Genus-group names of bees and supplemental family-group names / by Charles D. Michener.

no.1

The unbounded dead-end depth propertie is not a group invariant

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Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

The automorphism group of a free-by-cyclic group in rank 2

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A vegetação no município de Ilhéus Estado da Bahia: IV - Caracaterísticas analíticas e periodicidade sociológica

It is well-known that diverse groups of vegetation with an analogous but not identical floristic composition show an ecological similarity which leads to a determined type of vegetation. Starting from this fact it becomes evident that the scope of phytosociological work is the establishing of the significance of the species within the association and the discovery of the rules which govern associations. The floristic surveys made in the field have to be analysed statistically so as to obtain satisfactory results. The usefulness of this method depends largely on the possibilities of comparing the results with previous studies of the same kind, in the same country, or elsewhere. The method used in this paper is that of measuring circumferences and counting individuals in the different associations studied because it permits the presentation of the results in tables which show the phytosociological complexity of the Brazilian rain-forests. The classical method of characteristics is valuable because the more evolved an association is the less sociable are the species it contains, so that such groups do not show clear differences between species but rather between sinusia or strata of individuals. Five tables are presented in which several of the qualitative and quantitative characteristics are studied with a view to discussing their value in relation to groups and species. They are: I - Abundance (number of individuals). II - Density (distance in meters between the individuals belonging to each stratum). III - Basal coverture (circles measured in square meters of the mean projection of the individuals on the surface). IV - Basal area (mean circle in square meters occupied by individuals on the surface). V - Frequency, abundance and sociability in relation to occurrence. TABLE I. This table indicates first the number of individuals in relation to the sinusia studied: next, the sum total of the individuals belanging to the strata are given for each association, thus providing the numeric value of the sinusia: finally, the relation between the total number of individuals in the association and the total for the sinusium thus fursnishing the abundance per sinusium, in the classic sence, that is the percentage, or rather the relative number, of the elements which compose the group. CONCLUSIONS. The general character of abundance of the regional vegetation of Ilheos may be summed up in the following way: as an association evolves towards permanent equilibirum the number of individuals the inferior strata diminishes in relation to those of the superior strata which increase. For the shrub sinusium, two important facts were observed: a) in a given association the number of elements of the inferior strata diminishes as the diameter of the individuals increases; b) the percentage of individuals belonging to the shrub sinusium in the sere diminishes as the association evolve. In the subarboreal sinusium it is seen that: in the sere the number of subarboreal individuals does not vary much; whereas in the climax or the prisere there is a fall owing to the equilibrum of the biologic forms. In the arboreal sinusium the following conclusion can be deduced from analogous facts: the number of individuals of the lower strata diminishes as circumference increases. Also, in the sere there is a progressive sequence for the individuals belonging to the superior strata. TABLE II. The relation between the mean distances of individuals belonging to the same stratum and the area of an association is equal to the density. The table shows that the mean density of the association and the distance between the individuals belonging to the strata of the same sinusium in relation to the total number of individuals belonging to the association. CONCLUSIONS. As rule, the density of individuals in the associations studied follows a very general character or at least a regional one: the distance between the individuals in the diverse strata varies according to their abundance and sociability. Two other facts of some sociological importance are: a) in identical strata of the same sere the density of individuals oscillates in an analogous manner in teh subclimaces and varies in the stages which have reached equilibrium. b) the density of individuals varias in accordance with the sinusium and the distances between individuals of the same sinusium varg in accordance with the strata. TABLE III. This table presents the mean basal individual coverture, that is the mean projection of the frond of the various individuals belonging to the same stratum. The means were obtained by measurement in the field, of 100 individuals belonging to each stratum and their projection on the surface. In the latoratory these measurements were converted into mean circles (in square meters) and the result was multiplied by the individuals belonging to the strata corresponding to the sinusium of each association. The result obtained is named basal coverture. CONCLUSIONS. As a rule, the basal coverture of the vegetation of the county of Ilhéus indicates that: in the evolution of the vegetation the basal coverture of the arbustive sinusium diminishes progressively whereas that of the arboreal one increases. The special norms obtained are: 1) in the shrub sinusium the basal coverture seems to follow a uniform norm, that is, in stages of evolution of the subclimax the basal coverture oscillates with a certain uniformity. 2) in the subarboreal sinusium this fact is related to the vitality and age of the species, as in the subclimax the number of young trees is large and the vitality of the species very variable. This permits the conclusion that: in the sere the basal coverture increases with the evolution of the vegetation and diminishes when an equilibrium is reached. 3) in the tree sinusium the climax association of the prisere and subsere seem to obey a binomial rule, as the coverture (density-abundance) increases until a determined stratum is reached and...

Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Computational explorations in Thompson's group F

Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

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

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

When does universal peace prevail? Secession and group formation in rent seeking contests and policy conflicts

This paper analyzes secession and group formation in a general model of contest inspired by Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a symmetric coalition structure. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests.

The density of injective endomorphisms of a free group

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