Weakly coordinating anions: crystallographic and NQR studies of halogen-metal bonding in silver, thallium, sodium, and potassium halomethanesulfonates

35Cl, (79,81)Br, and (127)I NQR (nuclear quadrupole resonance) spectroscopy in conjunction with X-ray crystallography is potentially one of the best ways of characterizing secondary bonding of metal cations such as Ag(+) to halogen donor atoms on the surfaces of very weakly coordinating anions. We have determined the X-ray crystal structure of Ag(O(3)SCH(2)Cl) (a = 13.241(3) A; b = 7.544(2) A; c = 4.925(2) A; orthorhombic; space group Pnma; Z = 4) and compared it with the known structure of Ag(O(3)SCH(2)Br) (Charbonnier, F.; Faure, R.; Loiseleur, H. Acta Crystallogr., Sect. B 1978, 34, 3598-3601). The halogen atom in each is apical (three-coordinate), being weakly coordinated to two silver ions. (127)I NQR studies on Ag(O(3)SCH(2)I) show the expected NQR consequences of three-coordination of iodine: substantially reduced NQR frequencies nu(1) and nu(2) and a fairly small NQR asymmetry parameter eta. The reduction of the halogen NQR frequency of the coordinating halogen atom in Ag(O(3)SCH(2)X) becomes more substantial in the series X = Cl < Br < I, indicating that the coordination to Ag(+) strengthens in this series, as expected from hard-soft acid-base principles. The numbers of electrons donated by the organic iodine atom to Ag(+) have been estimated; these indicate that the bonding to the cation is weak but not insignificant. We have not found any evidence for the bonding of these organohalogen atoms to another soft-acid metal ion, thallium. A scheme for recycling of thallium halide wastes is included.     

Isomorphism of inclusion compounds built with composite host lattices of thiadiazole and V-shaped molecules with the existence of tetrabutylammonium guest template

By using 4,4′-dihydroxydiphenylsulfone (BPS) and 4,4′-dihydroxydiphenylsulfide (BTS) react with amidinethiourea and tetrabutylammonium respectively, two isomorphs of inclusion compounds of (n-C₄H₉)₄N⁺·C₁₂H₉O₄S^?·C₂H₄N₄S (1) and (n-C₄H₉)₄N⁺·C₁₂H₉O₂S^?·C₂H₄N₄S (2) were prepared and characterized by Single crystal X-ray diffraction. Although two varied types of V-shaped molecules were selected to react in the actual experimental process, two isomorphs with similar packing modes were finally obtained. Interestingly, amidinothiourea molecule occurred in situ oxidation reaction to generate a new compound of 3,5-dimido-1,2,4,-thiadiazole during the experiments, and these two inclusion compounds here are the pioneer examples of thiadiazole and tetraalkylammonium and can be regarded as two isomorphs due to their similar crystallization modes. In these two isomorphs, thiadiazole molecules derived from amidinothiourea link with various V-type molecules to develop the similar dumbbell-type hydrogen-bonded ribbons by the alike hydrogen bonding modes, then the ribbons interpenetrate with tetrabutylammonium to result in two stable isomorphism structures.     

The ecology of instructional teacher leadership

Instructional teacher leadership, in which classroom teachers intentionally influence the practice of their colleagues, is a complex social dynamic. In this article, we argue for the use of an analytic framework that acknowledges this complexity, and we apply it to three cases of teacher leaders, all in the context of elementary and middle grades mathematics instruction. In each case, Urie Bronfenbrenner’s ecological systems theory, complemented by social network analysis, proves useful for understanding the unique circumstances and the leadership activities in which the individual is able to engage. This comprehensive framework accounts for factors ranging from those internal to the individual to those inherent in the society at large, viewing the teacher leader as part of a complex social ecosystem of other individuals, institutions, policies and cultural norms. Following a brief overview of the theory, we apply it to the three cases in sequence. We conclude with implications for the field, both those who study instructional teacher leadership and those who train and support teacher leaders.     

Solving complex PDE systems for pricing American options with regime‐switching by efficient exponential time differencing schemes

In this article, we study the numerical solutions of a class of complex partial differential equation (PDE) systems with free boundary conditions. This problem arises naturally in pricing American options with regime‐switching, which adds significant complexity in the PDE systems due to regime coupling. Developing efficient numerical schemes will have important applications in computational finance. We propose a new method to solve the PDE systems by using a penalty method approach and an exponential time differencing scheme. First, the penalty method approach is applied to convert the free boundary value PDE system to a system of PDEs over a fixed rectangular region for the time and spatial variables. Then, a new exponential time differncing Crank–Nicolson (ETD‐CN) method is used to solve the resulting PDE system. This ETD‐CN scheme is shown to be second order convergent. We establish an upper bound condition for the time step size and prove that this ETD‐CN scheme satisfies a discrete version of the positivity constraint for American option values. The ETD‐CN scheme is compared numerically with a linearly implicit penalty method scheme and with a tree method. Numerical results are reported to illustrate the convergence of the new scheme. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

An efficient ETD method for pricing American options under stochastic volatility with nonsmooth payoffs

Based on Cox and Matthews Exponential Time Differencing (ETD) approach, a fourth–order strongly–stable method having real distinct poles is developed and applied to solve American options under stochastic volatility with nonsmooth payoffs. A computationally efficient version of the method is constructed using partial fraction splitting technique. This approach requires to solve several backward Euler‐type linear systems at each time step. Numerical experiments are presented to demonstrate the computational efficiency, accuracy, and reliability of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Invariant Kekulé structures in fullerene graphs

Fullerene graphs are trivalent plane graphs with only hexagonal and pentagonal faces. They are often used to model large carbon molecules: each vertex represents a carbon atom and the edges represent chemical bonds. A totally symmetric Kekulé structure in a fullerene graph is a set of independent edges which is fixed by all symmetries of the fullerene and molecules with totally symmetric Kekulé structures could have special physical and chemical properties, as suggested in [Austin, S.J, and J. Baker, P. W. Fowler, D. E. Manolopoulos, Bond-stretch Isomerism and the Fullerenes, J. Chem. Soc. Perkin Trans. 2 (1994), 2319–2323] and [Rogers, K.M., and P. W. Fowler, Leapfrog fullerenes, Huckel bond order and Kekulé structures, J. Chem. Soc. Perkin Trans. 2 (2001), 18–22]. All fullerenes with at least ten symmetries were studied in [Graver, J.E. The Structure of Fullerene Signature, DIMACS Series of Discrete Mathematics and Theoretical Computer Science 64, AMS (2005), 137–166.] and a complete catalog was given in [Graver, J. E. Catalog of All Fullerene with Ten or More Symmetries DIMACS Series of Discrete Mathematics and Theoretical Computer Science 64 AMS (2005), 167–188]. Starting from this catalog in [Bogaerts, M., and G. Mazzuoccolo, G.Rinaldi, Totally symmetric Kekulé structures in fullerene graphs with ten or more symmetries, MATCH Communications in Mathematical and in Computer Chemistry 69 (2013), 677–705] we established exactly which of them have at least one totally symmetric Kekulé structure.     

Panax quinquefolius (North American Ginseng) Polysaccharides as Immunomodulators: Current Research Status and Future Directions

Panax quinquefolius (North American ginseng, NAG) is a popular medicinal plant used widely in traditional medicine. NAG products are currently available in various forms such as roots, extracts, nutraceuticals, dietary supplements, energy drinks, etc. NAG polysaccharides are recognized as one of the major bioactive ingredients. However, most NAG reviews are focused on ginsenosides with little information on polysaccharides. NAG polysaccharides have demonstrated a therapeutic activity in numerous studies, in which many of the bioactivities involve regulation of the immune response. The purpose of this review is to summarize the structural features and the immunomodulatory properties of crude, partially purified, and pure polysaccharides isolated from NAG. Receptors of the innate immune system that potentially bind to NAG polysaccharides and the respective signal transduction pathways initiated by these compounds are discussed. Major challenges, recent innovations, and future directions in NAG polysaccharide research are also summarized.     

Developing teachers’ and teaching researchers’ professional competence in mathematics through Chinese Lesson Study

This study examines co-learning of mathematics practicing teachers and mathematics teaching researchers through parallel lesson study in China. Two cases are illustrated and compared to highlight what practicing teachers and teaching researchers learned. The practicing teachers developed their competence in identifying instructional objectives, improving instructional process, selecting and sequencing mathematical tasks, and developing professional vision. The mathematics teaching researchers developed their professional competence in effectively carrying out teaching research activities, effectively mentoring teachers, and deepening the understanding of teaching.     

Closed 2-cell embeddings of graphs with no V8-minors

A closed 2-cell embedding of a graph embedded in some surface is an embedding such that each face is bounded by a cycle in the graph. The strong embedding conjecture says that every 2-connected graph has a closed 2-cell embedding in some surface. In this paper, we prove that any 2-connected graph without V₈ (the Möbius 4-ladder) as a minor has a closed 2-cell embedding in some surface. As a corollary, such a graph has a cycle double cover. The proof uses a classification of internally-4-connected graphs with no V₈-minor (due to Kelmans and independently Robertson), and the proof depends heavily on such a characterization.