A Favard theorem for orthogonal rational functions on the unit circle

We consider forn=0, 1,... the nested spaces _n of rational functions of degreen at most with given poles . Given a finite measure supported on the unit circle, we associate with it a nested orthogonal basis of rational functions ₀,..., _n for _n ,n=0, 1,.... These _n satisfy a recurrence relation that generalizes the recurrence for Szeg polynomials.In this paper we shall prove a Favard type theorem which says that if one has a sequence of rational functions _{n n} which are generated by such a recurrence, then there will be a measure supported on the unit circle to which they are orthogonal. We shall give a sufficient condition for the uniqueness of this measure.     

Assessment of doped ceria as electrolyte

A model describing the performance of a fuel cell based on 10 mol% gadolinia-doped ceria, Ce_0.9Gd_0.1O_1.95−x (CG10), was formulated. The total electrical conductivity of CG10 was measured under very reducing conditions in the temperature range of 753 K to 948 K. Oxygen permeation experiments were carried out to measure the leak current through a ceria electrolyte. The results of the measurements are compared with predictions of the formulated model. Furthermore, the response of a fuel cell to changing operating conditions such as external load, temperature, electrode polarization resistances, and defect chemistry is investigated using the model. It is found that the maximum achievable efficiency of a CG10-based fuel cell is increased when (1) the temperature is decreased, when (2) the electrolyte thickness is increased, or when (3) the cathode polarization resistance is decreased. The efficiency can also in certain circumstances be increased by an increase of anode polarization resistance. Finally, the efficiency is reduced if the vacancy formation enthalpy is decreased to the level of fine-grained CG10. The performance of a CG10-based cell is evaluated by comparing it with a state-of-the-art zirconia-based cell. At 873 K, the efficiency of a fuel cell with a 10-μm CG10 electrolyte was limited to 0.74, whereas a cell with a perfect electrolyte would have an efficiency of 1. The power output of the CG10 cell at this efficiency is, however, four times larger than the zirconia-based cell at the same efficiency. This is due to the much lower cathode polarization resistance of -CG10 cathodes on CG10 compared to the (La_0.75Sr_0.25)_0.95MnO₃ cathodes on stabilized zirconia.     

Rhodium-mediated stereoselective polymerization of "carbenes"

Unprecedented rhodium-catalyzed stereoselective polymerization of "carbenes" from ethyl diazoacetate (EDA) to give high molecular mass poly(ethyl 2-ylidene-acetate) is described. The mononuclear, neutral [(N,O-ligand)M(I)(cod)] (M = Rh, Ir) catalytic precursors for this reaction are characterized by (among others) single-crystal X-ray diffraction. These species mediate formation of a new type of polymers from EDA: carbon-chain polymers functionalized with a polar substituent at each carbon of the polymer backbone. The polymers are obtained as white powders with surprisingly sharp NMR resonances. Solution and solid state NMR data for these new polymers reveal a highly stereoregular polymer, with a high degree of crystallinity. The polymer is likely syndiotactic. Material properties are very different from those of atactic poly(diethyl fumarate) polymer obtained by radical polymerization of diethyl fumarate. Other diazoacetates are also polymerized. Further studies are underway to reveal possible applications of these new materials.     

Nanostructuring of Self‐Assembled Porphyrin Networks at a Solid/Liquid Interface: Local Manipulation under Global Control

Molecules of (5,10,15,20‐tetraundecylporphyrinato)‐copper(II) [(TUP)Cu] can self‐assemble into four different polymorphs at the interface between highly oriented pyrolytic graphite and 1‐octanoic acid. Scanning tunneling microscopy (STM) reveals that it is possible to combine the global control over monolayer structure, provided by the composition and concentration of the supernatant solution, with local control, from nanomanipulation by the STM tip. In the initially formed monolayer, with a polymorph composition governed by the concentration of (TUP)Cu in the supernatant solution, the exchange of molecules physisorbed at the solid/liquid interface with those in the liquid is very limited. By using a nanoshaving procedure at the tip, defects are created in the monolayer, and these serve as local manipulation sites to create domains of higher or lower molecular density, and to incorporate a second molecular species, (TUP)Co into the monolayer of (TUP)Cu.     

Little exchange at the liquid/solid interface: defect-mediated equilibration of physisorbed porphyrin monolayers

The transition from low to high density 2D surface structures of copper porphyrins at a liquid/solid interface requires specific defects at which nearly all exchange of physisorbed molecules with those dissolved in the supernatant occurs.     

Growth properties of Nevanlinna matrices for rational moment problems

We consider rational moment problems on the real line with their associated orthogonal rational functions. There exists a Nevanlinna-type parameterization relating to the problem, with associated Nevanlinna matrices of functions having singularities in the closure of the set of poles of the rational functions belonging to the problem. We prove results related to the growth at the singularities of the functions in a Nevanlinna matrix, and in particular provide bounds on the growth analogous to the corresponding result in the classical polynomial case, when the number of singularities is finite.     

CO oxidation on Pt(110): scanning tunneling microscopy inside a high-pressure flow reactor

We have used a novel, high-pressure high-temperature scanning tunneling microscope, which is set up as a flow reactor, to determine simultaneously the surface structure and the reactivity of a Pt(110) model catalyst at semirealistic reaction conditions for CO oxidation. By controlled switching from a CO-rich to an O2-rich flow and vice versa, we can reversibly oxidize and reduce the platinum surface. The formation of the surface oxide has a dramatic effect on the CO2 production rate. Our results show that there is a strict one-to-one correspondence between the surface structure and the catalytic activity, and suggest a reaction mechanism which is not observed at low pressures.     

Aberrant S(RN)1 Reaction of 4-Aminophenol with alpha,p-Dinitrocumene: EPR Observation of Intermediates

The tert-butoxide-induced substitution of alpha,p-dinitrocumene by 4-aminophenol unexpectedly afforded the N-coupled product, 2-(4-hydroxyanilino)-2-(4-nitrophenyl)propane. EPR observations revealed arylaminyl radical intermediates as well as coupled anion radicals, hence the normal S(RN)1 process may compete with an alternative nonchain reaction pathway.