A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

The use of ferromagnetic dacron as solid-phase in enzyme immunoassays

Ferromagnetic dacron is proposed as an alternative solid-phase for magnetic enzyme immunoassays. Human serum albumin (HSA) was covalentlyimmobilized onto ferromagnetic dacron and as enzyme immunoassay was developed using anti-HSA rabbit sera. Peroxidase, o-phenylenediamine (OPD) and hydrogen peroxide were used anti-HSA rabbit sera. Peroxidase, o-phenylenediamine (OPD) and hydrogen peroxide were used as the enzymatic label and substrates, respectively. Best results were observed when particles of 63-100 µm (diameter) and 10 µg of immobilized antigen were used. Positive reactions were detected until dilutions of1:51200 of immune sera. Its reproducibility was similar to standard ELISA. Disruption of the immunocomplexes formed and recuperation of the immobilized antigen in other immunoassays also proved to be reliable.

Evaluation of oral versus intravenous dose of vinorelbine to achieve equivalent blood exposures in patients with solid tumours.

Patient's preference is for oral chemotherapy when both oral and i.v. are available, provided that efficacy is equivalent. Reliable switch from oral to i.v. is possible if correspondence between respective doses has been established. Vinorelbine oral was developed as a line extension of VRL i.v. on the basis that similar AUCs result in similar activities. From a first crossover study on 24 patients receiving VRL 25 mg/m2 i.v. and 80 mg/m2 oral data extrapolation concluded on AUCs bioequivalence between Vinorelbine 30 mg/m2 i.v. and 80 mg/m2 oral. A new trial was performed to support this calculation. In a crossover design study on patients (PS 0-1) with advanced solid tumours (44% breast carcinoma), VRL was administered (30 mg/m2 i.v., 80 mg/m2 oral) with a standard meal and 5-HT3 antagonists, at 2 weeks interval. Pharmacokinetics was performed over 168 h and VRL was measured by LC-MS/MS. Statistics included bioequivalence tests. Forty-eight patients were evaluable for PK: median age 58 years (25-71), PS0/PS1: 20/28, M/F: 11/37. Mean AUCs were 1,230 +/- 290 and 1,216 +/- 521 ng/ml for i.v. and oral, respectively. The confidence interval of the AUC ratio (0.83-1.03) was within the required regulatory range (0.8-1.25) and proved the bioequivalence between the two doses. The absolute bioavailability was 37.8 +/- 16.0%, and close to the value from the first study (40%). Patient tolerability was globally comparable between both forms with no significant difference on either haematological or non-haematological toxicities (grade 3-4). This new study, conducted on a larger population, confirmed the reliable dose correspondence previously established between vinorelbine 80 mg/m2 oral and 30 mg/m2 i.v.

Capsule permeability via polymer and protein ingress/egress.

Static incubation tests, where microcapsules and beads are contacted with polymer and protein solutions, have been developed for the characterization of permselective materials applied for bioartificial organs and drug delivery. A combination of polymer ingress, detected by size-exclusion chromatography, and protein ingress/ egress, assessed by gel electrophoresis, provides information regarding the diffusion kinetics, molar mass cutoff(MMCO) and permeability. This represents an improvement over existing permeability measurements that are based on the diffusion of a single type of solute. Specifically, the permeability of capsules based on alginate, cellulose sulfate, polymethylene-co-guanidine were characterized as a function of membrane thickness. Solid alginate beads were also evaluated. The MMCO of these capsules was estimated to be between 80 and 90 kDa using polymers, and between 116-150 kDa with proteins. Apparently, the globular shape of the proteins (radius of gyration (Rg) of 4.2-4.6 nm) facilitates their passage through the membrane, comparatively to the polysaccharide coil conformation (Rg of 6.5-8.3 nm). An increase of the capsule membrane thickness reduced these values. The MMCO of the beads, which do not have a membrane limiting their permselective properties, was higher, between 110 and 200 kDa with dextrans, and between 150 and 220 kDa with proteins. Therefore, although the permeability estimated with biologically relevant molecules is generally higher due to their lower radius of gyration, both the MMCO of synthetic and natural watersoluble polymers correlate well, and can be used as in vitro metrics for the immune protection ability of microcapsules and microbeads. This article shows, to the authors' knowledge, the first reported concordance between permeability measures based on model natural and biological macromolecules.

The use of polyvinyl alcohol glutaraldehyde as solid-phase in ELISA for plague

Discs of polyvinyl alcohol cross-linked with glutaraldehyde were synthesized under acid catalysis (H2SO4). Then, the antigen F1 purified from Yersinia pestis was covalently linked to this modified polymer. Afterwards, an enzyme-linked immunosorbent assay (ELISA) was established for the diagnosis of plague in rabbit and human. The best conditions for the method were achieved by using 1.3 ¼g of F1 prepared in 0.067 M phosphate buffer, pH 7.2, containing 1 M NaCl (PBS); anti-IgG peroxidase conjugate diluted 6,000 times and as a blocking agent 3% w/v skim milk in PBS. The titration of positive rabbit serum according to this procedure detected antibody concentrations up to 1:12,800 times. The present method, the conventional ELISA and passive haemagglutination assay are compared.

On stability of solutions to systems of convex inequalities

"Vegeu el resum a l'inici del document del fitxer adjunt."

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

A phase I study of the oral platinum agent satraplatin in sequential combination with capecitabine in the treatment of patients with advanced solid malignancies.

Abstract Background. The broad spectrum of antitumor activity of both the oral platinum analogue satraplatin (S) and capecitabine (C), along with the advantage of their oral administration, prompted a clinical study aimed to define the maximum tolerated dose (MTD) of the combination. Patients and methods. Four dose levels of S (mg/m(2)/day) and C (mg/m(2)/day) were evaluated in adult patients with advanced solid tumors: 60/1650, 80/1650, 60/2000, 70/2000; a course consisted of 28 days with sequential administration of S (days 1-5) and C (days 8-21) followed by one week rest. Results. Thirty-seven patients were treated, 24 in the dose escalation and 13 in the expansion phase; at the MTD, defined at S 70/C 2000, two patients presented dose limiting toxicities: lack of recovery of neutropenia by day 42 and nausea with dose skip of C. Most frequent toxicities were nausea (57%), diarrhea (51%), neutropenia (46%), anorexia, fatigue, vomiting (38% each). Two partial responses were observed in platinum sensitive ovarian cancer and one in prostate cancer. Conclusion. At S 70/C 2000 the combination of sequential S and C is tolerated with manageable toxicities; its evaluation in platinum and fluorouracil sensitive tumor types is worthwhile because of the easier administration and lack of nephro- and neurotoxicity as compared to parent compounds.

Development of a novel headspace sorptive extraction method to study the aging of volatile compounds in spent handgun cartridges

Estimating the time since the last discharge of firearms and/or spent cartridges may be a useful piece of information in forensic firearm-related cases. The current approach consists of studying the diffusion of selected volatile organic compounds (such as naphthalene) released during the shooting using solid phase micro-extraction (SPME). However, this technique works poorly on handgun car-tridges because the extracted quantities quickly fall below the limit of detection. In order to find more effective solutions and further investigate the aging of organic gunshot residue after the discharge of handgun cartridges, an extensive study was carried out in this work using a novel approach based on high capacity headspace sorptive extraction (HSSE). By adopting this technique, for the first time 51 gunshot residue (GSR) volatile organic compounds could be simultaneously detected from fired handgun cartridge cases. Application to aged specimens showed that many of those compounds presented significant and complementary aging profiles. Compound-to-compound ratios were also tested and proved to be beneficial both in reducing the variability of the aging curves and in enlarging the time window useful in a forensic casework perspective. The obtained results were thus particularly promising for the development of a new complete forensic dating methodology.