Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Low temperature crystal structures of two rhodanine derivatives, 3-amino rhodanine and 3-methyl rhodanine: geometry of the rhodanine ring

Rhodanines (2-thio-4-oxothiazolidines) are synthetic small molecular weight organic molecules with diverse applications in biochemistry, medicinal chemistry, photochemistry, coordination chemistry and industry. The X-ray crystal structure determination of two rhodanine derivatives, namely (I), 3-aminorhodanine [3-amino-2-thio-4-oxothiazolidine], C3H4N2OS2, and (II) 3-methylrhodanine [3-methyl-2-thio-4-oxothiazolidine], C4H5NOS2, have been conducted at 100 K. I crystallizes in the monoclinic space group P2(1)/n with unit cell parameters a = 9.662(2), b = 9.234(2), c = 13.384(2) angstrom, beta = 105.425(3)degrees, V = 1151.1(3) angstrom(3), Z = 8 (2 independent molecules per asymmetric unit), density (calculated) = 1.710 mg/m(3), absorption coefficient = 0.815 mm(-1). II crystallizes in the orthorhombic space group Iba2 with unit cell a = 20.117(4), b = 23.449(5), c = 7.852(2) angstrom, V = 3703.9(12) angstrom(3), Z = 24 (three independent molecules per asymmetric unit), density (calculated) = 1.584 mg/m(3), absorption coefficient 0.755 mm(-1). For I in the final refinement cycle the data/restraints/parameter ratios were 2639/0/161, goodness-of-fit on F-2 = 0.934, final R indices [I > 2sigma(I)] were R1 = 0.0299, wR2 = 0.0545 and R indices (all data) R1 = 0.0399, wR2 = 0.0568. The largest difference peak and hole were 0.402 and -0.259 e angstrom(-3). For II in the final refinement cycle the data/restraints/parameter ratios were 3372/1/221, goodness-of-fit on F(2) = 0.950, final R indices [I > 2sigma(I)] were R1 = 0.0407, wR2 = 0.1048 and R indices (all data) R1 = 0.0450, wR2 = 0.1088. The absolute structure parameter = 0.19(9) and largest difference peak and hole 0.934 and -0.301 e angstrom(-3). Details of the geometry of the five molecules (two for I and three for II) and the crystal structures are fully discussed. Corresponding features of the molecular geometry are highly consistent and firmly establish the geometry of the rhodanine

Central nervous system drugs: Low temperature X-ray structures of (I) the base 5-(2,3-dichlorophenyl)-2,4-diamino-6-fluoromethyl-pyrimidine (4030W92) and (II) 5-(2,6-dichlorophenyl)-1-H-2,4-diamino-6-methyl-pyrimidine methanesulphonic acid salt (227C89)

The X-ray crystal structures of (I), the base 4030W92, 5-(2,3-dichlorophenyl)-2,4-diamino-6-fluoromethyl-pyrimidine, C11H9Cl2FN4, and (II) 227C89, the methanesulphonic acid salt of 5-(2,6-dichlorophenyl)-1-H-2,4-diamino-6-methyl-pyrimidine, C11H11Cl2N4 center dot CH3O3S, have been carried out at low temperature. A detailed comparison of the two structures is given. Structure (I) is non-centrosymmetric, crystallizing in space group P2(1) with unit cell a = 10.821(3), b = 8.290(3), c = 13.819(4) angstrom, beta = 105.980(6)degrees, V = 1191.8(6) angstrom(3), Z = 4 (two molecules per asymmetric unit) and density (calculated) = 1.600 mg/m(3). Structure (II) crystallizes in the triclinic space group P (1) over bar with unit cell a = 7.686(2), b = 8.233(2), c = 12.234(2) angstrom, alpha = 78.379(4), beta = 87.195(4), gamma = 86.811(4)degrees, V = 756.6(2) angstrom(3), Z = 2, density (calculated) = 1.603 mg/m(3). Final R indices [I > 2sigma(I)] are R1 = 0.0572, wR2 = 0.1003 for (I) and R1 = 0.0558, wR2 = 0.0982 for (II). R indices (all data) are R1 = 0.0983, wR2 = 0.1116 for (I) and R1 = 0.1009, wR2 = 0.1117 for (II). 5- Phenyl-2,4 diaminopyrimidine and 6-phenyl-1,2,4 triazine derivatives, which include lamotrigine (3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine), have been investigated for some time for their effects on the central nervous system. The three dimensional structures reported here form part of a newly developed data base for the detailed investigation of members of this structural series and their biological activities.

A vibrational spectroscopic investigation of rhodanine and its derivatives in the solid state

Raman and infrared spectra are reported for rhodanine, 3-aminorhodanine and 3-methylrhodanine in the solid state. Comparisons of the spectra of non-deuterated/deuterated species facilitate discrimination of the bands associated with N-H, NH2, CH2 and CH3 vibrations. DFT calculations of structures and vibrational spectra of isolated gas-phase molecules, at the B3-LYP/cc-pVTZ and B3-PW91/cc-pVTZ level, enable normal coordinate analyses in terms of potential energy distributions for each vibrational normal mode. The cis amide I mode of rhodanine is associated with bands at ~ 1713 and 1779 cm-1, whereas a Raman and IR band at ~ 1457 cm-1 is assigned to the amide II mode. The thioamide II and III modes of rhodanine, 3-aminorhodanine and 3-methylrhodanine are observed at 1176 and 1066/1078; 1158 and 1044; 1107 and 984 cm-1 in the Raman and at 1187 and 1083; 1179 and 1074; 1116 and 983 cm-1 in the IR spectra, respectively.

Low temperature crystal structure of N-Acetyl-L-Glutamic acid: comparison with the DFT calculated structure

N-acetyl-L-glutamic acid, crystallizes in the orthorhombic space group P2(1)2(1)2(1) with unit cell parameters a = 4.747(3), b = 12.852(7), c = 13.906(7) Å, V = 848.5(8) Å3, Z = 4, density (calculated) = 1.481 mg/m3, linear absorption coefficient 0.127 mm−1. The crystal structure determination was carried out with MoKalpha X-ray data measured with liquid nitrogen cooling at 100(2) K temperature. In the final refinement cycle the data/restraints/parameter ratios were 1,691/0/131; goodness-of-fit on F(2) = 1.122. Final R indices for [I > 2sigma(I)] were R1 = 0.0430, wR2 = 0.0878 and R indices (all data) R1 = 0.0473, wR2 = 0.0894. The largest electron density difference peak and hole were 0.207 and −0.154 eÅ(−3). Details of the molecular geometry are discussed and compared with a model DFT structure calculated using Gaussian 98.

Low temperature X-ray structures of two crystalline forms (I) and (II) of the pyrimidine derivative and sodium channel blocker BW1003C87: 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine

The X-ray crystal structures of two crystalline forms of 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine, C10H7Cl3N4 (code name BW1003C87) (I) and (II), have been carried out at liquid nitrogen temperature. A detailed comparison of the two structures is given. Both are centrosymmetric, with structure (I) in the triclinic space group P (1) over bar unit cell a = 6.4870(10), b = 9.216(2), c = 12.016(2) angstrom, alpha = 75.78(3)degrees, beta = 89.95(3)degrees, gamma = 83.45(3)degrees, V = 691.5(2) angstrom(3), Z = 2 and density (calculated) = 1.544 Mg/m(3); and (II) in the monoclinic space group P2(1)/c, unit cell a = 12.000(2), b = 7.518(2), c = 13.450(3) angstrom, beta = 97.87(3)degrees, V = 1202.0(5) angstrom(3), Z = 4, Density (calculated) = 1.600 Mg/m(3). Structure (I) includes a solvated CH3OH in the lattice. Final R indices [I > 2sigma(I)] are R1 = 0.0427, wR2 = 0.1075 for (I) and R1 = 0.0487, wR2 = 0.1222 for (II). R indices (all data) are R1 = 0.0470, wR2 = 0.1118 for (I) and R1 = 0.0623, wR2 = 0.1299 for (II). 5-Phenyl-2,4 diaminopyrimidine and 6-phenyl-1,2,4 triazine derivatives, which include lamotrigine (3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine), have been investigated for some time for their effects on the central nervous system. Both lamotrigine and 5-(2,3,5-trichlorophenyl)-2,4-diaminopyrimidine (code name BW1003C87), the subject of the present study, are anticonvulsant as well as neuroprotective in models of brain ischaemia and in a model of white matter ischaemia. BW1003C87 is a sodium channel blocker which also reduces the release of the neurotransmitter glutamate. The three dimensional structures reported here form part of a newly developed data base for the detailed investigation of members of this drug family and their biological activities.

X-ray crystallographic structures of two lamotrigine analogues: (I) 3,5-diamino-6-(2-chlorophenyl)-1,2,4-triazine water solvate and (II) 3,5-diamino-6-(3,6-dichlorophenyl)-1,2,4-triazine methanol solvate

The X-ray crystal structures of two lamotrigine derivatives (I) 3,5-diamino-6-(2-chlorophenyl)-1,2,4-triazine, C9H8ClN5, (465BL) as a hydrate, and (II) 3,5-diamino-6-(3,6-dichlorophenyl)-1,2,4-triazine, C9H7Cl2N5, (469BR) as a methanol solvate, have been carried out at liquid nitrogen temperature and room temperature, respectively. A detailed comparison of the two structures is given. Both are centrosymmetric with (I) in the orthorhombic space group Pbca, a = 12.2507(3), b = 15.7160(6), c = 21.71496(9) angstrom, Z = 16, and (II) in the monoclinic space group C2/c, a = 38.553(3), b = 4.9586(2), c = 14.546(2) angstrom, beta = 111.59(1)degrees, Z = 8. Final R indices [I > 2sigma(I)] for (I) are R1 = 0.0670, wR2 = 0.1515 and for (II) R1 = 0.0434, wR2 = 0.1185. Structure (I) has water of crystallization in the lattice and (II) includes a solvated CH3OH. Structure (I) is characterized by having two crystallographically independent molecules, A and B, of 465BL, per asymmetric unit. Molecule B has a very unusual feature in that the 2-chlorophenyl ring is statistically disordered, occupying site (1) in 87.5% of the structure and site (2) in 12.5% of the structure. Sites (1) and (2) are related by an exact 180 degrees pivot of the phenyl ring about the ring linkage bond. The presence of two independent molecules per asymmetric unit provides an ideal opportunity for the conformational flexibility of the molecule 465BL to be studied. Structure (I) also includes a further unusual feature in that the lattice contains one fully occupied water molecule and an additional solvated water which is only 33% occupied.

Low temperature X-ray crystallographic structures of two lamotrigine analogues: (I) 2-methyl,3-amino, 5-imino-6-(2,3-dichlorophenyl)-1,2,4-triazine water solvate and (II) 2-methyl,3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine isethionate, hemi-hydrate

The X-ray crystal structures of two lamotrigine derivatives (I) 2-methyl, 3-amino, 5-imino-6-(2, 3-dichlorophenyl)-1,2,4-triazine, C10H9Cl2N5, as the hemi hydrate and (II) 2-methyl,3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine, C10H10Cl2N5, as the isethionate-water solvate, have been carried out at liquid nitrogen temperature. A detailed comparison of the two structures is given. Both are monoclinic and centrosymmetric, with (I) in space group C2/c, and (II) in space group P2(1)/n. For (I) the unit cell dimensions are a = 19.5466(10), b = 7.5483(4), c = 15.7861(8) angstrom, beta = 91.458(3)degrees, volume = 2328.4(2) angstrom(3), Z = 8, density = 1.590 Mg/m(3); for (II). For (II) the unit cell dimensions are a = 6.0566(2), b = 11.0084(4) c = 23.9973(9) angstrom, beta = 92.587(3)degrees, volume = 1598.35(10) angstrom(3), Z = 4, density = 1.597 Mg/m(3). For (I) final R indices [I > 2sigma(I)] are R1 = 0.0356, wR2 = 0.0782 and R indices (all data) are R1 = 0.0424, wR2 = 0.0817. For (II) final R indices [I > 2sigma(I)] are R1 = 0.0380, wR2 = 0.0871 and R indices (all data) R1 = 0.0558, wR2 = 0.0949. Both structures have a molecule of water of crystallization and (II) also includes a solvated CH3SO3. Comparisons are made between the two structures. Structure (I) is very unusual in having a = NH group at position C5' on the triazine ring. No other examples of this particular substitution, which is usually -NH2, have been reported.

Journal citation among heterodox economists 1995-2007: Dynamics of community emergence

Purpose – This study aims to investigate the pattern among 17 heterodox economic journals over a prolonged period to provide evidence about the social dynamics among the group of researchers who publish in them and the extent to which they hold or develop a collective identity as heterodox economists. Design/methodology/approach – Traditional approaches to citation analysis are extended by the use of techniques from social network analysis. In addition to citation counts, measures of network position and clique membership are used to identify key journals and turning points in a longitudinal analysis. Findings – Important shifts in the nature of citation within the network of journals are identified in the 1998-2001 period and evidence is found of the emergence of a collective identity. Research limitations/implications – The methods prove a valuable extension of citation analysis and also focus greater consideration on the social relationships that citations represent. They are well suited to addressing the principal limitation of the study, its restriction to journals within the defined community rather than journals in general. Originality/value – This extends traditional approaches to citation analysis, provides an important new technique in identifying emergent collective identities and provides insight into the history and nature of the heterodox economic community.

X-ray crystallographic structures of neuroprotective pyrimidine derivatives: (I) the mesylate salt of BW1003C87 and (II) sipatrigine base

Drugs based on 5-phenyl-2,4 diamino pyrimidine and 6-phenyl-1,2,4 triazine derivatives are well known for their effects on the central nervous system. The study presented here provides detailed crystal structures of two pyrimidine derivatives which have neuroprotective properties in models of both grey and white matter ischemia. Recently published studies suggest that the compounds lamotrigine (a triazine derivative), and the two pyrimidines BW1003C87 (I) and sipatrigine (II) mediate their primary in vivo mode of action by inhibiting voltage-gated Na+ channels. The X-ray crystal structures will contribute valuable data for applications involving binding and modelling studies of the biological actions of these drugs.