Buyer-seller exactness in the assignment game

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyer-seller exact games and satisfy the condition that each mixed-pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyer-seller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer-seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed-pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a “45^o-lattice” by means of the core of an assignment game can now be answered. Received: March 2002/Revised version: January 2003 RID="*" ID="*"  Institutional support from research grants BEC 2002-00642 and SGR2001-0029 is gratefully acknowledged RID="**" ID="**"  The authors thank the referees for their comments     

De Rham and Infinitesimal Cohomology in Kapranov's Model for Non commutative Algebraic Geometry

The title refers to the nilcommutative or NC-schemes introduced by M. Kapranov in Noncommutative Geometry Based on Commutator Expansions, J. Reine Angew. Math 505 (1998) 73–118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson or NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306–358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.     

Thermal expansion of cadmium fluoride crystals at high temperatures

The thermal expansion coefficient of cadmium fluoride crystals has been measured over the temperature range of 300 to 1070 K. The data fit well to measurements done by other authors in the range 80–300 K. At temperatures above 1070 K the thermal expansion coefficient shows an anomalous behaviour which has been attributed to the formation of cadmium oxide on the surface of the sample.     

Optical fiber refractometers based on indium tin oxide coatings fabricated by sputtering

This Letter presents the fabrication of optical fiber refractometers based on indium tin oxide (ITO) coatings deposited by sputtering with response in the visible region. ITO thin films have been sputtered by means of a rotating mechanism that enables the fabrication of smooth and homogeneous coatings onto the optical fiber core. The ITO coating acts as a resonance supporting layer. This permits us to couple light from the waveguide to the ITO-coating/external medium region at specific wavelength ranges. The device is sensitive to external medium refractive index, which allows its utilization as a refractometer. The sensitivity is dependent on the coating thickness, ranging from 523.21 to 1221 nm/refractive index unit in the explored sensors. The sensor development process is time effective compared to other techniques such as dip coating or layer-by-layer self-assembly, which is interesting in terms of mass production.     

Identification of phototransformation products of sildenafil (Viagra) and its N-demethylated human metabolite under simulated sunlight

Recent publications on pharmaceutical monitoring are increasingly covering the field of illicit drugs and lately the forensic evaluation of designing illegal analogs of lifestyle drugs like the phosphodiesterase type 5 (PDE-5) inhibitors Viagra (sildenafil), Levitra (vardenafil) and Cialis (tadalafil). Recently, the presence of all three erectile dysfunction treatment drugs has been reported in wastewaters at very low concentrations. In the environment, contaminants undergo various physical or chemical processes classified into abiotic (photolysis, hydrolysis) and biotic (biodegradation) reactions. Thus, changes in the chemical structure lead to the formation of new transformation products, which may persist in the environment or be further degraded. This study describes the photolysis of sildenafil (SDF) and its human metabolite N-demethylsildenafil (DM-SDF) under simulated solar radiation (Xenon lamp). Following chromatographic separation of the irradiated samples, eight photoproducts in the SDF samples and six photoproducts for DM-SDF were detected and characterized. The combination of ultra performance liquid chromatography-electrospray ionization-quadrupole time-of-flight-mass spectrometry (UPLC-ESI-QToF-MS), liquid chromatography-atmospheric pressure chemical ionization-triple quadrupole mass spectrometry (LC-APCI-QqQ-MS) and hydrogen/deuterium-exchange experiments allowed to propose plausible chemical structures for the photoproducts, taking into account the characteristic fragmentation patterns and the accurate mass measurements. These mass spectral data provided sound evidence for the susceptibility of the piperazine ring toward photodegradation. A gradual breakdown of this heterocyclic structure gave rise to a series of products, which in part were identical for SDF and DM-SDF. The sulfonic acid, as the formal product of sulfonamide hydrolysis, was identified as key intermediate in the photolysis pathway. In both drug/metabolite molecules, phototransformation processes taking place beyond the sulfonamide group were deemed to be of minor relevance.     

New precision limit on the strange vector form factors of the proton

The parity-violating cross-section asymmetry in the elastic scattering of polarized electrons from unpolarized protons has been measured at a four-momentum transfer squared Q2 = 0.624 GeV2 and beam energy E(b) = 3.48 GeV to be A(PV) = -23.80 ± 0.78(stat) ± 0.36(syst) parts per million. This result is consistent with zero contribution of strange quarks to the combination of electric and magnetic form factors G(E)(s) + 0.517G(M)(s) = 0.003 ± 0.010(stat) ± 0.004(syst) ± 0.009(ff), where the third error is due to the limits of precision on the electromagnetic form factors and radiative corrections. With this measurement, the world data on strange contributions to nucleon form factors are seen to be consistent with zero and not more than a few percent of the proton form factors.     

Resolving overlapping peaks in ARXPS data: The effect of noise and fitting method

Peak-fitting of X-ray photoelectron spectroscopy (XPS) data can be very sensitive to noise when the difference on the binding energy among the peaks is smaller than the width of the peaks. This sensitivity depends on the fitting algorithm. Angle-resolved XPS (ARXPS) analysis offers the opportunity of employing the combined information contained in the data at the various angles to reduce the sensitivity to noise. The assumption of shared peak parameters (center and width) among the spectra for the different angles, and how it is introduced into the analysis, plays a basic role. Sequential fitting is the usual practice in ARXPS data peak-fitting. It consist on first estimating the center and width of the peaks from the data acquired at one of the angles, and then using those parameters as a starting approximation for fitting the data for each of the rest of the angles. An improvement of this method consists of averaging the centers and widths of the peaks obtained at the different angles, and then employing these values to assess the areas of the peaks for each angle. Another strategy for using the combined information is by assessing the peak parameters from the sum of the experimental data. The complete use of the combined information contained in the data-set is optimized by the simultaneous fitting method. It consists of the assessment of the center and width of the peaks by fitting the data at all the angles simultaneously. Computer-generated data was employed to compare the sensitivity with respect to noise between the sequential, averaged-sequential, sum, and simultaneous fitting methods. It is shown that the latter is significantly more robust and could provide reliable results even for noisy data and small peak separation. The fundamentals for the robustness of the simultaneous method are discussed, as well as the possibility of fitting many parameters at the same time. As an added feature of ARXPS, it was found that the estimation of the error intervals on the peak parameters is done remarkably more precisely by employing XPS data at various angles.     

Magnetocaloric effect and magnetic properties in NdMnO3 perovskite: A Monte Carlo approach

The magnetic properties and magnetocaloric effect in $\text{NdMn}{\text{O}}_3$ have been investigated, as well as the effect of magnetic anisotropy in the magnetocaloric properties of the perovskite-type compound. A classical Heisenberg Hamiltonian with nearest and next-nearest neighbors interactions was implemented. Hamiltonian parameters were fitted in order to reproduce experimental results. Magnetic field dependence on the magnetization, for isothermal processes, was performed. In this way, the magnetic entropy change $\left(\mathrm{\Delta }{S}_m\right)$ was computed as well as the relative cooling power (RCP). Results show that as the magnetic anisotropy constant increases, there was not only a sharpening, but also an increase in peak height of $?\mathrm{\Delta }{S}_m$. Finally, the magnetic field and anisotropy dependences on the RCP were obtained, showing that the highest values of the RCP were found for low anisotropy values.     

Indirect strong coupling regime between a quantum emitter and a cavity mediated by a mechanical resonator

Achieving strong coupling between light and matter is usually a challenge in Cavity Quantum Electrodynamics (cQED), especially in solid state systems. For this reason is useful taking advantage of alternative approaches to reach this regime, and then, generate reliable quantum polaritons. In this work we study a system composed of a quantized single mode of a mechanical resonator interacting linearly with both a single mode cavity and a quantum two-level system. In particular, we focus on the behavior of the indirect light-matter interaction when the phonon mode interfaces both parts. By diagonalization of the Hamiltonian and computing the density matrix in a master equation approach, we evidence several features of strong coupling between photons and matter excitations. For large energy detuning between the cavity and the mechanical resonator it is obtained a phonon-dispersive effective Hamiltonian which is able to retrieve much of the physics of the conventional Jaynes–Cummings model (JCM). In order to characterize this mediated coupling, we make a quantitative comparison between both models and analyze light-matter entanglement and purity of the system leading to similar results in cQED.