-time and hybrid systems is very difficult, even for a well-formed class of hybrid systems—the class of linear hybrid automata—the problem is still undecidable in general. So an important question for the analysis and design of real-time and hybrid systems is the identification of subclasses of such systems and corresponding restricted classes of analysis problems that can be settled algorithmically. In this paper, we show that for a class of linear hybrid automata called positive loop-closed automata, the satisfaction problem for linear duration properties can be solved by linear programming. We extend the traditional regular expressions with duration constraints and use them as a language to describe the behaviour of this class of linear hybrid automata. The extended notation is called duration-constrained regular expressions. Based on this formalism, we show that the model-checking problem can be reduced formally to linear programs

(2,9-Dimethyl-1,10-phenanthroline-κ2 N,N′)bis­(2-hydroxy­benzoato)-κO;κ2 O,O′-cobalt(II)

In the title compound, [Co(C7H5O3)2(C14H12N2)], the CoII ion is five-coordinated by two N atoms from one 2,9-dimethyl-1,10-phenanthroline (dmphen) ligand and three O atoms from two 2-hydroxy­benzoate anions in a distorted trigonal bipyramidal geometry. The carboxyl­ate group of one of the two 2-hydroxy­benzoate anions is monodentate with a normal Co—O distance [1.9804 (18) Å], while the other is bidentate with two longer Co—O bonds [2.1981 (18) and 2.1359 (19) Å]. The crystal structure is stabilized by aromatic π–π stacking inter­actions [centroid–centroid distances of 4.0380 (3) and 3.8216 (3) Å between dmphen/dmphen and benzene/dmphen rings, respectively] and C—H⋯π(benzene) inter­actions

Aqua­(2,9-dimethyl-1,10-phenanthroline-κ2 N,N′)bis­(2-hydroxy­benzoato-κO)manganese(II) 2,9-dimethyl-1,10-phenanthroline hemisolvate

In the asymmetric unit of the title complex, [Mn(C7H5O3)2(C14H12N2)(H2O)]·0.5C14H12N2, the MnII ion is coordinated by a bidentate 2,9-dimethyl-1,10-phenanthroline (dmphen) mol­ecule, one water mol­ecule and two monodentate 2-hydroxy­benzoate anions in a distorted trigonal-bipyramidal geometry. The OH group of the 2-hydroxy­benzoate anion is disordered over two positions with site-occupancy factors of 0.5. The asymmetric unit is completed with by an uncoordinated half-mol­ecule of dmphen, disordered about a crystallographic twofold axis. In the crystal structure, mol­ecules are linked into a two-dimensional framework by O—H⋯N, O—H⋯O and C—H⋯O hydrogen bonds. The packing of the structure is further stabilized by π–π stacking inter­actions involving dmphen mol­ecules, with centroid–centroid separations of 3.8027 (3) and 3.6319 (3) Å

Aqua­(dicyanamido-κN 1)(2,9-dimethyl-1,10-phenanthroline-κ2 N,N′)(nitrato-κ2 O,O′)cobalt(II)–2,9-dimethyl-1,10-phenanthroline–water (2/1/2)

In the title compound, 2[Co(C2N3)(NO3)(C14H12N2)(H2O)]·C14H12N2·2H2O, the CoII ion is coordinated by a bidentate 2,9-dimethyl-1,10-phenanthroline (dmphen) ligand, a bidentate nitrate anion, a water mol­ecule and a monodentate dicyan­amide group in a distorted octa­hedral geometry. One uncoordinated dmphen mol­ecule is situated on a crystallographic twofold axis and the asymmetric unit is completed by one water mol­ecule. In the crystal, mol­ecules form a one-dimensional framework in the [001] direction through O—H⋯N and O—H⋯O hydrogen bonds. The crystal packing is further stabilized by π–π stacking inter­actions between the dmphen rings of neighboring mol­ecules, with a centroid–centroid separation of 3.5641 (8) Å and a partially overlapped arrangement of parallel dmphen rings with a distance of 3.407 (2) Å

catena-Poly[[(2,9-dimethyl-1,10-phenanthroline-κ2 N,N′)lead(II)]-di-μ-2-hydroxy­benzoato-κ3 O 1,O 1′:O 2;κ3 O 2:O 1,O 1′]. Corrigendum

Corrigendum to Acta Cryst. (2007), E63, m2678

Bis(μ-3-hydroxy­benzoato-κ3 O,O′:O)bis­[aqua­(3-hydroxy­benzoato-κ2 O,O′)(1,10-phenanthroline-κ2 N,N′)lead(II)] monohydrate

In the centrosymmetric binuclear title complex, [Pb2(C7H5O3)4(C12H8N2)2(H2O)2]·H2O, each Pb atom is eight-coordinated in a PbO6N2 environment by two N atoms from the 1,10-phenanthroline (phen) ligand, five carboxylate O atoms from four 3-hydroxy­benzoate anions and one O atom from the coordinated water mol­ecule in a distorted bicapped trigonal-prismatic geometry. The benzoate groups coordinate each PbII atom in two different ways. Two benzoate ions behave as bidentate ligands to the Pb atom, and another benzoate ion bridges the Pb atoms, forming a binuclear structure. The dimeric units are packed via O—H⋯O hydrogen bonds and π–π inter­actions between the aromatic rings of neighboring mol­ecules, with centroid–centroid distances of 3.552 (2) and 3.641 (2) Å

Thermoset Shape‐Memory Polyurethane with Intrinsic Plasticity Enabled by Transcarbamoylation

Thermoset polymers are known for their superior thermomechanical properties, but the chemical crosslinking typically leads to intractability. This is reflected in the great differences between thermoset and thermoplastic shape‐memory polymers; the former exhibit a robust shape memory but are not capable of redefining the permanent shape. Contrary to current knowledge, we reveal here that a classical thermoset shape‐memory polyurethane is readily capable of permanent reshaping (plasticity) after a topological network rearrangement that is induced by transcarbamoylation. By employing the Jianzhi technique (also known as kirigami), unexpected shape‐shifting versatility was observed for this otherwise classical material. As the essential carbamate moiety in polyurethanes is one of the most common polymer building units, we anticipate that our finding will have significant benefits beyond shape shifting.Thermoset polymers are known for their superior thermomechanical properties, but the chemical crosslinking typically leads to intractability. However, a classical thermoset shape‐memory polyurethane was now shown to be readily capable of permanent reshaping (plasticity) after a topological network rearrangement that is induced by transcarbamoylation.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137615/1/anie201602847.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137615/2/anie201602847-sup-0001-misc_information.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137615/3/anie201602847_am.pd

The economic burden of chronic neurological disease

Figure S2. Forest plots of the 5 studies evaluating the association between EP and endometriosis according to the endometriosis stage (stage 4 versus stage 1, and stages 3–4 versus stages 1–2). (TIFF 2134 kb

Bis(benzoato-κ2 O,O′)(2,9-dimethyl-1,10-phenanthroline-κ2 N,N′)cobalt(II)

In the title compound, [Co(C7H5O2)2(C14H12N2)], the CoII ion is located on a twofold rotation axis and is chelated by a 2,9-dimethyl-1,10-phenanthroline (dmphen) ligand and two benzoate anions in a distorted octa­hedral geometry. The crystal packing is stabilized by π–π inter­actions between parallel dmphen ligands of neighbouring mol­ecules, with a face-to-face distance of 3.411 (2) Å