Surgery on a Stratified Space

Let Y be a closed manifold with a locally flat submanifold \({Z\subset Y}\) and X be a manifold with a boundary \({\partial X}\) . In this paper we construct the algebraic surgery theory of a stratified space that is homeomorphic to \({Y\cup X}\) with transversal intersection \({Y\cap X= Z=\partial X}\) . We develop the algebraic surgery theory of Ranicki to this case and we obtain relations between the introduced spectra that realize the obstruction groups and the structure sets.     

Splitting theorems for pro-<Emphasis Type="Italic">p</Emphasis> groups acting on pro-<Emphasis Type="Italic">p</Emphasis> trees

Let G be an infinite finitely generated pro-p group acting on a pro-p tree such that the restriction of the action to some open subgroup is free. We prove that G splits over an edge stabilizer either as an amalgamated free pro-p product or as a pro-p \({\text {HNN}}\)-extension. Using this result, we prove under a certain condition that free pro-p products with procyclic amalgamation inherit from its amalgamated free factors the property of each 2-generated pro-p subgroup being free pro-p. This generalizes known pro-p results, as well as some pro-p analogues of classical results in abstract combinatorial group theory.     

Synthesis of Tri-O-acetyl-d-allal from Levoglucosenone

Tri-O-acetyl-d-allal has been enantiospecifically synthesized in six steps from levoglucosenone in 55% overall yield. A key step in the synthesis is the anhydro bridge ring-opening with concomitant formation of a 1,3-oxathiolane-2-thione ring.     

Full Molecular Weight Distribution in RAFT Polymerization. New Mechanistic Insight by Direct Integration of the Equations

The full molecular weight distribution (FMWD) equations in RAFT polymerization are solved by direct integration for three models: intermediate radical termination (IRT), slow fragmentation (SF), and IRT with oligomers (IRTO). It is shown that the quasi steady state approximation (QSSA) is always applicable to living radicals, and also applicable to intermediate radicals in the IRT and IRTO models. The application of the QSSA allows for considerable simplification of the numerical solution of the equations. A marked bimodality is found for the FMWD of the SF model only. This suggests model discrimination by radical trapping experiments followed by GPC measurement of the total MWD.

     

A New,Practical Formulation of the Multicomponent Copolymerization Equation

A general and rigorous new formulation of the multicomponent extension to the Mayo Lewis copolymerization equation is presented based in matrix notation. In contrast to the original Walling and Briggs formulation, which was based on determinants and difficult to apply in practice, this new formulation is explicit, easy to implement, and introduces a natural scaling to the problem. The approach is illustrated with calculation of instantaneous composition and compositional drift with conversion for 4 and 6 monomers.

     

Fluorescent charge-assisted halogen-bonding macrocyclic halo-imidazolium receptors for anion recognition and sensing in aqueous media

The synthesis and anion binding properties of a new family of fluorescent halogen bonding (XB) macrocyclic halo-imidazolium receptors are described. The receptors contain chloro-, bromo-, and iodo-imidazolium motifs incorporated into a cyclic structure using naphthalene spacer groups. The large size of the iodine atom substituents resulted in the isolation of anti and syn conformers of the iodo-imidazoliophane, whereas the chloro- and bromo-imidazoliophane analogues exhibit solution dynamic conformational behavior. The syn iodo-imidazoliophane isomer forms novel dimeric isostructural XB complexes of 2:2 stoichiometry with bromide and iodide anions in the solid state. Solution phase DOSY NMR experiments indicate iodide recognition takes place via cooperative convergent XB-iodide 1:1 stoichiometric binding in aqueous solvent mixtures. (1)H NMR and fluorescence spectroscopic titration experiments with a variety of anions in the competitive CD(3)OD/D(2)O (9:1) aqueous solvent mixture demonstrated the bromo- and syn iodo-imidazoliophane XB receptors to bind selectively iodide and bromide respectively, and sense these halide anions exclusively via a fluorescence response. The protic-, chloro-, and anti iodo-imidazoliophane receptors proved to be ineffectual anion complexants in this aqueous methanolic solvent mixture. Computational DFT and molecular dynamics simulations corroborate the experimental observations that bromo- and syn iodo-imidazoliophane XB receptors form stable cooperative convergent XB associations with bromide and iodide.     

Optimal reparametrization and large sample likelihood inference for the location-scale skew-normal model

Motivated by results in Rotnitzky et al. (2000), a family of parametrizations of the location-scale skew-normal model is introduced, and it is shown that, under each member of this class, the hypothesis H ₀: ?? = 0 is invariant, where ?? is the asymmetry parameter. Using the trace of the inverse variance matrix associated to a generalized gradient as a selection index, a subclass of optimal parametrizations is identified, and it is proved that a slight variant of Azzalini??s centred parametrization is optimal. Next, via an arbitrary optimal parametrization, a simple derivation of the limit behavior of maximum likelihood estimators is given under H ₀, and the asymptotic distribution of the corresponding likelihood ratio statistic for this composite hypothesis is determined.     

Contractive mappings and existence of cycle times for a monotone and homogeneous function

Given a monotone and homogeneous self-mapping f$f$ of the n$n$-dimensional positive cone, a family of contractive mappings is used to define an equivalence relation in the index set, as well as a total order among the equivalence classes. Then, it is shown (i) that the cycle times are well-defined at each index belonging to the maximal and minimal classes, and (ii) that the cycle times of f$f$ exist at every index whenever a weak convexity condition is satisfied.     

Efficient solvability of Hamiltonians and limits on the power of some quantum computational models

One way to specify a model of quantum computing is to give a set of control Hamiltonians acting on a quantum state space whose initial state and final measurement are specified in terms of the Hamiltonians. We formalize such models and show that they can be simulated classically in a time polynomial in the dimension of the Lie algebra generated by the Hamiltonians and logarithmic in the dimension of the state space. This leads to a definition of Lie-algebraic "generalized mean-field Hamiltonians." We show that they are efficiently (exactly) solvable. Our results generalize the known weakness of fermionic linear optics computation and give conditions on control needed to exploit the full power of quantum computing.     

2-Aza-1,3-butadiene derivatives featuring an anthracene or pyrene unit: highly selective colorimetric and fluorescent signaling of Cu2+ cation

[Structure: see text] A new probe based on an anthryl derivative bearing an azadiene side chain selectively senses Cu2+ in acetonitrile through two different channels: the yellow-to-orange color change and a remarkable enhancement of the fluorescence, whereas the pyrenyl analogous behaves as a fluorescent sensor for Cu2+ and Hg2+ in aqueous environment.