Mass spectra of some aminonaphthyridines and aminoquinolines

The mass spectra of all the aminoquinolines, the 2–, 3– and 4-amino-1,5-naphthyridines, some amino-1,6-naphthyridines, and two amino-1,8-naphthyridines with methyl substituents are reported. The major fragment in the aminoquinolines is formed by the loss of HCN from the molecular ion. The most abundant fragment in the aminonaphthyridines is formed by the loss of HCN from the molecular ion except in the 2-amino-1,5-naphthyridine isomer. In both 1,8-naphthyridine isomers investigated, the loss of C₂H₂ is an alternate fragmentation pathway of significance. In all of the compounds investigated, the loss of the primary amino group from the molecular ion was found to be an insignificant fragmentation.     

Potential histidine decarboxylase inhibitors. II. 3-(4-Imidazolyl)-2-pyridine and piperidinecarboxylates

The synthesis of methyl 3-(4-imidazolyl)-2-pyridine ( 12 ) and piperidineearboxylates ( 13 ) is described. Hydrolysates of these esters were found to be devoid of inhibitory activity against histidine decarboxylase. 3-Bromoacetyl-2-pieoline ( 2 ) could be converted to 3-(4-imidazolyl)-2-picoline ( 6 ) by two different routes. Treatment of 6 with peroxide and acetic anhydride, followed by transesterification yielded the 2-hydroxymcthyl pyridine ( 9 ). Oxidation of 9 followed by esterification gave the imidazole pyridine acid ester ( 12 ) which after hydrogenation afforded the imidazolylpiperidine ester ( 13 ).     

Aspects of chloride interference in zinc determination by atomic-absorption spectroscopy with electrothermal atomization

During the determination of zinc in a polluted stream by atomic-absorption with electrothermal atomization, chloride was found to exercise a large negative interference (40%) when a carbon-filament atomizer was used, but not when a graphite-furnace atomizer was used. The effect on the filament method was confirmed and shown to be due to the formation of zinc chloride, and further complicated by interaction of this with iron. This interference could be overcome by the use of aqueous ammonia solution or silver nitrate added as matrix modifier. The absence of interference in the graphite-furnace method is attributed to the liberation of hydrogen and removal of chloride as hydrogen chloride. It is further suggested that these observations offer a basis for the exploration of apparently contradictory reports in the literature.     

Synthetic, Structural, Spectroscopic, and Theoretical Studies of Structural Isomers of the Cluster Pt(3)(&mgr;-PPh(2))(3)Ph(PPh(3))(2). A Unique Example of Core Isomerism in Phosphine Phosphido-Rich Clusters

Two isomers of the phosphido-bridged platinum cluster Pt(3)(&mgr;-PPh(2))(3)Ph(PPh(3))(2) (2 and 3) have been isolated, and their structures have been solved by single-crystal X-ray diffraction. Compound 2 crystallizes in the orthorhombic space group Cmc2(1) with a = 22.192(10) ?, b = 17.650(9) ?, c = 18.182(8) ?, and Z = 4. Compound 3 crystallizes with 2 molecules of dichloromethane in the monoclinic space group C2/c with a = 21.390(10) ?, b = 18.471(9) ?, c = 19.021(11) ?, beta = 105.27(5) degrees, and Z = 4. The two isomers differ essentially in their metal-metal distances and Pt-(&mgr;-PPh(2))-Pt angles. Thus 2, having an imposed C(s) symmetry, contains a bent chain of metal atoms with two short Pt-Pt distances of 2.758(3) ? and a long separation of 3.586(2) ?. In 3, which has an imposed C(2) symmetry, the metal atoms form an isosceles triangle with two Pt-Pt distances of 2.956(3) ? and one of 3.074(4) ?. These isomers can be smoothly interconverted by changing the crystallization solvents. Solution and solid-state (31)P NMR studies have been performed in order to assign the resonances of the different P nuclei and relate their chemical shifts with their structural environments. Raman spectroscopy was used to assign the nu(Pt-Pt) modes of the two structural isomers. Theoretical studies based on extended Hückel calculations and using the fragment molecular orbital approach show that the isomer with the three medium Pt-Pt distances is slightly more stable, in agreement with earlier theoretical predictions. Cluster core isomerism remains a rare phenomenon, and the present example emphasizes the role and the importance of flexible phosphido bridges in stabilizing clusters as well as the unprecedented features which can be observed in phosphine phosphido-rich metal clusters.     

X-ray crystal structures of Ru3(μ-H)(μ-C,N-C5H4N)(CO)10-n (P i Pr3) n,n=0,1: A A case of the hydride following the Phosphine?

The reaction ofRu₃(-H)(-C,N-C₅H₄N)(CO)₁₀ (1) with Pt(P ⁱ Pr₃)(nb)₂ {nb = bicyclo-[2.2.1]hept-2-ene} does not afford any Ru-Pt mixed metal clusters, but gives instead the mono-substituted phosphine derivative Ru₃(-H) (-C,N-C₅H₄N)(CO)₉(P ⁱ Pr₃) (2) as the sole isolable product. Single crystal X-ray studies have been carriedout on 1 and 2. Crystal data for 1: monoclinic, space group P2₁/c,a = 16.9637(10) A,b = 7.6632(5) Á,c = 17.4058(11) Á, = 117.214(5)°,V = 2009.0(2) Á³,R(R _w) = 0.022 (0.034) for 3090 independent absorption corrected data. Crystal data for 2: triclinic, space group P,a = 9.3389(5) Á,b = 11.4376(6) Á,c = 15.1781(8) Á, = 76.454(4), = 79.900(5), = 67.428(5)°,V = 1448.8(2) Á³ R(R _w ) = 0.024 (0.034) for 4564 independent absorption corrected data. In cluster 1 the Ru-Ru bonds are in the range 2.8462(4)-2.8986(4) Á. The hydride and-pyridyl ligand bridge the same Ru-Ru vector, and the Ru(-H) bridge is symmetric, with Ru-H = 1.78(4) and 1.77(4) Á. In cluster 2 the Ru-Ru distances show a greater ranger 2.7267(3)-3.0604(3) Á. The phosphine ligand is bonded to the Ru atom which is not involved in the-pyridyl bridge. In contrast to 1, the hydride and-pyridyl ligands in 2 bridge different Ru-Ru vectors and the resultant Ru(-H)Ru bridge is asymmetric, with Ru-H = 1.70(4) and 1.89(4) Á.     

Juntas in the ℓ1‐grid and Lipschitz maps between discrete tori

We show that if , then is ‐close to a junta depending upon at most coordinates, where denotes the edge‐boundary of in the ‐grid. This bound is sharp up to the value of the absolute constant in the exponent. This result can be seen as a generalisation of the Junta theorem for the discrete cube, from [6], or as a characterisation of large subsets of the ‐grid whose edge‐boundary is small. We use it to prove a result on the structure of Lipschitz functions between two discrete tori; this can be seen as a discrete, quantitative analogue of a recent result of Austin [1]. We also prove a refined version of our junta theorem, which is sharp in a wider range of cases. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 49, 253–279, 2016     

An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students’ initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students’ thinking and learning over time in relation to a set of tasks and activities developed to engender a view of exponential growth as a relation between two continuously covarying quantities. Developed out of two teaching experiments with early adolescents, the EGLT identifies three major stages of students’ conceptual development: prefunctional reasoning, the covariation view, and the correspondence view. The learning trajectory is presented along with three individual students’ progressions through the trajectory as a way to illustrate the variation present in how the participants made sense of ideas about exponential growth.     

Models for single-sector stochastic air traffic flow management under reduced airspace capacity

Air traffic efficiency is heavily influenced by unanticipated factors that result in capacity reduction. Of these factors, weather is the most significant cause of delays in airport and airspace operations. Considering weather-related uncertainty, air traffic flow management involves controlling air traffic through allocation of available airspace capacity to flights. The corresponding decision process results in a stochastic dynamic problem where aircraft on the ground and in the air are controlled based on the evolution of weather uncertainty. We focus on the single-sector version of the problem that is applicable to a majority of cases where a volume of airspace has reduced capacity due to convective weather. We model the decision process through stochastic integer programming formulations and computationally analyse it for tractability. We then demonstrate through actual flight schedule data that a simplistic but practically implementable approximation procedure is a generally effective solution approach for these models.     

The conjugacy problem for automorphism groups of countable homogeneous structures

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.