Relative reactivities of bicyclo[3.2.1]octa-2,3-diene and 1,2-cycloheptadiene with conjugated dienes and styrene

Bicyclo[3.2.1]octa-2,3-diene (2) and 1,2-cycloheptadiene (3), generated by treatment of the corresponding dichlorides 4 and 5 with magnesium, were found to undergo cycloaddition reactions with 2,3-dimethylbutadiene, styrene, and 1,3-cyclopentadiene. 2, but not 3, was also found to undergo a (2 + 2) cycloaddition reaction with cis-pentadiene. The relative reactivities of 2 and 3 with cis-pentadiene, 2,3-dimethylbutadiene, styrene, and 1,3-cyclopentadiene at 60° in THF were found to be: 0·18, —; 1·0, 1·0; 0·60, 7·5; and 4·0, 150.     

Critical star multigraphs

A star-multigraphG is a multigraph in which there is a vertexv ⁺ which is incident with each non-simple edge. It is critical if it is connected, Class 2 and(G\e) < (G) for eache E(G). We show that, ifG is any star multigraph, then(G) (G) + 1. We investigate the edge-chromatic class of star multigraphs with at most two vertices of maximum degree. We also obtain a number of results on critical star multigraphs. We shall make use of these results in later papers.     

PEG-400 as an efficient reaction medium for the synthesis of 2,4,5-triaryl-1H-imidazoles and 1,2,4,5-tetraaryl-1H-imidazoles

An efficient protocol for the one-pot multicomponent synthesis of various 2,4,5-triaryl- IH-imidazoles and 1,2,4,5-tetraaryl-1H-imidazoles using PEG-400 as reaction medium is described. This method has the advantages of good yields, less pollution and simple reaction conditions.     

Substituting open educational resources for commercial curriculum materials: effects on student mathematics achievement in elementary schools

Open Educational Resources (OER) have the potential to replace commercial learning materials in education. An empirical examination of this potential was conducted, comparing the end-of-year mathematics test results of 12,110 elementary school students clustered within 95 schools from five school districts in the state of Washington in the United States of America. Of this group, 6796 students used open learning materials, and 5314 used commercial educational resources. When three years of test scores were considered, there were no statistically significant differences in the exam scores of students who used open versus commercial curriculum materials. The lack of statistical significance may have practical significance, demonstrating that OER can replace conventional materials without impacting student performance, while potentially reducing costs and allowing for local modification.     

High resolution electrospray ionization ion mobility spectrometry

Current commercially available ion mobility spectrometers are intended for the analysis of chemicals in the gas phase. Sample introduction methods, such as direct air sampling, a GC injector or a thermal desorber, are commonly an integral part of these instruments. This paper describes an electrospray ionization ion mobility spectrometer system that allows direct introduction samples in solution phase. This allows direct analysis of non-volatile organic and biological samples, and avoids decomposition of thermally liable samples, providing reliable chemical identification. In addition, the new ion mobility spectrometer allows mobility analysis with high resolving power. Commonly used commercial IMS systems provide resolving powers between 10 and 30; this new ion mobility spectrometer has resolving power greater than 60 for routine analysis. A high resolution instrument is necessary for many applications where a complex mixture needs to be separated and quantified. This paper demonstrates the advantages of using a high resolution ion mobility spectrometer and an electrospray ionization source for the analysis of non-volatile pharmaceuticals as well as dissolved explosive in solution phase.     

On the number of (r,r+1)‐ factors in an (r,r+1)‐factorization of a simple graph

For integers d≥0, s≥0, a (d, d+s)‐graph is a graph in which the degrees of all the vertices lie in the set {d, d+1, …, d+s}. For an integer r≥0, an (r, r+1)‐factor of a graph G is a spanning (r, r+1)‐subgraph of G. An (r, r+1)‐factorization of a graph G is the expression of G as the edge‐disjoint union of (r, r+1)‐factors. For integers r, s≥0, t≥1, let f(r, s, t) be the smallest integer such that, for each integer d≥f(r, s, t), each simple (d, d+s) ‐graph has an (r, r+1) ‐factorization with x (r, r+1) ‐factors for at least t different values of x. In this note we evaluate f(r, s, t). © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 257‐268, 2009     

Flexible N,N,N-chelates as supports for iron and cobalt chloride complexes; synthesis, structures, DFT calculations and ethylene oligomerisation studies

The aryl-substituted N-picolylethylenediamine and diethylenetriamine ligands, (ArNHCH(2)CH(2))[(2-C(5)H(4)N)CH(2)]NH and (ArNHCH(2)CH(2))(2)NH (Ar = 2,6-Me(2)C(6)H(3), 2,4,6-Me(3)C(6)H(2)), have been prepared by employing palladium-catalysed N-C(aryl) coupling reactions of the corresponding primary amines with aryl bromide. Treatment of MCl(2) with (ArNHCH(2)CH(2))[(2-C(5)H(4)N)CH(2)]NH affords [[(ArNHCH(2)CH(2))((2-C(5)H(4)N)CH(2))NH]CoCl(2)](Ar = 2,6-Me(2)C(6)H(3) 1a; 2,4,6-Me(3)C(6)H(2)) 1b and [[(ArNHCH(2)CH(2))((2-C(5)H(4)N)CH(2))NH]FeCl(2)](n)(n= 1, Ar = 2,6-Me(2)C(6)H(3) 2a; n= 2, 2,4,6-Me(3)C(6)H(2) 2b) in high yield. The X-ray structures of 1a and 1b are isostructural and reveal the metal centres to adopt distorted trigonal bipyramidal geometries with the N,N,N-chelates adopting fac-structures. A facial coordination mode of the ligand is also observed in bimetallic 2b, however, in 2a the N,N,N-chelate adopts a mer-configuration with the metal centre adopting a geometry best described as square pyramidal. Solution studies indicate that mer-fac isomerisation is a facile process for these systems at room temperature. Quantum mechanical calculations (DFT) have been performed on 1a and 2a, in which the ligands employed are identical, and show the fac- to be marginally more stable than the mer-configuration for cobalt (1a) while for iron (2a) the converse is evident. Reaction of (ArNHCH(2)CH(2))(2)NH with CoCl(2) gave the five-coordinate complexes [[(ArNHCH(2)CH(2))(2)NH]CoCl(2)](Ar = 2,6-Me(2)C(6)H(3) 3a, 2,4,6-Me(3)C(6)H(2) 3b), in which the ligand adopts a mer-configuration; no reaction occurred with FeCl(2). All complexes 1-3 act as modest ethylene oligomerisation catalysts on activation with excess methylaluminoxane (MAO); the iron systems giving linear alpha-olefins while the cobalt systems give mixtures of linear and branched products.     

Dielectrophoretic force microscopy of aqueous interfaces

A novel scanning probe microscopy technique has allowed dielectrophoretic force imaging with nanoscale spatial resolution. Dielectrophoresis (DEP) traditionally describes the mobility of polarizable particles in inhomogeneous alternating current (ac) electric fields. Integrating DEP with atomic force microscopy allows for noncontact imaging with the image contrast related to the local electric polarizability. By tuning the ac frequency, dielectric spectroscopy can be performed at solid/liquid interfaces with high spatial resolution. In studies of cells, the frequency-dependent dielectrophoretic force is sensitive to biologically relevant electrical properties, including local membrane capacitance and ion mobility. Consequently, dielectrophoretic force microscopy is well suited for in vitro noncontact scanning probe microscopy of biological systems.