Synthesis of aliphatic polyesters by polycondensation using inorganic acid as catalyst

An effective route for the synthesis of aliphatic polyesters made from adipic or sebacic acid and alkanediols, using inorganic acid as a catalyst is reported. The monomer composition, reaction time, catalyst type, and reaction conditions were optimized to yield polyesters with weight average molecular weights of 23,000 for adipic acid and 85,000 for sebacic acid‐based polyesters. The polymers melt at temperatures of 52–65°C and possess melt viscosity in the range of 5600–19,400cP. This route represents an alternative method for producing aliphatic polyesters for possible use in the preparation of degradable disposable medical supplies. Copyright © 2009 John Wiley & Sons, Ltd.     

Spanning cactus of a graph: Existence,extension, optimization,and approximation

We show that testing if an undirected graph contains a bridgeless spanning cactus is NP-hard. As a consequence, the minimum spanning cactus problem (MSCP) on an undirected graph with 0–1 edge weights is NP-hard. For any subgraph $S$ of $K_n$, we give polynomially testable necessary and sufficient conditions for $S$ to be extendable to a cactus in $K_n$ and the weighted version of this problem is shown to be NP-hard. A spanning tree is shown to be extendable to a cactus in $K_n$ if and only if it has at least one node of even degree. When $S$ is a spanning tree, we show that the weighted version can also be solved in polynomial time. Further, we give an $O\left(n^3\right)$ algorithm for computing a minimum cost spanning tree with at least one vertex of even degree on a graph on $n$ nodes. Finally, we show that for a complete graph with edge-costs satisfying the triangle inequality, the MSCP is equivalent to a general class of optimization problems that properly includes the traveling salesman problem and they all have the same approximation hardness.     

Solving Non-Homogeneous Nested Recursions Using Trees

The solutions to certain nested recursions, such as Conolly’s C(n) = C(n?C(n?1)) + C(n?1?C(n?2)), with initial conditions C(1) = 1, C(2) = 2, have a well-established combinatorial interpretation in terms of counting leaves in an infinite binary tree. This tree-based interpretation, and its generalization to a similar k-term nested recursion, only apply to homogeneous recursions and only solve each recursion for one set of initial conditions determined by the tree. In this paper, we extend the tree-based interpretation to solve a non-homogeneous version of the k-term recursion that includes a constant term. To do so we introduce a tree-grafting methodology that inserts copies of a finite tree into the infinite k-ary tree associated with the solution of the corresponding homogeneous k-term recursion. This technique also solves the given non-homogeneous recursion with various sets of initial conditions.     

Rotational isomerism in aldehydes

A study is made of the Rydberg levels in CH₂ and CH₃ which are associated with the outer electron in a carbon 3d-orbital. A preliminary discussion of some Rydberg states in the lithium atom showed that penetration and exchange effects between the Rydberg orbital and the core were of comparable magnitude, and strongly dependent on the correct form of the Rydberg orbital wave function in the region where this overlaps the core. In the cases of CH₃ and CH₂ some conclusions of G. Herzberg about the symmetry of excited states where a 3d-orbital is involved have been confirmed, and certain other ionization potentials estimated. In CH₂ spin-orbit forces were included, but comparison with experiment is limited. The need to orthogonalize the Rydberg orbital to any core orbitals of similar overall symmetry, and to allow mixing with other orbitals (e.g. carbon 3s with carbon 3d₀) is stressed. One of the chief causes of error at present is our ignorance about the degree of validity of Koopman's theorem for situations of this kind. It is important to know to what extent the core changes its charge distribution after the ejection of the Rydberg electron.     

Optimal benchmarking for active portfolio managers

Within an agency theoretic framework adapted to the portfolio delegation issue, we show how to construct optimal benchmarks. In accordance with US regulations, the benchmark-adjusted compensation scheme is taken to be symmetric. The investor’s control consists in forcing the manager to adopt the appropriate benchmark so that his first-best optimum is attained. Solving simultaneously the manager’s and the investor’s dynamic optimization programs in a fairly general framework, we characterize the optimal benchmark. We then provide completely explicit solutions when the investor’s and the manager’s utility functions exhibit different CRRA parameters. We find that, even under optimal benchmarking, it is never optimal for the manager, and therefore for the investor, to follow exactly the benchmark, except in a very restrictive case. We finally assess by simulation the practical importance, in particular in terms of the investor’s welfare, of selecting a sub-optimal benchmark.     

A linear time algorithm for the Koopmans–Beckmann QAP linearization and related problems

An instance of the quadratic assignment problem (QAP) with cost matrix $Q$ is said to be linearizable if there exists an instance of the linear assignment problem (LAP) with cost matrix $C$ such that for each assignment, the QAP and LAP objective function values are identical. The QAP linearization problem can be solved in $O\left(n^4\right)$ time. However, for the special cases of Koopmans–Beckmann QAP and the multiplicative assignment problem the input size is of $\Omega \left(n^2\right)$. We show that the QAP linearization problem for these special cases can be solved in $O\left(n^2\right)$ time. For symmetric Koopmans–Beckmann QAP, Bookhold [I. Bookhold, A contribution to quadratic assignment problems, Optimization 21 (1990) 933–943.] gave a sufficient condition for linearizability and raised the question if the condition is necessary. We show that Bookhold’s condition is also necessary for linearizability of symmetric Koopmans–Beckmann QAP.     

New insights into silica-based NMR "chromatography"

Silica is used as an important component for NMR “chromatography”. In this study the effect of the binding strength to silica of a variety of compounds on their diffusion rate is measured for the first time. Over two orders of magnitude of diffusion difference enhancement was obtained in the presence of silica for some compounds. An explanation of the enhancement is given that also allows one to predict the “chromatographic” behavior of new compounds or mixtures. The binding strength is divided into categories of weakly bound, singly bound and multiply bound. Carboxylates, sulfonates, and diols are found to be particularly strongly bound and to diffuse up to 2½ orders of magnitude more slowly in the presence of silica.     

Cytotoxicity and fluorescence studies of silica-coated CdSe quantum dots for bioimaging applications

The toxicological effects of silica-coated CdSe quantum dots (QDs) were investigated systematically on human cervical cancer cell line. Trioctylphosphine oxide capped CdSe QDs were synthesized and rendered water soluble by overcoating with silica, using aminopropyl silane as silica precursor. The cytotoxicity studies were conducted by exposing cells to freshly synthesized QDs as a function of time (0–72 h) and concentration up to micromolar level by Lactate dehydrogenase assay, MTT [3-(4,5-Dimethylthiazol-2-yl)-2,5-Diphenyltetrazolium Bromide] assay, Neutral red cell viability assay, Trypan blue dye exclusion method and morphological examination of cells using phase contrast microscope. The in vitro analysis results showed that the silica-coated CdSe QDs were nontoxic even at higher loadings. Subsequently the in vivo fluorescence was also demonstrated by intravenous administration of the QDs in Swiss albino mice. The fluorescence images in the cryosections of tissues depicted strong luminescence property of silica-coated QDs under biological conditions. These results confirmed the role of these luminescent materials in biological labeling and imaging applications.     

Hydrogen-Bonded Crystalline Molecular Machines with Ultrafast Rotation and Displacive Phase Transitions

Two new crystalline rotors 1 and 2 assembled through N−H⋅⋅⋅N hydrogen bonds by using halogenated carbazole as stators and 1,4-diaza[2.2.2]bicyclooctane (DABCO) as the rotator, are described. The dynamic characterization through ¹H T₁ relaxometry experiments indicate very low rotational activation barriers (E_a) of 0.67 kcal mol⁻¹ for 1 and 0.26 kcal mol⁻¹ for 2 , indicating that DABCO can reach a THz frequency at room temperature in the latter. These E_a values are supported by solid-state density functional theory computations. Interestingly, both supramolecular rotors show a phase transition between 298 and 250 K, revealed by differential scanning calorimetry and single-crystal X-ray diffraction. The subtle changes in the crystalline environment of these rotors that can alter the motion of an almost barrierless DABCO are discussed here.