Equilibria of two-sided matching games with common preferences

Problems of matching have long been studied in the operations research literature (assignment problem, secretary problem, stable marriage problem). All of these consider a centralized mechanism whereby a single decision maker chooses a complete matching which optimizes some criterion. This paper analyzes a more realistic scenario in which members of the two groups (buyers–sellers, employers–workers, males–females) randomly meet each other in pairs (interviews, dates) over time and form couples if there is mutual agreement to do so. We assume members of each group have common preferences over members of the other group. Generalizing an earlier model of Alpern and Reyniers [Alpern, S., Reyniers, D.J., 2005. Strategic mating with common preferences. J. Theor. Biol. 237, 337–354], we assume that one group (called males) is r   times larger than the other, r?1$r?1$. Thus all females, but only 1/r$1/r$ of the males, end up matched. Unmatched males have negative utility -c$-c$. We analyze equilibria of this matching game, depending on the parameters r   and c$c$. In a region of (r,c)$(r\text{,}c)$ space with multiple equilibria, we compare these, and analyze their ‘efficiency’ in several respects. This analysis should prove useful for designers of matching mechanisms who have some control over the sex ratio (e.g. by capping numbers of males at a ‘singles event’or by having ‘ladies free’ nights) or the nonmating cost c (e.g. tax benefits to married couples).     

Hardy and BMO spaces associated to divergence form elliptic operators

Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie beyond the scope of the Calderón–Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some L ^p spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includes, in particular, a molecular decomposition, maximal and square function characterizations, duality of Hardy and BMO spaces, and a John–Nirenberg inequality. S. Hofmann was supported by the National Science Foundation.     

Hardy Spaces, Singular Integrals and The Geometry of Euclidean Domains of Locally Finite Perimeter

We study the interplay between the geometry of Hardy spaces and functional analytic properties of singular integral operators (SIO’s), such as the Riesz transforms as well as Cauchy–Clifford and harmonic double-layer operator, on the one hand and, on the other hand, the regularity and geometric properties of domains of locally finite perimeter. Among other things, we give several characterizations of Euclidean balls, their complements, and half-spaces, in terms of the aforementioned SIO’s.     

Models as lab equipment: science from computational experiments

Computer models are artifacts that facilitate conducting computational experiments. In that sense they are laboratory equipment. The utility of a piece of laboratory equipment comes from the range of useful experiments it supports. However, general purpose models are in general much more costly to create and maintain. Consequently, issues regarding the design of computer models are best understood as pragmatic questions regarding the costs and utility of alternative designs.

A mixed-valent ruthenium-oxo oxalato cluster Na7[Ru4(mu3-O)4(C2O4)6] with potent anti-HIV activities

A structurally characterized mixed-valent tetranuclear ruthenium-oxo oxalato cluster exhibits anti-viral activities toward R5- and X4-tropic HIV-1, and possesses cytoprotective activity toward HIV-1 infected cells.     

Synthesis and application of chiral N-heterocyclic carbene-oxazoline ligands: iridium-catalyzed enantioselective hydrogenation

Two libraries of enantiomerically pure imidazolium salts bearing an oxazoline unit were synthesized. Deprotonation of the imidazolium salts and complexation of the resulting oxazoline-carbene ligands to iridium(I) was achieved in one step by mixing the imidazolium salts with NaOtBu and [(eta(4)-cod)IrCl](2) in THF at room temperature. The air-stable complexes were purified by flash chromatography. All complexes were analyzed by two-dimensional (2D) NMR methods and one compound from each family was characterized by X-ray structure analysis. The two libraries of iridium complexes were successfully tested in the asymmetric hydrogenation of unfunctionalized and functionalized olefins. Enantioselectivities of up to 90 % ee were obtained with trans-alpha-methylstilbene. Upon complexation of imidazolium salt 15 p with R(1) = phenyl, C-H bond activation of the phenyl ring gave rise to iridium(III) complex 17, which was fully characterized by NMR spectroscopy and X-ray structure analysis. Complex 17 proved to be catalytically inactive in the hydrogenation.     

Dual emission from luminescent nonalanthanide clusters

Clusters containing nine lanthanide and six sodium ions are crystallized with the help of a tridentate ligand bearing a phosphonic acid group; the structure of the Eu(III) compound reveals a host-guest assembly Eu [symbol: see text] Na6Eu8L16 with a substantial quantum yield (32%). A similar Eu(III)-Yb(III) structure displays dual luminescence in the visible (Eu(III)) and NIR (Yb(III)) ranges.     

Developments with anion exchange stationary phases for HPLC-ICP-MS analysis of antimony species

Novel HPLC-ICP-MS methodologies are developed using strong anion exchange (Phenomenex SAX-SB) and weak anion exchange (Alltec HAAX) stationary phases in conjunction with a range of aqueous mobile phases to enable simultaneous separations of inorganic Sb(III), Sb(V) and organic trimethylantimony dichloride (TMSb) species in synthetic solutions. Optimum isocratic separations of inorganic Sb(V) and Sb(III) species are achieved using mobile phases comprised of ammonium tartrate under controlled pH conditions, and rapid pH gradient elution profiles are developed to facilitate separations of the Sb(V), Sb(III) and TMSb species in a single chromatographic run. Optimum peak resolution is achieved when using the 100 x 4.6 mm HAAX column at 20 degrees C and 100 mM ammonium tartrate mobile phases with a gradient from pH 3.0 to pH 1.2, although a system peak co-elutes with TMSb under these conditions and precludes quantitative analyses. Interestingly, the elution order of Sb(V), Sb(III) and TMSb species reverses when the temperature of the HAAX stationary phase is increased to 60 degrees C, and concurrent use of a less acidic pH gradient elution profile from pH 2.3 to pH 1.5 is shown to enable successful species separations whilst preventing occurrence of the co-eluting system peak. Limits of detection are achieved in the sub ng mL(-1) range using these novel HPLC-ICP-MS methodologies and provide scope for future environmental analysis applications.     

Synthesis of a naphthyridone p38 MAP kinase inhibitor

Compound 1 is a p38 MAP kinase inhibitor potentially useful for the treatment of rheumatoid arthritis and psoriasis. A novel six-step synthesis suitable for large-scale preparation was developed in support of a drug development program at Merck Research Laboratories. The key steps include a tandem Heck-lactamization, N-oxidation, and a highly chemoselective Grignard addition of 4-(N-tert-butylpiperidinyl)magnesium chloride to a naphthyridone N-oxide. The N-oxide exerted complete chemoselectivity via chelation in directing the Grignard addition to the alpha position as opposed to 1,4-addition on the ene-lactam. The dihydropyridyl adduct was in situ aromatized with isobutylchloroformate followed by heating in pyridine. Syntheses of Grignard precursor, N-tert-butyl-4-chloro-piperidine, were accomplished via transamination with a quaternary ammonium piperidone or via addition of methylmagnesium chloride to an iminium ion. Utilizing this chemistry, multi-kilogram preparation of compound 1 was successfully demonstrated.     

Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum

We prove well-posedness for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) =  C _γ ρ ^γ for γ > 1. The physical vacuum singularity requires the sound speed c to go to zero as the square-root of the distance to the moving boundary, and thus creates a degenerate and characteristic hyperbolic free-boundary system wherein the density vanishes on the free-boundary, the uniform Kreiss–Lopatinskii condition is violated, and manifest derivative loss ensues. Nevertheless, we are able to establish the existence of unique solutions to this system on a short time-interval, which are smooth (in Sobolev spaces) all the way to the moving boundary, and our estimates have no derivative loss with respect to initial data. Our proof is founded on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term, chosen to preserve as much of the geometric structure of the Euler equations as possible. We first construct solutions to this degenerate parabolic regularization using a higher-order version of Hardy’s inequality; we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter. Solutions to the compressible Euler equations are found in the limit as the artificial viscosity tends to zero. Our regular solutions can be viewed as degenerate viscosity solutions. Our methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws.