Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Error Bounds and Implicit Multifunction Theorem in Smooth Banach Spaces and Applications to Optimization

In this paper we provide an error bound estimate and an implicit multifunction theorem in terms of smooth subdifferentials and abstract subdifferentials. Then, we derive a subdifferential calculus and Fritz–John type necessary optimality conditions for constrained minimization problems.     

Polymorphism in alternating polyketones studied by x-ray diffraction and calorimetry

Differential scanning calorimetry and high temperature x-ray diffraction were used to study the perfectly alternating copolymer of ethene and carbon monoxide (polyketone; POKC2). It was found that oriented POK-C2 fibers show a crystalline phase transition at a temperature between 110–125°C with a 10% change in crystalline density. At this temperature, the crystal structure reported recently (POK-α) is transformed to a crystal structure that was reported in the past for room temperature imperfectly alternating polyketone. The latter structure will be designated as POK-β. The influence of chain defects on the crystal structure was studied by synthesizing terpolymers (POK-C2/C3), in which small amounts of propylene-CO units are incorporated into the polymer backbone. The resulting terpolymers differ from the copolymer by the presence of methyl groups randomly distributed along the polyketone backbone chain. Evidence is presented that indicates that the methyl groups are built into the crystal lattice as defects. With more than 5 mole-% propene the terpolymer fibers crystallize exclusively in the β-modification. Below this level the α/β ratio (at room temperature) increases with decreasing amounts of propene. Both as-synthesized and as-spun POK-C2 were found to consist of both POK-α and POK-β; the α/β ratio depends on the method of preparation. Because the drawn POK-C2 fibers studied here consist exclusively of POK-α, the process of spinning and drawing leads to the transformation of unoriented β-rich material into oriented POK-α. © 1995 John Wiley & Sons, Inc.     

Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.     

Chaotic Maps, Control Parameter, and Liapunov Exponent

We describe a one-dimensional chaotic map wherethe Liapunov exponent is a smooth function of a controlparameter.     

Measurement of the transverse Doppler shift using a stored relativistic7Li+ ion beam

We have performed for the first time precision spectroscopy on a coasting fast⁷Li⁺ ion beam in a storage ring. The ion beam moving with 6.4% speed of light was first electron cooled and then merged with two counterpropagating laser beams acting on two different hyperfine transitions sharing a common upper level (λ-system). One laser was frequency locked to thea ₃ ¹²⁷J₂ hfs frequency component established as a secondary frequency standard at 514 nm. The second laser was tuned over theλ-resonance, which was recorded relative to¹²⁷J₂ hfs components. This experiment is sensitive to the time dilation in fast moving frames and will lead to new limits for the verification of special relatively. The present status of the experiment and perspectives in accuracy are discussed.