Anfíbios Anuros da coleção Adolpho Lutz: III - Hyla claresignata Lutz & B. Lutz, 1939

Hyla claresignata Lutz & Lutz, 1939, is a large species apparently not closely allied to the other known Brazilian hylas. It is characterized by the very small tympanum; the head is short and the snout rounded; the legs are long, the hands and feet unusually large, the latter extensively webbbed. The specific name is derived from the insular, irregular, or roughly triangular, dark spots, with a light halo, found mostly in the dorso-lateral region and on the legs. It belongs to the rain-forest fauna of the Marítime Range. The adult is a bromeliad-dweller and the tadpole rhyacophilous. DESCRIPTION. Vomerine teeth in two separate, oblique, groups, behind the large choanae, parallel to the posterior half of their inner border. Tongue entire, short, very broad and hardly free behind. Snout short, rounded, with distinct canthus rostralis and gradually sloping loreal region. Eye very large and prominent, its horizontal diameter almost equal to the distance between its anterior corner and the tip of the snout. Tympanum very small, less than one third of the diameter of the eye, but distinct, partly covered by a short, heavy ridge. Lateral fingers less than one third webbed; fourth finger slightly longer than the second, just reaching the base of the disk of the third; subarticular tubercles well developed; an angular pollex rudiment, more noticeable in the males. Toes almost completely webbed, the edge of the web inserted at the base of the disk on the third and the fifth; an inner metatarsal tubercle. Skin smooth above, granular beneath, on the throat minutely so. No dermal appendage on the hell. Habit robust, head broader than long, body rather heavy, slightly narrowed in the postaxillary region. Legs long, the tibiotarsal articulation reaching beyond the tip of the snout when adpressed. Type (female): 61 mm. (Fig. 1.) DIAGNOSIS of TADPOLE (by G. Orton). "A large specialized, mountain-stream tadpole, with wide head an elongated, flattened snout, greatly enlarged lips and high tooth formula. Eyes dorsal. Spiracle sinistral, projecting, situated far back on side. Anus dextral. Tooth formula 8/12 to 9/14 in fully grown larvae. Tail with a prominent, vertical dark band across musculature and fins; a second concentration of dark pigment near tip of tail, may or may not form a similar but narrower band. Maximum known total length: 60mm.; head and body length 25mm. (Figs. 6 e 7). For further details see Lutz & Lutz, 1939 and Lutz B. & Orton G. 1946.

Chain conditions for Leavitt path algebras

In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the algebras L(E)for which every corner is left (equivalently, right)artinian. They are also precisely the algebras L(E) for which every finitely generated left (equivalently, right) L(E)-module is artinian. In our second main result, we give necessary and sufficient conditions for every corner of L(E) to be left (equivalently, right) noetherian. They also turn out to be precisely those algebras L(E) for which every finitely generated left(equivalently, right) L(E)-module is noetherian. In both situations, isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x−1] are provided. Likewise, in both situations, equivalent graph theoretic conditions on E are presented.

When Do We Learn to Cooperate? The Role of Social Learning in Social Dilemmas

In this paper, I look at the interaction between social learning and cooperative behavior. I model this using a social dilemma game with publicly observed sequential actions and asymmetric information about pay offs. I find that some informed agents in this model act, individually and without collusion, to conceal the privately optimal action. Because the privately optimal action is socially costly the behavior of informed agents can lead to a Pareto improvement in a social dilemma. In my model I show that it is possible to get cooperative behavior if information is restricted to a small but non-zero proportion of the population. Moreover, such cooperative behavior occurs in a finite setting where it is public knowledge which agent will act last. The proportion of cooperative agents within the population can be made arbitrarily close to 1 by increasing the finite number of agents playing the game. Finally, I show that under a broad set of conditions that it is a Pareto improvement on a corner value, in the ex-ante welfare sense, for an interior proportion of the population to be informed.

Emissions distribution in post-Kyoto international negotiations: a policy

An abundant scientific literature about climate change economics points out that the future participation of developing countries in international environmental policies will depend on their amount of pay offs inside and outside specific agreements. These studies are aimed at analyzing coalitions stability typically through a game theoretical approach. Though these contributions represent a corner stone in the research field investigating future plausible international coalitions and the reasons behind the difficulties incurred over time to implement emissions stabilizing actions, they cannot disentangle satisfactorily the role that equality play in inducing poor regions to tackle global warming. If we focus on the Stern Review findings stressing that climate change will generate heavy damages and policy actions will be costly in a finite time horizon, we understand why there is a great incentive to free ride in order to exploit benefits from emissions reduction efforts of others. The reluctance of poor countries in joining international agreements is mainly supported by historical responsibility of rich regions in generating atmospheric carbon concentration, whereas rich countries claim that emissions stabilizing policies will be effective only when developing countries will join them.Scholars recently outline that a perceived fairness in the distribution of emissions would facilitate a wide spread participation in international agreements. In this paper we overview the literature about distributional aspects of emissions by focusing on those contributions investigating past trends of emissions distribution through empirical data and future trajectories through simulations obtained by integrated assessment models. We will explain methodologies used to elaborate data and the link between real data and those coming from simulations. Results from this strand of research will be interpreted in order to discuss future negotiations for post Kyoto agreements that will be the focus of the next. Conference of the Parties in Copenhagen at the end of 2009. A particular attention will be devoted to the role that technological change will play in affecting the distribution of emissions over time and to how spillovers and experience diffusion could influence equality issues and future outcomes of policy negotiations.

Hominoid fission of chromosome 14/15 and the role of segmental duplications.

Ape chromosomes homologous to human chromosomes 14 and 15 were generated by a fission event of an ancestral submetacentric chromosome, where the two chromosomes were joined head-to-tail. The hominoid ancestral chromosome most closely resembles the macaque chromosome 7. In this work, we provide insights into the evolution of human chromosomes 14 and 15, performing a comparative study between macaque boundary region 14/15 and the orthologous human regions. We construct a 1.6-Mb contig of macaque BAC clones in the region orthologous to the ancestral hominoid fission site and use it to define the structural changes that occurred on human 14q pericentromeric and 15q subtelomeric regions. We characterize the novel euchromatin-heterochromatin transition region (∼20 Mb) acquired during the neocentromere establishment on chromosome 14, and find it was mainly derived through pericentromeric duplications from ancestral hominoid chromosomes homologous to human 2q14-qter and 10. Further, we show a relationship between evolutionary hotspots and low-copy repeat loci for chromosome 15, revealing a possible role of segmental duplications not only in mediating but also in "stitching" together rearrangement breakpoints.

Double-bundle transtibial posterior cruciate ligament reconstruction with a tendon-patellar bone-semitendinosus tendon autograft: clinical results with a minimum of 2 years' follow-up.

PURPOSE: The purpose of this study was to evaluate the clinical and subjective outcomes after arthroscopic-assisted double-bundle posterior cruciate ligament (PCL) reconstruction. METHODS: A series of 15 patients with grade III isolated chronic PCL tears underwent double-bundle PCL reconstruction. Of these patients, 8 (53%) had simultaneous fractures. The mean time from accident to surgery was 10.8 months (range, 8 to 15 months). The mean age at the time of surgery was 28.2 years (range, 17 to 43 years). All of the patients reported knee insecurity during activities of daily living or light sporting activities, with associated anterior knee pain in 5 patients. Preoperatively, posterolateral or posteromedial corner injuries were ruled out through accurate clinical examination. The knees were assessed before surgery and at a mean follow-up of 3.2 years (range, 2 to 5 years) with a physical examination, 4 different rating scales, and stress radiographs obtained with a Telos device (Telos, Marburg, Germany). RESULTS: Postoperative physical examination revealed a reduction of the posterior drawer and tibial step-off in all cases, although the posterior laxity was not completely normalized. Nevertheless, the patients were subjectively better after surgery. The subjective International Knee Documentation Committee score was significantly ameliorated. With regard to the objective International Knee Documentation Committee score, 6 knees (40%) were graded as abnormal because of posterior displacement of 6 mm or greater on follow-up stress radiographs with the Telos device. On the Lysholm knee scoring scale, the score was excellent in 13% of patients and good in 87%. The mean score on the Hospital for Special Surgery knee ligament rating scale was 85.8. The Tegner activity score showed an amelioration after surgery, but no patient resumed his or her preinjury level of activities. The postoperative stress radiographs revealed an improvement in posterior instability of 50% or more in all but 3 knees (20%). CONCLUSIONS: Our technique of double-bundle PCL reconstruction produced a significant reduction in knee symptoms and allowed the patients to return to moderate or strenuous activity, although the posterior tibial translation was not completely normalized and our results appear to be no better than the results of single-bundle PCL reconstruction. LEVEL OF EVIDENCE: Level IV, therapeutic case series.

Guidelines for the Conversion of Urban Four-Lane Undivided Roadways to Three-Lane Two-Way Left-turn Lane Facilities, April 2001

Four-lane undivided roadways in urban areas can experience a degradation of service and/or safety as traffic volumes increase. In fact, the existence of turning vehicles on this type of roadway has a dramatic effect on both of these factors. The solution identified for these problems is typically the addition of a raised median or two-way left-turn lane (TWLTL). The mobility and safety benefits of these actions have been proven and are discussed in the “Past Research” chapter of this report along with some general cross section selection guidelines. The cost and right-of-way impacts of these actions are widely accepted. These guidelines focus on the evaluation and analysis of an alternative to the typical four-lane undivided cross section improvement approach described above. It has been found that the conversion of a four-lane undivided cross section to three lanes (i.e., one lane in each direction and a TWLTL) can improve safety and maintain an acceptable level of service. These guidelines summarize the results of past research in this area (which is almost nonexistent) and qualitative/quantitative before-and-after safety and operational impacts of case study conversions located throughout the United States and Iowa. Past research confirms that this type of conversion is acceptable or feasible in some situations but for the most part fails to specifically identify those situations. In general, the reviewed case study conversions resulted in a reduction of average or 85th percentile speeds (typically less than five miles per hour) and a relatively dramatic reduction in excessive speeding (a 60 to 70 percent reduction in the number of vehicles traveling five miles per hour faster than the posted speed limit was measured in two cases) and total crashes (reductions between 17 to 62 percent were measured). The 13 roadway conversions considered had average daily traffic volumes of 8,400 to 14,000 vehicles per day (vpd) in Iowa and 9,200 to 24,000 vehicles per day elsewhere. In addition to past research and case study results, a simulation sensitivity analysis was completed to investigate and/or confirm the operational impacts of a four-lane undivided to three-lane conversion. First, the advantages and disadvantages of different corridor simulation packages were identified for this type of analysis. Then, the CORridor SIMulation (CORSIM) software was used x to investigate and evaluate several characteristics related to the operational feasibility of a four-lane undivided to three-lane conversion. Simulated speed and level of service results for both cross sections were documented for different total peak-hour traffic, access densities, and access-point left-turn volumes (for a case study corridor defined by the researchers). These analyses assisted with the identification of the considerations for the operational feasibility determination of a four -lane to three-lane conversion. The results of the simulation analyses primarily confirmed the case study impacts. The CORSIM results indicated only a slight decrease in average arterial speed for through vehicles can be expected for a large range of peak-hour volumes, access densities, and access-point left-turn volumes (given the assumptions and design of the corridor case study evaluated). Typically, the reduction in the simulated average arterial speed (which includes both segment and signal delay) was between zero and four miles per hour when a roadway was converted from a four-lane undivided to a three-lane cross section. The simulated arterial level of service for a converted roadway, however, showed a decrease when the bi-directional peak-hour volume was about 1,750 vehicles per hour (or 17,500 vehicles per day if 10 percent of the daily volume is assumed to occur in the peak hour). Past research by others, however, indicates that 12,000 vehicles per day may be the operational capacity (i.e., level of service E) of a three-lane roadway due to vehicle platooning. The simulation results, along with past research and case study results, appear to support following volume-related feasibility suggestions for four-lane undivided to three-lane cross section conversions. It is recommended that a four-lane undivided to three-lane conversion be considered as a feasible (with respect to volume only) option when bi-directional peak-hour volumes are less than 1,500 vehicles per hour, but that some caution begin to be exercised when the roadway has a bi-directional peak-hour volume between 1,500 and 1,750 vehicles per hour. At and above 1,750 vehicles per hour, the simulation indicated a reduction in arterial level of service. Therefore, at least in Iowa, the feasibility of a four-lane undivided to three-lane conversion should be questioned and/or considered much more closely when a roadway has (or is expected to have) a peak-hour volume of more than 1,750 vehicles. Assuming that 10 percent of the daily traffic occurs during the peak-hour, these volume recommendations would correspond to 15,000 and 17,500 vehicles per day, respectively. These suggestions, however, are based on the results from one idealized case xi study corridor analysis. Individual operational analysis and/or simulations should be completed in detail once a four-lane undivided to three-lane cross section conversion is considered feasible (based on the general suggestions above) for a particular corridor. All of the simulations completed as part of this project also incorporated the optimization of signal timing to minimize vehicle delay along the corridor. A number of determination feasibility factors were identified from a review of the past research, before-and-after case study results, and the simulation sensitivity analysis. The existing and expected (i.e., design period) statuses of these factors are described and should be considered. The characteristics of these factors should be compared to each other, the impacts of other potentially feasible cross section improvements, and the goals/objectives of the community. The factors discussed in these guidelines include • roadway function and environment • overall traffic volume and level of service • turning volumes and patterns • frequent-stop and slow-moving vehicles • weaving, speed, and queues • crash type and patterns • pedestrian and bike activity • right-of-way availability, cost, and acquisition impacts • general characteristics, including - parallel roadways - offset minor street intersections - parallel parking - corner radii - at-grade railroad crossings xii The characteristics of these factors are documented in these guidelines, and their relationship to four-lane undivided to three-lane cross section conversion feasibility identified. This information is summarized along with some evaluative questions in this executive summary and Appendix C. In summary, the results of past research, numerous case studies, and the simulation analyses done as part of this project support the conclusion that in certain circumstances a four-lane undivided to three-lane conversion can be a feasible alternative for the mitigation of operational and/or safety concerns. This feasibility, however, must be determined by an evaluation of the factors identified in these guidelines (along with any others that may be relevant for a individual corridor). The expected benefits, costs, and overall impacts of a four-lane undivided to three-lane conversion should then be compared to the impacts of other feasible alternatives (e.g., adding a raised median) at a particular location.

Topographic organization of V1 projections through the corpus callosum in humans.

The visual cortex in each hemisphere is linked to the opposite hemisphere by axonal projections that pass through the splenium of the corpus callosum. Visual-callosal connections in humans and macaques are found along the V1/V2 border where the vertical meridian is represented. Here we identify the topography of V1 vertical midline projections through the splenium within six human subjects with normal vision using diffusion-weighted MR imaging and probabilistic diffusion tractography. Tractography seed points within the splenium were classified according to their estimated connectivity profiles to topographic subregions of V1, as defined by functional retinotopic mapping. First, we report a ventral-dorsal mapping within the splenium with fibers from ventral V1 (representing the upper visual field) projecting to the inferior-anterior corner of the splenium and fibers from dorsal V1 (representing the lower visual field) projecting to the superior-posterior end. Second, we also report an eccentricity gradient of projections from foveal-to-peripheral V1 subregions running in the anterior-superior to posterior-inferior direction, orthogonal to the dorsal-ventral mapping. These results confirm and add to a previous diffusion MRI study (Dougherty et al., 2005) which identified a dorsal/ventral mapping of human splenial fibers. These findings yield a more detailed view of the structural organization of the splenium than previously reported and offer new opportunities to study structural plasticity in the visual system.

Analysis of acute brain slices by electron microscopy: A correlative light-electron microscopy workflow based on Tokuyasu cryo-sectioning.

Acute brain slices are slices of brain tissue that are kept vital in vitro for further recordings and analyses. This tool is of major importance in neurobiology and allows the study of brain cells such as microglia, astrocytes, neurons and their inter/intracellular communications via ion channels or transporters. In combination with light/fluorescence microscopies, acute brain slices enable the ex vivo analysis of specific cells or groups of cells inside the slice, e.g. astrocytes. To bridge ex vivo knowledge of a cell with its ultrastructure, we developed a correlative microscopy approach for acute brain slices. The workflow begins with sampling of the tissue and precise trimming of a region of interest, which contains GFP-tagged astrocytes that can be visualised by fluorescence microscopy of ultrathin sections. The astrocytes and their surroundings are then analysed by high resolution scanning transmission electron microscopy (STEM). An important aspect of this workflow is the modification of a commercial cryo-ultramicrotome to observe the fluorescent GFP signal during the trimming process. It ensured that sections contained at least one GFP astrocyte. After cryo-sectioning, a map of the GFP-expressing astrocytes is established and transferred to correlation software installed on a focused ion beam scanning electron microscope equipped with a STEM detector. Next, the areas displaying fluorescence are selected for high resolution STEM imaging. An overview area (e.g. a whole mesh of the grid) is imaged with an automated tiling and stitching process. In the final stitched image, the local organisation of the brain tissue can be surveyed or areas of interest can be magnified to observe fine details, e.g. vesicles or gold labels on specific proteins. The robustness of this workflow is contingent on the quality of sample preparation, based on Tokuyasu's protocol. This method results in a reasonable compromise between preservation of morphology and maintenance of antigenicity. Finally, an important feature of this approach is that the fluorescence of the GFP signal is preserved throughout the entire preparation process until the last step before electron microscopy.

Testing the response of macroinvertebrate functional structure and biodiversity to flooding and confinement

The aim of the present study was to investigate the relative importance of flooding- and confinement-related environmentalfeatures in explaining macroinvertebrate trait structure and diversity in a pool of wetlands located in a Mediterranean riverfloodplain. To test hypothesized trait-environment relationships, we employed a recently implemented statistical procedure, thefourth-corner method. We found that flooding-related variables, mainly pH and turbidity, were related to traits that confer an abilityof the organism to resist flooding (e.g., small body-shape, protection of eggs) or recuperate faster after flooding (e.g., short life-span, asexual reproduction). In contrast, confinement-related variables, mainly temperature and organic matter, enhanced traits that allow organisms to interact and compete with other organisms (e.g., large size, sexual reproduction) and to efficiently use habitat and resources (e.g., diverse locomotion and feeding strategies). These results are in agreement with predictions made under the River Habitat Templet for lotic ecosystems, and demonstrate the ability of the fourth-corner method to test hypothesis that posit traitenvironment relationships. Trait diversity was slightly higher in flooded than in confined sites, whereas trait richness was not significantly different. This suggests that although trait structure may change in response to the main environmental factors, as evidenced by the fourth-corner method, the number of life-history strategies needed to persist in the face of such constraints remains more or less constant; only their relative dominance differs

Case Management Program For Frail Elders Manual, August 2008

The purpose of this manual is to guide operation of the Case Management Program for Frail Elders. After Background, Program Administration, Definitions, Consumer Eligibility, and Program Standards, the order follows the flow of a consumer entering the pro-gram from referral through ongoing case activities. The manual is written assuming the reader is the Case Manager. The effective date will appear in the bottom left hand corner of each page. This manual will be updated as needed via Iowa Aging Program Instructions (IAPI). This manual is used in conjunction with the Department of Human Services’ manuals which provide more detail about policies and procedures within the Medicaid elderly waiver program.

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.

Slow Dynamics of Ising Models with Energy Barriers

Using Monte Carlo simulations we study the dynamics of three-dimensional Ising models with nearest-, next-nearest-, and four-spin (plaquette) interactions. During coarsening, such models develop growing energy barriers, which leads to very slow dynamics at low temperature. As already reported, the model with only the plaquette interaction exhibits some of the features characteristic of ordinary glasses: strong metastability of the supercooled liquid, a weak increase of the characteristic length under cooling, stretched-exponential relaxation, and aging. The addition of two-spin interactions, in general, destroys such behavior: the liquid phase loses metastability and the slow-dynamics regime terminates well below the melting transition, which is presumably related with a certain corner-rounding transition. However, for a particular choice of interaction constants, when the ground state is strongly degenerate, our simulations suggest that the slow-dynamics regime extends up to the melting transition. The analysis of these models leads us to the conjecture that in the four-spin Ising model domain walls lose their tension at the glassy transition and that they are basically tensionless in the glassy phase.

Upper Triassic to Cretaceous radiolaria from Nicaragua and northern Costa Rica - The Mesquito composite oceanic terrane

We propose a new terrane subdivision of Nicaragua and Northern Costa Rica, based on Upper Triassic to Upper Cretaceous radiolarian biochronology of ribbon radiolarites, the newly studied Siuna Serpentinite Mélange, and published 40Ar/39Ar dating and geochemistry of mafic and ultramafic igneous rock units of the area. The new Mesquito Composite Oceanic Terrane (MCOT) comprises the southern half of the Chortis Block, that was assumed to be a continental fragment of N-America. The MCOT is defined by 4 corner localities characterized by ultramafic and mafic oceanic rocks and radiolarites of Late Triassic, Jurassic and Early Cretaceous age: 1. The Siuna Serpentinite Mélange (NE-Nicaragua), 2. The El Castillo Mélange (Nicaragua/Costa Rica border), 3.The Santa Elena Ultramafics (N-Costa Rica) and, 4. DSDP Legs 67/84. 1. The Siuna Serpentinite Mélange contains, high pressure metamorphic mafics and Middle Jurassic (Bajocian-Bathonian) radiolarites in original, sedimentary contact with arc-metandesites. The Siuna Mélange also contains Upper Jurassic black detrital chert formed in a marginal (fore-arc?) basin shortly before subduction. A phengite 40Ar/39Ar -cooling age dates the exhumation of the high pressure rocks as 139 Ma (earliest Cretaceous). 2. The El Castillo Mélange comprises a radiolarite block tectonically embedded in serpentinite that yielded a diverse Rhaetian (latest Triassic) radiolarian assemblage, the oldest fossils recovered so far from S-Central America. 3. The Santa Elena Ultramafics of N-Costa Rica together with the serpentinite outcrops near El Castillo (2) in Southern Nicaragua, are the southernmost outcrops of the MCOT. The Santa Elena Unit (3) itself is still undated, but it is thrust onto the middle Cretaceous Santa Rosa Accretionary Complex (SRAC), that contains Lower to Upper Jurassic, highly deformed radiolarite blocks, probably reworked from the MCOT, which was the upper plate with respect to the SRAC. 4. Serpentinites, metagabbros and basalts have long been known from DSDP Leg 67/84 (3), drilled off Guatemala in the Nicaragua-Guatemala forearc basement. They have been restudied and reveal 40Ar/39Ar dated Upper Triassic to middle Cretaceous enriched Ocean Island Basalts and Jurassic to Lower Cretaceous depleted Island arc rocks of probable Pacific origin. The area between localities 1-4 is largely covered by Tertiary to Recent arcs, but we suspect that its basement is made of oceanic/accreted terranes. Earthquake seismic studies indicate an ill-defined, shallow Moho in this area. The MCOT covers most of Nicaragua and could extend to Guatemala to the W and form the Lower (southern) Nicaragua Rise to the NE. Some basement complexes of Jamaica, Hispaniola and Puerto Rico may also belong to the MCOT. The Nicoya Complex s. str. has been regarded as an example of Caribbean crust and the Caribbean Large Igneous Province (CLIP). However, 40Ar/39Ar - dates on basalts and intrusives indicate ages as old as Early Cretaceous. Highly deformed Jurassic and Lower Cretaceous radiolarites occur as blocks within younger intrusives and basalts. Our interpretation is that radiolarites became first accreted to the MCOT, then became reworked into the Nicoya Plateau in Late Cretaceous times. This implies that the Nicoya Plateau formed along the Pacific edge of the MCOT, independent form the CLIP and most probably unrelated with he Galapagos hotspot. No Jurassic radiolarite, no older sediment age than Coniacian-Santonian, and no older 40Ar/39Ar age than 95 Ma is known from S-Central America between SE of Nicoya and Colombia. For us this area represents the trailing edge of the CLIP s. str.

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.