Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

Dynamic matching and bargaining: the role of deadlines

We consider a dynamic model where traders in each period are matched randomly into pairs who then bargain about the division of a fixed surplus. When agreement is reached the traders leave the market. Traders who do not come to an agreement return next period in which they will be matched again, as long as their deadline has not expired yet. New traders enter exogenously in each period. We assume that traders within a pair know each other's deadline. We define and characterize the stationary equilibrium configurations. Traders with longer deadlines fare better than traders with short deadlines. It is shown that the heterogeneity of deadlines may cause delay. It is then shown that a centralized mechanism that controls the matching protocol, but does not interfere with the bargaining, eliminates all delay. Even though this efficient centralized mechanism is not as good for traders with long deadlines, it is shown that in a model where all traders can choose which mechanism to

Tacit collusion and capacity withholding in repeated uniform price auctions

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this out-come. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor

Double implementation in a market for indivisible goods with a price constraint

I consider the problem of assigning agents to objects where each agent must pay the price of the object he gets and prices must sum to a given number. The objective is to select an assignment-price pair that is envy-free with respect to the true preferences. I prove that the proposed mechanism will implement both in Nash and strong Nash the set of envy-free allocations. The distinguishing feature of the mechanism is that it treats the announced preferences as the true ones and selects an envy-free allocation with respect to the announced preferences.

Search and bargaining in large markets with homogeneous traders

We study pair-wise decentralized trade in dynamic markets with homogeneous, non-atomic, buyers and sellers that wish to exchange one unit. Pairs of traders are randomly matched and bargaining a price under rules that offer the freedom to quit the match at any time. Market equilbria, prices and trades over time, are characterized. The asymptotic behavior of prices and trades as frictions (search costs and impatience) vanish, and the conditions for (non) convergence to walrasian prices are explored. As a side product of independent interest, we present a self-contained theory of non-cooperative bargaining with two-sided, time-varying, outside options.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Terceira contribuicäo ao conhecimento do gênero Archytas Jaennicke, 1867: (Diptera, Tachinidae)

Twelve species of the genus Archytas Jennicke, 1867, eight of which described as new are studied and figured in detail. Definitions of the species are based mainly on characters of male genitalia. The male genital characters are the most significant for separation of the species and most demonstrative of their affinities. By examining a long series of species of this genus we came to the conclusion that the presence of one pair of median marginal bristles on the third abdominal tergite seems to be characteristic of the genus. This caracter apparently so important, is not however considered fundamental. The most significant example is found in Archytas lenkoi sp. n. and Archytas vexor Curran, 1928. In A. lenkoi we can find one or two pairs or thay may, less frquently, be absent. In A. vexor these bristles are lacking. The shape of the male copulatory apparatus of Jurinia nitidiventris Curran, 1928 refered to by CURRAN in his "Revision of Archytas", is not characteristic of any species of the group and so, is not considered in this paper. To help in the identification, the species studied here are divided into groups. The analis group" includes: A. apicifer (Walker, 1894), A. californiae (Walker, 1856), A. nivalis Curran, 1928, a. giacomellii (Blanchard, 1941), A. basifulvus (Walker, 1849), A. incasanus Townsend, 1912 and A. cirphis Curran, 1927. The identification of members of these group is extremely difficult owing both to their similarity in colour pattern and to their variability. They all have black testaceous or dark brown abdomen, the last segment pale or brownish pollinose; second segment without bristles; third with a pair of strong marginals, fourth and fifth with two rows of discals on apical third. The final determination often rests upon the structure of the male copulatory apparatus. Fortunately in this group, many of the forcipes superiores and palpi genitalium are strikingly different from one another. The "zikani group" includes: A. zikani sp. n., A seabrai sp. n., A. duckei sp. n. and A. vernalis Curran, 1928. This group may be characterized as follows: forcipes interiores absent; forcipes superiores strongly chitinized an dilated at anex. Within this group, the forcipes of. A. seabrai sp. n. do not present an aberrant form. The "dissimilis group" will be studied in forthcoming papers. The limits of the genus Archyta Jaen. are not as yet sharply difined, the evaluation of the significance of each character used in the definition remaining as most difficult problem. The distinction between Archytas and other related genera is very difficult, chiefly because it is based on variable characters. In this paper we place the genera Parafabricia Towsend, 1931, Itachytas Blanchard, 1940, Archynemochaeta Blanchard, 1941, Proarchytoides Blanchard, 1941 and Archytodejeania Blanchard, 1941 in the synonymy of Archytas Jaen. The detailed examination of the characters used in their definition, proved them to be fundamentally proposed on basis of chaetotasy, these characters alone being precarious, because of the considerabel intraspecifical variation. The type of the new species are in the Oswaldo Cruz Institute collection. Rio de Janeiro, Brazil, and paratypes in the collections of the followings institutions: Departamento de Zoologia da Secretaria de Agricultura do Estado de São Paulo; Instituto de Ecologia e Experimemtação Agrícolas; Departamento de Defesa Sanitária Vegetal; Campos Seabra collection; and Barbiellini collection.

Contribuição ao conhecimento da sistemática e biologia de buprestídeos minadores do gênero Pachyschelus Solier, 1833: (Coleoptera, Buprestidae)

Buprestid leaf-miners are generally included in the subtribe Trachytes. The genera belonging to this subtribe are commonly very rich in number of species and their systematics envolves huge difficulties. On the other hand the biological knowledge on those insects is very poor. The A. tries to clarify the systematical status of two species of Pachyschelus - P. subundulatus Kerr. and P. fulgidipennis Lucas, and redescribes also P. binderi Obenberger. The hosts of the first two species are recorded, namely: Terminalia catappa (Combretaceae) - host-plant of P. subundulatus and Luhea spp. (Tiliaceae) - host-plant of P. fulgidipennis. The mines, developmental stages and habits of the three species are described and is made a full redescription of the adults, both male and female. The study is based on reared material from mined leaves, as well as insects assembled in several brazilian collections, both private and public ones. The importance of some biological facts as well as some morphological characters are stressed. The knowledge of the host-plants and the shape and other structural features of the mine were found to be helpfull to the identification of the species. Some morphological features of adults also prooved to be of systematical value. Besides the female pygidium and the male genitalia, the tibiae of the third pair of legs show some intersting structural details, reasonably alike in both sexes and quite different in each species.

Notas sôbre o gênero Colobogaster Solier, 1833, com a descrição de duas novas espécies da Região Amazônica: (Coleoptera, Buprestidae)

The study of materials belonging to several brazilian collections led us discover 2 new species of the genus Colobogaster which are here described. C. seabrai sp. n. seems to be related to C. puncticollis Waterhouse, 1882, from which it can be distinguished by: a) apical alitral tooth placed suturally, b) pronotum with 3 pairs of depressions, the 1st. pair transversal and conigous to the 2nd one, c) elitral suture brilliantgreen coloured but not the marginal edge, d) front without a horse-shoe shaped structure, e) pronotum with the discal region concolor. The structures of pronotum, the elitral and pronotal colour paterns and the genial morphology separate this one from other species of the genus. C. paraensis sp. n. is closely related to C. cupricollis Kerremans, 1897, but it is distinguished by the absence of depressions on the pronotum, by the elitral tooth placed suturally, by the abscence of humeral rip and by the general colour. Eleven other species were studied and their apical segment of the abdomen and scutellum were illustrated. It was also established the synonymy of C. ecuadoricus Obengerger, 1926.

Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

Anatomy and histology of Embolyntha batesi MacLahlan, 1877 (Embiidina)

The Embioptera are rather generalized insects whose internal anatomy is simple and not subject to great modifications. For this reason these insects form an ideal group for elementary anatomical and histological studies (fig. 2). The digestive tract is a long, simple tube without convolutions or diverticulae from the buccal cavity to the rectum. The buccal structures are of the chewing type. The oesophagus and ingluvia are differentiated only by slight dilation of their walls. In nymphs and females the proventriculus is very distinct due to folds which flatten as the structure becomes packed with food. The enteron is the largest in such forms and in both sexes limited caudally by the Malpighian tubules. The proctodeus has six large rectal papillae. The nervous system is complete with only the fifth abdominal segment lacking a ganglion in the metathorax includes the ganglion of the first abdominal segment. The brain exhibits very clear structure in histological sections. The tracheal system includes two pairs of thoracic spiracles and eight abdominal pairs. Only th metathoracic spiracle has an air expiration function; all others serve for inspiration. Various structures in the spiracles protect the atrium. The circulatory system includes a long, simple dorsal vessel which extends forward from the ninth abdominal segment into the cranium. It opens anteriorly near the circumoesophageal connectives. The dorsal vessel has a pair of ostia and valves corresponding to each abdominal and thoracic segment. It lacks the diverticulae or folds commonly found in more highly evolved insects. The excretory system is represented by Malphighian tubules, pericardial cells, and fat-body. The number and disposition of Malpighian tubules is variable within the order. The pericardial cells are localized around the entire dorsal vessel up to the opening of the aorta in the head. The fat-bodies form compact layers in the dorsal and ventral regions of the body. In males they are more developed in the abdominal region. The mandibles, maxillae, and salivary glands are of a simple type with very few cytological modifications. Only the salivary glands which extend into the mesothoracic region show appreciable specialization. The reproductive system is bi-sixual and shows considerable sexual dimorphism. Males have five pair of testes with a metameric disposition, two distinct ducts, two epidymis, and the ejaculatory organs. The accessory glands vary in number and size and open in the anterior portion of the ejaculatory duct. The female reproductive organs are of the panoistic type. The system includes five pairs of ovarioles, two long paired oviducts a small, unpaired oviduct and the spermatheca which opens in the vagina. Reproduction usually involves a union of male and female gametes, and eggs are usually laid in clusters attached to a substrate.

Efficient and stable collective choices under gregarious preferences

We consider collective choice problems where a set of agents have to choose an alternative from a finite set and agents may or may not become users of the chosen alternative. An allocation is a pair given by the chosen alternative and the set of its users. Agents have gregarious preferences over allocations: given an allocation, they prefer that the set of users becomes larger. We require that the final allocation be efficient and stable (no agent can be forced to be a user and no agent who wants to be a user can be excluded). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium outcome is an efficient and stable allocation which also satisfies a maximal participation property.

Reproductive isolation between different forms of Lutzomyia longipalpis (Lutz & Neiva), (Diptera: Psychodidae), the vector of Leishmania donovani chagasi Cunha & Chagas and its significance to kala-azar distribution in South America

The males of the sandfly Lutzomyia longipalpis occur in two forms, one which bears a single pair of pale spots on tergite 4 and another in which an additional pair of spots characterizes tergite 3. In crosses between laboratory reared stocks of the two forms originating from allopatric and sympatric sites in Brazil nearly all males of one form fail to inseminate females of the other. In addition, insemination failure between some allopatric populaytions of Lu. longipalpis with similar tergal spot patterns is recorded, indicating the existence of additional forms in an apparent species complex. The possibility that Lu. longipalpis sensu latu represents more than a single taxon is discussed and the relevance of these findings to future epidemiological studies on kala-azar is considered.

The distribution of two morphological forms of Lutzomyia longipalpis (Lutz & Neiva) (Diptera: Psychodidae)

The males of the sandfly Lutzomyia longipalpis occur in two forms, one which bears a single pair of pale spots on tergite 4 and another in which an additional pair of spots characterizes tergite 3. Almost complete reproductive isolation between sumpatric populations of the two forms and between allopatric populations of the one-spot form has been reported (Ward et al., 1983). Micromorphological differences in cuticular structures on the spots have also been observed and may be sites of pheromone release (Lane & Ward, 1984). Detais of the known distribution of the two are based on the examination of new specimens captured in Brazil during 1982, as well as museum collections and specimens from other laboratories. Males with a single pair of pale spots have been found from Mexico to southern Brazil, whilst the two-spot form is found only from the state of Maranhão in North Brazil to Minas Gerais and the border with Paraguay. In the eastern area of Brazil the two forms occur sympatrically in some locations and separately in others.