An Approach to the stability of international environmental agreements: the absorbing sets solution

We study international environmental negotiations when agreements between countries can not be binding. A problem with this kind of negotiations is that countries have incentives for free-riding from such agreements. We develope a notion of equilibrium based on the assumption that countries can create and dissolve agreements in their seeking of a larger welfare. This approach leads to a larger degree of cooperation compared to models based on the internal-external stability approach.

The von Neumann-Morgenstern stable sets for 2x2 games

We analyze the von Neumann and Morgenstern stable sets for the mixed extension of 2 2 games when only single profitable deviations are allowed. We show that the games without a strict Nash equilibrium have a unique vN&M stable set and otherwise they have infinite sets.

Scenario sets

The outputs from the pilot work with CIBT to develop scenario guide based on existing work across European business, adding an education and more specifically IT perspective to generic scenarios.

Distribution of Atlantic menhaden, Brevoortia tyrannus, purse-seine sets and catches from southern New England to North Carolina, 1985-96

Sets and catches of Atlantic menhaden, Brevoortia tyrannus, made in 1985-96 by purse-seine vessels from Virginia and North Carolina were studied by digitizing and analyzing Captain's Daily Fishing Reports (CDFR's), daily logs of fishing activities completed by captains of menhaden vessels. 33,674 CDFR's were processed, representing 125,858 purse-seine sets. On average, the fleet made 10,488 sets annually. Virginia vessels made at least one purse-seine set on 67%-83% of available fishing days between May and December. In most years, five was the median number of sets attempted each fishing day. Mean set duration ranged from 34 to 43 minutes, and median catch per set ranged from 15 to 30 metric tons (t). Spotter aircraft assisted in over 83% of sets overall. Average annual catch in Chesapeake Bay (149,500 t) surpassed all other fishing areas, and accounted for 52% of the fleet's catch. Annual catch from North Carolina waters (49,100 t) ranked a distant second. Fishing activity in ocean waters clustered off the Mid-Atlantic states in June-September, and off North Carolina in November-January. Delaware Bay and the New Jersey coast were important alternate fishing grounds during summer. Across all ocean fishing areas, most sets and catch occurred within 3 mi. of shore, but in Chesapeake Bay about half of all fishing activity occurred farther offshore. In Virginia, areas adjacent to fish factories tended to be heavily fished. Recent regulatory initiatives in various coastal states threaten the Atlantic menhaden fleet's access to traditional nearshore fishing grounds. (PDF file contains 26 pages.)

Variation in size of yellowfin tuna (Thunnus albacares) within individual purse-seine sets

ENGLISH:Length-frequency samples of yellowfin tuna from 276 individual purse-seine sets were examined. Evidence of schooling by size is presented. Yellowfin schooled with skipjack are smaller and more homogeneous in length than are yellowfin from pure schools. Yellowfin in schools associated with porpoise appear to be more variable in size than yellowfin from other types of schools. No relationship was found between the tonnage of yellowfin in a school and the mean length of the yellowfin. Despite the tendency to school by size, the size variation within individual schools was judged to be enough to complicate greatly any program of regulation aimed at maximizing the yield-per-recruit through increasing the minimum size of yellowfin at first capture. SPANISH: Fueron examinadas las muestras frecuencia-longitud de atún aleta amarilla, de 276 lances individuales de redes de cerco. Se presenta la evidencia de agrupación por tamaños. Los atunes aleta amarilla agrupados con barrilete, son más pequeños y más homogéneos en longitud, que los atunes aleta amarilla de cardúmenes puros. El atún aleta amarilla en cardúmenes asociados con delfines parece ser más variable en tamaño, que el atún aleta amarilla proveniente de otros tipos de cardúmenes. No se encontró relac¡'ón entre el tonelaje del atún aleta amarilla en un cardumen y la longitud media de esta especie. A pesar de la tendencia a agruparse por tamaño, se juzgó, que la variación de tamaño en cardúmenes individuales, sería suficiente para complicar grandemente cualquier programa de reglamentación, dirigido a obtener el máximo del rendimiento por recluta a través del incremento del tamaño mínimo del atún aleta amarilla en la primera captura.

Estimation of the number of purse-seiner sets on tuna associated with dolphins in the Eastern Pacific Ocean during 1959-1980

ENGLISH: Annual estimates of the number of purse-seine sets made on tunas associated with dolphins are needed to estimate the total number of dolphins killed incidentally by the eastern Pacific tuna fishery. The most complete source of data, the Inter-American Tropical Tuna Commission's logbook data base, was used in this study. In the logbook data base, most sets are identified as being either associated with dolphins or not associated with dolphins. Some sets are not identified in this respect. However, the number of these unidentified sets which were associated with dolphins have been estimated by stratifying the logbook data according to whether or not any tuna were caught, whether or not the nearest identified set was associated with dolphins, and the distance to the nearest identified set. Most of the unidentified sets fell in strata characterized by a proportion of sets on tuna associated with dolphins that was lower than the overall unstratified proportion. Landings data were used to estimate the number of sets on tunas associated with dolphins from fishing trips not included in the logbook data base. SPANISH: Se necesitan las estimaciones anuales de la cantidad de lances realizados sobre atunes asociados con delfines para calcular todo el número de delfines muertos accidentalmente en la pesca atunera del Pacífico oriental. Se empleó en este estudio la fuente más completa-los datos de la Comisión Interamericana del Atún Tropical, proveniente de los cuadernos de bitácora. En éstos, la mayoría de los lances han sido identificados ya sea como asociados o no asociados con delfines. Algunos de los lances no han sido identificados a este respecto. Sin embargo, se ha estimado el número de estos lances asociados con delfines que no se habían identificado, al estratificar los datos de bitácora de acuerdo a si se había o no capturado atún, a si el lance identificado más próximo era o no un lance asociado con delfines y al averiguar la distancia del lance identificado más cercano. La mayoría de los lances sin identificar se colocan en los estratos caracterizados por una proporción de lances sobre atunes asociados con delfines, inferior a la proporción general sin estratificar. Se usaron los datos de los desembarques para calcular la cantidad de lances sobre atunes asociados con delfines en viajes pesqueros que no fueron incluídos en la base de los datos de bitácora. (PDF contains 73 pages.)

An arithmetical theorem for partially ordered sets

The simplest multiplicative systems in which arithmetical ideas can be defined are semigroups. For such systems irreducible (prime) elements can be introduced and conditions under which the fundamental theorem of arithmetic holds have been investigated (Clifford (3)). After identifying associates, the elements of the semigroup form a partially ordered set with respect to the ordinary division relation. This suggests the possibility of an analogous arithmetical result for abstract partially ordered sets. Although nothing corresponding to product exists in a partially ordered set, there is a notion similar to g.c.d. This is the meet operation, defined as greatest lower bound. Thus irreducible elements, namely those elements not expressible as meets of proper divisors can be introduced. The assumption of the ascending chain condition then implies that each element is representable as a reduced meet of irreducibles. The central problem of this thesis is to determine conditions on the structure of the partially ordered set in order that each element have a unique such representation.

Part I contains preliminary results and introduces the principal tools of the investigation. In the second part, basic properties of the lattice of ideals and the connection between its structure and the irreducible decompositions of elements are developed. The proofs of these results are identical with the corresponding ones for the lattice case (Dilworth (2)). The last part contains those results whose proofs are peculiar to partially ordered sets and also contains the proof of the main theorem.

Smooth sets for borel equivalence relations and the covering property for σ-ideals of compact sets

This thesis is divided into three chapters. In the first chapter we study the smooth sets with respect to a Borel equivalence realtion E on a Polish space X. The collection of smooth sets forms σ-ideal. We think of smooth sets as analogs of countable sets and we show that an analog of the perfect set theorem for Σ¹₁ sets holds in the context of smooth sets. We also show that the collection of Σ¹₁ smooth sets is ∏¹₁ on the codes. The analogs of thin sets are called sparse sets. We prove that there is a largest ∏¹₁ sparse set and we give a characterization of it. We show that in L there is a ∏¹₁ sparse set which is not smooth. These results are analogs of the results known for the ideal of countable sets, but it remains open to determine if large cardinal axioms imply that ∏¹₁ sparse sets are smooth. Some more specific results are proved for the case of a countable Borel equivalence relation. We also study I(E), the σ-ideal of closed E-smooth sets. Among other things we prove that E is smooth iff I(E) is Borel.

In chapter 2 we study σ-ideals of compact sets. We are interested in the relationship between some descriptive set theoretic properties like thinness, strong calibration and the covering property. We also study products of σ-ideals from the same point of view. In chapter 3 we show that if a σ-ideal I has the covering property (which is an abstract version of the perfect set theorem for Σ¹₁ sets), then there is a largest ∏¹₁ set in I^int (i.e., every closed subset of it is in I). For σ-ideals on 2^ω we present a characterization of this set in a similar way as for C₁, the largest thin ∏¹₁ set. As a corollary we get that if there are only countable many reals in L, then the covering property holds for Σ¹₂ sets.