A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

Security strategies and equilibria in multiobjetives matrix games

Multiobjective matrix games have been traditionally analyzed from two different points of view: equiibrium concepts and security strategies. This paper is based upon the idea that both players try to reach equilibrium points playing pairs of security strategies, as it happens in scalar matrix games. We show conditions guaranteeing the existence of equilibria in security strategies, named security equilibria

Security strategies and equilibria in multiobjetives matrix games

Multiobjective matrix games have been traditionally analyzed from two different points of view: equiibrium concepts and security strategies. This paper is based upon the idea that both players try to reach equilibrium points playing pairs of security strategies, as it happens in scalar matrix games. We show conditions guaranteeing the existence of equilibria in security strategies, named security equilibria

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

Stable isotope geochemistry and phase-equilibria of coesite-bearing whiteschists, Dora Maira massif, Western Alps

Peak metamorphic temperatures for the coesite-pyrope-bearing whiteschists from the Dora Maira Massif, western Alps were determined with oxygen isotope thermometry. The deltaO-18(SMOW) values of the quartz (after coesite) (delta O-18 = 8.1 to 8.6 parts per thousand, n = 6), phengite (6.2 to 6.4 parts per thousand, n = 3), kyanite (6.1 parts per thousand, n = 2), garnet (5.5 to 5.8 parts per thousand, n = 9), ellenbergerite (6.3 parts per thousand, n = 1) and rutile (3.3. to 3.6 parts per thousand, n = 3) reflect isotopic equilibrium. Temperature estimates based on quartz-garnet-rutile fractionation are 700-750-degrees-C. Minimum pressures are 31-32 kb based on the pressure-sensitive reaction pyrope + coesite = kyanite + enstatite. In order to stabilize pyrope and coesite by the temperature-sensitive dehydration reaction talc + kyanite = pyrope + coesite + H2O, the a(H2O) must be reduced to 0.4-0.75 at 700 750-degrees-C. The reduced a(H2O) cannot be due to dilution by CO2, as pyrope is not stable at X (CO2) > 0.02 (T = 750-degrees-C; P = 30 kb). In the absence of a more exotic fluid diluent (e.g. CH4 or N2), a melt phase is required. Granite solidus temperatures are approximately 680-degrees-C/30 kb at a(H2O) = 1.0 and are calculated to be approximately 70-degrees-C higher at a(H2O) = 0.7, consistent with this hypothesis. Kyanite-jadeite-quartz bands may represent a relict melt phase. Peak P-T-f(H2O) estimates for the whiteschist are 34 +/- 2 kb, 700-750-degrees-C and 0.4-0.75. The oxygen isotope fractionation between quartz (deltaO-18 = 11.6%.) and garnet (deltaO-18 = 8.7 parts per thousand) in the surrounding orthognesiss is identical to that in the coesite-bearing unit, suggesting that the two units shared a common, final metamorphic history. Hydrogen isotope measurements were made on primary talc and phengite (deltaD(smow) = -27 to -32 parts per thousand), on secondary talc and chlorite after pyrope (deltaD = - 39 to - 44 parts per thousand) and on the surrounding biotite (deltaD = -64 parts per thousand) and phengite (deltaD = -44 parts per thousand) gneiss. All phases appear to be in near-equilibrium. The very high deltaD values for the primary hydrous phases is consistent with an initial oceanic-derived/connate fluid source. The fluid source for the retrograde talc + chlorite after pyrope may be fluids evolved locally during retrograde melt crystallization. The similar deltaD, but dissimilar deltaO-18 values of the coesite-bearing whiteschists and hosting orthogneiss suggest that the two were in hydrogen isotope equilibrium, but not oxygen isotope equilibrium. The unusual hydrogen and oxygen isotope compositions of the coesite-bearing unit can be explained as the result of metasomatism from slab-derived fluids at depth.

Quantification of magmatic and hydrothermal processes in a peralkaline syenite-alkali granite complex based on textures, phase equilibria, and stable and radiogenic isotopes

The Puklen complex of the Mid-Proterozoic Gardar Province, South Greenland, consists of various silica-saturated to quartz-bearing syenites, which are intruded by a peralkaline granite. The primary mafic minerals in the syenites are augite +/- olivine + Fe-Ti oxide + amphibole. Ternary feldspar thermometry and phase equilibria among mafic silicates yield T = 950-750degreesC, a(SiO2) = 0.7-1 and an f(O2) of 1-3 log units below the fayalite-magnetite-quartz (FMQ) buffer at 1 kbar. In the granites, the primary mafic minerals are ilmenite and Li-bearing arfvedsonite, which crystallized at temperatures below 750degreesC and at f(O2) values around the FMQ buffer. In both rock types, a secondary post-magmatic assemblage overprints the primary magmatic phases. In syenites, primary Ca-bearing minerals are replaced by Na-rich minerals such as aegirine-augite and albite, resulting in the release of Ca. Accordingly, secondary minerals include ferro-actinolite, (calcite-siderite)(ss), titanite and andradite in equilibrium with the Na-rich minerals. Phase equilibria indicate that formation of these minerals took place over a long temperature interval from near-magmatic temperatures down to similar to300degreesC. In the course of this cooling, oxygen fugacity rose in most samples. For example, late-stage aegirine in granites formed at the expense of arfvedsonite at temperatures below 300degreesC and at an oxygen fugacity above the haematite-magnetite (HM) buffer. The calculated delta(18)O(melt) value for the syenites (+5.9 to +6.3parts per thousand) implies a mantle origin, whereas the inferred delta(18)O(melt) value of <+5.1parts per thousand for the granitic melts is significantly lower. Thus, the granites require an additional low-delta(18)O contaminant, which was not involved in the genesis of the syenites. Rb/Sr data for minerals of both rock types indicate open-system behaviour for Rb and Sr during post-magmatic metasomatism. Neodymium isotope compositions (epsilonNd(1170 Ma) = -3.8 to -6.4) of primary minerals in syenites are highly variable, and suggest that assimilation of crustal rocks occurred to variable extents. Homogeneous epsilon(Nd) values of -5.9 and -6.0 for magmatic amphibole in the granites lie within the range of the syenites. Because of the very similar neodymium isotopic compositions of magmatic and late- to post-magmatic minerals from the same syenite samples a principally closed-system behaviour during cooling is implied. In contrast, for the granites an externally derived fluid phase is required to explain the extremely low epsilon(Nd) values of about -10 and low delta(18)O between +2.0 and +0.5parts per thousand for late-stage aegirine, indicating an open system in the late-stage history. In this study we show that the combination of phase equilibria constraints with stable and radiogenic isotope data on mineral separates can provide much better constraints on magma evolution during emplacement and crystallization than conventional whole-rock studies.

Solution equilibria of cytosine- and guanine-rich sequences near the promoter region of the n-myc gene that contain stable hairpins within lateral loops

Cytosine-and guanine-rich regions of DNA are capable of forming complex structures named i-motifs and G-quadruplexes, respectively. In the present study the solution equilibria at nearly physiological conditions of a 34 -bases long cytosine-rich sequence and its complementary guanin e-rich strand corresponding to the first intron of the n-mycgene were studied. Both sequences , not yet studied, contain a 12 - base tract capable of forming stable hairpins inside the i-motif and G-quadruplex structures, respectively ...

The Role of Surfactant Properties of Extractants in Hydrometallurgical LiquidLiquid Extraction Processes

The amphiphilic nature of metal extractants causes the formation of micelles and other microscopic aggregates when in contact with water and an organic diluent. These phenomena and their effects on metal extraction were studied using carboxylic acid (Versatic 10) and organophosphorus acid (Cyanex 272) based extractants. Special emphasis was laid on the study of phase behaviour in a pre neutralisation stage when the extractant is transformed to a sodium or ammonium salt form. The pre neutralised extractants were used to extract nickel and to separate cobalt and nickel. Phase diagrams corresponding to the pre neutralisation stage in a metal extraction process were determined. The maximal solubilisation of the components in the system water(NH3)/extractant/isooctane takes place when the molar ratio between the ammonia salt form and the free form of the extractant is 0.5 for the carboxylic acid and 1 for the organophosphorus acid extractant. These values correspond to the complex stoichiometry of NH4A•HA and NIi4A, respectively. When such a solution is contacted with water a microemulsion is formed. If the aqueous phase contains also metal ions (e.g. Ni²+), complexation will take place on the microscopic interface of the micellar aggregates. Experimental evidence showing that the initial stage of nickel extraction with pre neutralised Versatic 10 is a fast pseudohomogeneous reaction was obtained. About 90% of the metal were extracted in the first 15 s after the initial contact. For nickel extraction with pre neutralised Versatic 10 it was found that the highest metal loading and the lowest residual ammonia and water contents in the organic phase are achieved when the feeds are balanced so that the stoichiometry is 2NH4+(org) = Nit2+(aq). In the case of Co/Ni separation using pre neutralised Cyanex 272 the highest separation is achieved when the Co/extractant molar ratio in the feeds is 1 : 4 and at the same time the optimal degree of neutralisation of the Cyanex 272 is about 50%. The adsorption of the extractants on solid surfaces may cause accumulation of solid fine particles at the interface between the aqueous and organic phases in metal extraction processes. Copper extraction processes are known to suffer of this problem. Experiments were carried out using model silica and mica particles. It was found that high copper loading, aromacity of the diluent, modification agents and the presence of aqueous phase decrease the adsorption of the hydroxyoxime on silica surfaces.

Bifurcation of relative equilibria of the (1+3)-body problem

We study the relative equilibria of the limit case of the pla- nar Newtonian 4{body problem when three masses tend to zero, the so-called (1 + 3){body problem. Depending on the values of the in- nitesimal masses the number of relative equilibria varies from ten to fourteen. Always six of these relative equilibria are convex and the oth- ers are concave. Each convex relative equilibrium of the (1 + 3){body problem can be continued to a unique family of relative equilibria of the general 4{body problem when three of the masses are su ciently small and every convex relative equilibrium for these masses belongs to one of these six families.

Potentiometric and conductimetric studies of chemical equilibria for pyridoxine hydrochloride in aqueous solutions: simple experimental determination of pKa values and analytical applications to pharmaceutical analysis

The combination of two low-cost classical procedures based on titrimetric techniques is presented for the determination of pyridoxine hydrochloride in pharmaceuticals samples. Initially some experiments were carried out aiming to determine both pKa1 and pKa2 values, being those compared to values of literature and theoretical procedures. Commercial samples containing pyridoxine hydrochloride were electrochemically analysed by exploiting their acid-base and precipitation reactions. Potentiometric titrations accomplished the reaction between the ionizable hydrogens present in pyridoxine hydrochloride, being NaOH used as titrant; while the conductimetric method was based on the chemical precipitation between the chloride of pyridoxine hydrochloride molecule and Ag+ ions from de silver nitrate, changing the conductivity of the solution. Both methods were applied to the same commercial samples leading to concordant results when compared by statistical tests (95 and 98% confidence levels). Recoveries ranging from 99.0 to 108.1% were observed, showing no significant interference on the results.

Modeling of electrolyte sorption – from phase equilibria to dynamic separation systems

In this thesis, general approach is devised to model electrolyte sorption from aqueous solutions on solid materials. Electrolyte sorption is often considered as unwanted phenomenon in ion exchange and its potential as an independent separation method has not been fully explored. The solid sorbents studied here are porous and non-porous organic or inorganic materials with or without specific functional groups attached on the solid matrix. Accordingly, the sorption mechanisms include physical adsorption, chemisorption on the functional groups and partition restricted by electrostatic or steric factors. The model is tested in four Cases Studies dealing with chelating adsorption of transition metal mixtures, physical adsorption of metal and metalloid complexes from chloride solutions, size exclusion of electrolytes in nano-porous materials and electrolyte exclusion of electrolyte/non-electrolyte mixtures. The model parameters are estimated using experimental data from equilibrium and batch kinetic measurements, and they are used to simulate actual single-column fixed-bed separations. Phase equilibrium between the solution and solid phases is described using thermodynamic Gibbs-Donnan model and various adsorption models depending on the properties of the sorbent. The 3-dimensional thermodynamic approach is used for volume sorption in gel-type ion exchangers and in nano-porous adsorbents, and satisfactory correlation is obtained provided that both mixing and exclusion effects are adequately taken into account. 2-Dimensional surface adsorption models are successfully applied to physical adsorption of complex species and to chelating adsorption of transition metal salts. In the latter case, comparison is also made with complex formation models. Results of the mass transport studies show that uptake rates even in a competitive high-affinity system can be described by constant diffusion coefficients, when the adsorbent structure and the phase equilibrium conditions are adequately included in the model. Furthermore, a simplified solution based on the linear driving force approximation and the shrinking-core model is developed for very non-linear adsorption systems. In each Case Study, the actual separation is carried out batch-wise in fixed-beds and the experimental data are simulated/correlated using the parameters derived from equilibrium and kinetic data. Good agreement between the calculated and experimental break-through curves is usually obtained indicating that the proposed approach is useful in systems, which at first sight are very different. For example, the important improvement in copper separation from concentrated zinc sulfate solution at elevated temperatures can be correctly predicted by the model. In some cases, however, re-adjustment of model parameters is needed due to e.g. high solution viscosity.

Modelling the super-equilibria in thermal biomass conversion : applications and limitations of the constrained free energy method

Bioenergi ses som en viktig del av det nu- och framtida sortimentet av inhemsk energi. Svartlut, bark och skogsavfall täcker mer än en femtedel av den inhemska energianvändningen. Produktionsanläggningar kan fungera ofullständigt och en mängd gas-, partikelutsläpp och tjära produceras samtidigt och kan leda till beläggningsbildning och korrosion. Orsaken till dessa problem är ofta obalans i processen: vissa föreningar anrikas i processen och superjämviktstillstånd är bildas. I denna doktorsavhandling presenteras en ny beräkningsmetod, med vilken man kan beskriva superjämviktstillståndet, de viktigaste kemiska reaktionerna, processens värmeproduktion och tillståndsstorheter samtidigt. Beräkningsmetoden grundar sig på en unik frienergimetod med bivillkor som har utvecklats vid VTT. Den här så kallade CFE-metoden har tidigare utnyttjats i pappers-, metall- och kemiindustrin. Applikationer för bioenergi, vilka är demonstrerade i doktorsavhandlingen, är ett nytt användingsområde för metoden. Studien visade att beräkningsmetoden är väl lämpad för högtemperaturenergiprocesser. Superjämviktstillstånden kan uppstå i dessa processer och det kemiska systemet kan definieras med några bivillkor. Typiska tillämpningar är förbränning av biomassa och svartlut, förgasning av biomassa och uppkomsten av kväveoxider. Också olika sätt att definiera superjämviktstillstånd presenterades i doktorsavhandlingen: empiriska konstanter, empiriska hastighetsuttryck eller reaktionsmekanismer kan användas. Resultaten av doktorsavhandlingen kan utnyttjas i framtiden i processplaneringen och i undersökning av nya tekniska lösningar för förgasning, förbränningsteknik och biobränslen. Den presenterade metoden är ett bra alternativ till de traditionella mekanistiska och fenomenmodeller och kombinerar de bästa delarna av både. --------------------------------------------------------------- Bioenergia on tärkeä osa nykyistä ja tulevaa kotimaista energiapalettia. Mustalipeä, kuori ja metsätähteet kattavat yli viidenneksen kotimaisesta energian kulutuksesta. Tuotantolaitokset eivät kuitenkaan aina toimi täydellisesti ja niiden prosesseissa syntyy erilaisia kaasu- ja hiukkaspäästöjä, tervoja sekä prosessilaitteita kuluttavia saostumia ja ruostumista. Usein syy näihin ongelmiin on prosessissa esiintyvä epätasapainotila: tietyt yhdisteet rikastuvat prosessissa ja muodostavat supertasapainotiloja. Väitöstyössä kehitettiin uusi laskentamenetelmä, jolla voidaan kuvata nämä supertasapainotilat, tärkeimmät niihin liittyvät kemialliset reaktiot, prosessin lämmöntuotanto ja tilansuureet yhtä aikaa. Laskentamenetelmä perustuu VTT:llä kehitettyyn ainutlaatuiseen rajoitettuun vapaaenergiamenetelmään. Tätä niin kutsuttua CFE-menetelmää on aiemmin sovelluttu onnistuneesti muun muassa paperi-, metalli- ja kemianteollisuudessa. Väitöstyössä esitetyt bioenergiasovellukset ovat uusi sovellusalue menetelmälle. Työ osoitti laskentatavan soveltuvan hyvin korkealämpöisiin energiatekniikan prosesseihin, joissa kemiallista systeemiä rajoittavia tekijöitä oli rajallinen määrä ja siten super-tasapainotila saattoi muodostua prosessin aikana. Tyypillisiä sovelluskohteita ovat biomassan ja mustalipeän poltto, biomassan kaasutus ja typpioksidipäästöt. Työn aikana arvioitiin myös erilaisia tapoja määritellä super-tasapainojen muodostumista rajoittavat tekijät. Rajoitukset voitiin tehdä teollisiin mittauksiin pohjautuen, kokeellisia malleja hyödyntäen tai mekanistiseen reaktiokinetiikkaan perustuen. Tulevaisuudessa väitöstyön tuloksia voidaan hyödyntää prosessisuunnittelussa ja tutkittaessa uusia teknisiä ratkaisuja kaasutus- ja polttotekniikoissa sekä biopolttoaineiden tutkimuksessa. Kehitetty menetelmä tarjoaa hyvän vaihtoehdon perinteisille mekanistisille ja ilmiömalleille yhdistäen näiden parhaita puolia.

HIGH PRESSURE VAPOR-LIQUID EQUILIBRIA OF PALM FATTY ACIDS DISTILLATES-CARBON DIOXIDE SYSTEM

Vapor-Liquid equilibria of palm fatty acids distillates/carbon dioxide system has been investigated experimentally at temperatures of 333, 353, and 373 K and pressures of 20, 23, 26, and 29 MPa using the static method. Experimental data for the quasi-binary system palm fatty acids distillates/carbon dioxide has been correlated with Redlich-Kwong-Aspen equation of state. Modeling shows good agreement with experimental data. Selectivity obtained indicates that supercritical carbon dioxide is a reasonable solvent for separating saturated (palmitic acid) and unsaturated (oleic+linoleic acids) fatty acids from palm fatty acids distillates in a continuous multistage countercurrent column.

On Stackelberg Equilibria with Differentiated Products: the Critical Role of the Strategy Space.

Nous Considerons Dans Cet Article un Modele de Duopole Avec Produits Differencies; Nous Montrons Que le Caractere Substituts Vs Complements de Ces Produits Est un Facteur Important Dans la Determination du Mode de Concurrence Strategique (Cournot-Bertrand, Nash Mixte, Stackelberg; En Prix Ou Quantites) Que L'on Est Susceptible D'observer. Si les Produits Sont Substituts (Complements), la Concurrence Sera du Type Cournot (Bertrand) Plutot Que du Type Nash Mixte a Moins Qu'une Firme Puisse Affirmer Son Leadership et Forcer une Concurrence a la Stackelberg Mais Quel Soit le Role Tenu Par une Firme, Il Sera Preferable Pour Elle Que la Concurrence S'exprime En Quantite (Prix). Par Ailleurs, la Concurrence a la Bertrand Est Toujours la Meilleure du Point de Vue des Consommateurs et du Point de Vue de L'efficacite Sociale, et Ce, Que les Produits Soient Susbtituts Ou Complements.