Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

An illustrated flora of the northern United States, Canada and the British possessions, from Newfoundland to the parallel of the southern boundary of Virginia, and from the Atlantic Ocean westward to the 102d meridian, by Nathaniel Lord Britton and Addison Brown. The descriptive text chiefly prepared by Britton, with the assistance of specialists in several groups; the figures also drawn under his supervision.

2

A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished infinite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Metrics on diagram groups and uniform embeddings in a Hilbert space

"Vegeu el resum a l'inici del document del fitxer adjunt".

An illustrated flora of the northern United States, Canada and the British possessions, from Newfoundland to the parallel of the southern boundary of Virginia, and from the Atlantic Ocean westward to the 102d meridian, by Nathaniel Lord Britton and Addison Brown. The descriptive text chiefly prepared by Britton, with the assistance of specialists in several groups; the figures also drawn under his supervision.

3

Pressure groups and experts in environmental regulation

We study a problem of adverse selection in the context of environmental regulation, where the firm may suffer from a certain degree of ignorance about its own type. In a framework like the construction of a certain infrastructure project, the presence of ignorance about its impact on the environment, can play an important role in the determination of the regulatory policy. First, an optimal contract is constructed for any exogenous level of ignorance. Second, the presence of potentially informed third-parties is studied from the perspective of the regulator, which allows us to analyze the impact on the efficiency of the contract, of the presence of environmentalists and of experts. Then, we obtain some insights on how the problem differs when the degree of ignorance is a choice variable for the firm. We finally use our results to derive policy implications concerning the existing envoronmental regulation, and the potential role of interested parties as information providers.

Sôbre u'a modificação do meio de Monteverde

It is well known that the culture media used in the presumptive diagnosis of suspiciuous colonies from plates inoculated with stools for isolation of enteric organisms do not always correctly indicate the major groups of enterobacteria. In an effort to obtain a medium affording more exact indications, several media (1-9) have been tested. Modifications of some of these media have also been tested with the result that a satisfactory modification of Monteverde's medium was finaly selected. This proved to be most satisfactory, affording, as a result of only one inoculation, a complete series of basic indications. The modification involves changes in the formula, in the method of preparation and in the manner of storage. The formulae are: A. Thymol blue indicator: NaOH 0.1/N .............. 34.4 ml; Thymol blue .............. 1.6 g; Water .................... 65.6 ml. B. Andrade's indicator. C. Urea and sugar solution: Urea ..................... 20 g; Lactose ................... 30 g; Sucrose ................... 30 g; Water .................... 100 ml. The mixture (C.) should be warmed slightly in order to dissolve the ingredients rapidly. Sterilise by filtration (Seitz). Keep stock in refrigeratior. The modification of Monteverde's medium is prepared in two parts. Semi-solid part - Peptone (Difco) 2.0 g; NaCl 0.5 g; Agar 0.5 g; Water 100.0 ml. Boil to dissolve the ingredients. Adjust pH with NaOH to 7.3-7.4. Boil again for precipitation. Filter through cotton. Ad indicators "A" 0.3 ml and "B" 1.0 ml. Sterilise in autoclave 115ºC, 15 minutes in amounts not higher than 200 ml. Just before using, add solution "C" asseptically in amounts of 10 ml to 200 ml of the melted semi-solid medium, maintained at 48-50ºC. Solid part - Peptone (Difco) 1.5 g; Trypticase (BBL) 0.5 g; Agar 2.0 g; Water 100,00 ml. Boil to dissolve the ingredients. Adjust pH with NaOH to 7.3-7.4. Boils again. Filter through cotton. Add indicators "A" 0.3 ml and "B" 1.0 ml; ferrous ammonium sulfate 0.02 g; sodiun thiosulfate 0.02 g. Sterilise in autoclave 115ºC, 15 minutes in amounts not higher than 200 ml. Just before using, add solution "C" asseptically in amounts of 10 ml to 200 ml of the melted solid medium, maintained at 48-50ºC. Final medium - The semi-solid part is dispensed first (tubes about 12 x 120 mm) in 2.5 ml amounts and left to harden at room temperature, in vertical position. The solid part is dispensed over the hardened semi-solid one in amounts from 2.0 ml to 2.5 ml and left to harden in slant position, affording a butt of 12 to 15 mm. The tubes of medium should be subjected to a sterility test in the incubator, overnight. Tubes showing spontaneous gas bubbles (air) should then be discarded. The medium should be stored in the incubator (37ºC), for not more than 2 to 4 days. Storage of the tubes in the ice-box produces the absorption of air which is released as bubbles when the tubes are incubated at 37ºC after inoculation. This fact confirmed the observation of ARCHAMBAULT & McCRADY (10) who worked with liquid media and the aplication of their observation was found to be essential to the proper working conditions of this double-layer medium. Inoculation - The inoculation is made by means of a long straight needle, as is usually done on the triple sugar, but the needel should penetrate only to about half of the height of the semi-solid column. Indol detection - After inoculation, a strip of sterelized filter papaer previously moistened with Ehrlich's reagent, is suspended above the surface of the medium, being held between the cotton plug and the tube. Indications given - In addition to providing a mass of organisms on the slant for serological invetigations, the medium gives the following indications: 1. Acid from lactose and/or sucrose (red, of yellowsh with strains which reduce the indicators). 2. Gas from lactose and/or sucrose (bubbles). 3. H[2]S production, observed on the solid part (black). 4. Motility observed on the semi-solid part (tubidity). 5. Urease production, observed on solid and semi-solid parts (blue). 6. Indol production, observed on the strip of filter paper (red or purplish). Indol production is not observed with indol positive strains which rapidly acidify the surface o the slant, and the use of oxalic acid has proved to give less sensitive reaction (11). Reading of results - In most cases overnight incubation is enough; sometimes the reactions appear within only a few hours of incubation, affording a definitive orientation of the diagnosis. With some cultures it is necessary to observe the medium during 48 hours of incubation. A description showing typical differential reaction follows: Salmonella: Color of the medium unchanged, with blackening of the solid part when H[2]S is positive. The slant tends to alkalinity (greenish of bluish). Gas always absent. Indol negative. Motility positive or negative. Shigella: Color of the medium unchanged at the beginning of incubation period, but acquiring a red color when the strain is late lactose/sucrose positive. Slant tending to alkalinity (greenish or purplish). Indol positive or negative. Motility, gas and H[2]S always negative. Proteus: Color of the medium generally changes entirely to blue or sometimes to green (urease positive delayed), with blackening of solid part when H[2]S is positive. Motility positive of negative. Indol positive. Gas positive or negative. The strains which attack rapidly sucrose may give a yellow-greenish color to the medium. Sometimes the intense blue color of the medium renders difficult the reading of the H[2]S production. Escherichiae and Klebsiellae: Color of the medium red or yellow (acid) with great and rapid production of gas. Motility positive or negative. Indol generally impossible to observe. Paracoli: Those lactose of sucrose positive give the same reaction as Esherichia. Those lactose or sucrose negatives give the same reactions as Salmonellae. Sometimes indol positive and H[2]S negative. Pseudomonas: Color of the medium unchanged. The slant tends to alkalinity. It is impossible to observe motility because there is no growth in the bottom. Alkaligenes: Color of the medium unchanged. The slant tends to alkalinity. The medium does not alter the antigenic properties of the strains and with the mass of organisms on the slant we can make the serologic diagnosis. It is admitted that this medium is somewhat more laborious to prepare than others used for similar purposes. Nevertheless it can give informations generally obtained by two or three other media. Its use represents much saving in time, labor and material, and we suggest it for routine laboratory work in which a quick presumptive preliminary grouping of enteric organisms is needed.

Pure braid subgroups of braided Thompson's groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty

Distortion of wreath products in some finitely presented groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

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.

Minimal truncations of supersingular p-divisible groups

"Vegeu el resum a l'inici del document del fitxer adjunt."