Instability of matchings in decentralized markets with various preference structures

In any two-sided matching market, a stable matching can be found by a central agency using the deferred acceptance procedure of Gale and Shapley. But if the market is decentralized and information is incomplete then stability of the ensuing matching is not to be expected. Despite the prevalence of such matching situations, and the importance of stability, little theory exists concerning instability. We discuss various measures of instability and analyze how they interact with the structure of the underlying preferences. Our main result is that even the outcome of decentralized matching with incomplete information can be expected to be “almost stable” under reasonable assumptions.     

On the central limit theorem for geometrically ergodic Markov chains

Let X₀,X₁,... be a geometrically ergodic Markov chain with state space and stationary distribution . It is known that if h: R satisfies (|h|²⁺)< for some >0, then the normalized sums of the X_is obey a central limit theorem. Here we show, by means of a counterexample, that the condition (|h|²⁺)< cannot be weakened to only assuming a finite second moment, i.e., (h²)<.Reasearch supported by the Swedish Research Council.     

Packed column supercritical fluid chromatography of a peroxysome proliferator-activating receptor agonist drug. Achiral and chiral purity of substance, formulation assay and its enantiomeric purity

This paper describes packed column supercritical fluid chromatography (SFC) for the analysis of a peroxysome proliferator-activating gamma-receptor agonist that is a carboxylic acid. Evaluation of conditions for the separation of this candidate drug and related compounds in bulk substance is described. A Chiralcel OD column was used for this purpose due to its high selective retention of related substances and relative inertness, though the enantioselectivity was negligible, with methanol as polar modifier. A high enantioselectivity was obtained on Chiralpak AD and it was possible to determine the enantiomeric purity within 10 min on a 5 cm short column. Both the achiral and the chiral systems were run without acid additive in the mobile phase and the level of detection of impurities by area was about 0.1%. For the analysis of samples dissolved in water, without any isolation step, 2-propanol was used as modifier. Due to the column surface activity, evidently generated by injected water, citric acid 1 mM was included as additive in the 2-propanol in order to maintain symmetric and undistorted peak shape. The detection limit for the assay was 21 microg mL(-1) (50 nmol mL(-1)) for 5 microL injected (R.S.D. 6.4%, n = 8). A 5 cm short Chiralcel OD column was used. Determination of enantiomeric purity of the drug in aqueous samples required increased sensitivity. The sample was acidified and extracted into a small volume of 1-pentanol, out of which 25 microl was analyzed by SFC. The minor enantiomer at the 3% (w/w) level added could be confirmed. Its ratio remained constant during the procedure as measured relative to a reference solution in organic media.     

Conditions for noncollinear instabilities of ferromagnetic materials

Two criteria have been identified here which determine whether a magnetic metal orders in a collinear (e.g., ferromagnet) or noncollinear (e.g., spin-spiral) arrangement. These criteria involve the ratio between the strength of the exchange interaction and the width of the electron bands, as well as Fermi-surface nesting between spin-up and spin-down sheets of the Fermi surface. Based on our analysis we predict that even typical ferromagnetic materials (e.g., Fe, Co, and Ni) should be possible to stabilize in a noncollinear magnetic order in, e.g., high pressure experiments.     

Uniaxial magnetocrystalline anisotropy of metal/semiconductor interfaces: Fe/ZnSe(001)

A theoretical study of the magnetic moments and the in-plane magnetic anisotropy of an interface between a cubic ferromagnet and a cubic semiconductor, Fe/ZnSe(001), is presented. Theory confirms the observed, much debated, uniaxial anisotropy of the iron film. This result is important since the calculations are for perfect interfaces with squarelike environments, proving that the fourfolded symmetry of the interface Fe atoms is broken beyond the nearest neighboring semiconducting layer, effects that are usually assumed small. It is demonstrated how the uniaxial anisotropy is produced by the directional covalent bonds at the interface, even without atomic relaxations.     

Nitrogen kinetic isotope effects for the monoamine oxidase B-catalyzed oxidation of benzylamine and (1,1-(2)H2)benzylamine: nitrogen rehybridization and CH bond cleavage are not concerted

Nitrogen kinetic isotope effects for the oxidation of benzylamine and (1,1-(2)H(2))benzylamine by recombinant human monoamine oxidase B show that cleavage of the CH bond is not concerted with rehybridization of the nitrogen atom.     

Spontaneous vesicle formation in catanionic mixtures of amino acid-based surfactants: chain length symmetry effects

The use of amino acids for the synthesis of novel surfactants with vesicle-forming properties potentially enhances the biocompatibility levels needed for a viable alternative to conventional lipid vesicles. In this work, the formation and characterization of catanionic vesicles by newly synthesized lysine- and serine-derived surfactants have been investigated by means of phase behavior mapping and PFG-NMR diffusometry and cryo-TEM methods. The lysine-derived surfactants are double-chained anionic molecules bearing a pseudogemini configuration, whereas the serine-derived amphiphile is cationic and single-chained. Vesicles form in the cationic-rich side for narrow mixing ratios of the two amphiphiles. Two pairs of systems were studied: one symmetric with equal chain lengths, 2C12/C12, and the other highly asymmetric with 2C8/C16 chains, where the serine-based surfactant has the longest chain. Different mechanisms of the vesicle-to-micelle transition were found, depending on symmetry: the 2C12/C12 system entails limited micellar growth and intermediate phase separation, whereas the 2C8/C16 system shows a continuous transition involving large wormlike micelles. The results are interpreted on the basis of currently available models for the micelle-vesicle transitions and the stabilization of catanionic vesicles (energy of curvature vs mixing entropy).