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.

Estudos dos agrupamentos vegetativos relacionados com as áreas onde foram efetuadas as pesquisas sôbre a febre amarela silvestre no Município de Passos, Estado de Minas Gerais

The work reported here was carried-out on the invitation of Dr. Henry Kumm, Director of the Rockefeller Foundation, and by appointment from Dr. Henrique Aragão, Director of the Instituto Oswaldo Cruz. It was done during the investigation of sylvan yellow fever, in June 1947, with a view to establishing the phyto-ecological conditions of the county of Passos. The pe¬riod was, however, too short for definite conclusions to be reached. Thanks are due to Dr. O. R. Causey, Chief of Research on Yellow Fever for transpor¬tation and other help. THE REGIONAL VEGETATION. Aerial photographs of the county of Passos shoto that it is covered by three great types of vegetation: Rain Forest, Secondary Pasture Land and Scrub.1 Detailed investigation, however, brings out the fact that these correspond to different seres; furthermore, each type presents not only the specific, characteristics of the biological form dominant for the climate, but also are at various stages, which express HABITATS differing from those of the normal sere. The phytogeographic survey of the region shows that most of it is now covered by secondary pasture land (disclimax) in which Melinis minutiflora, v. "fat grass" (fig. 1), predominates. The mosaic of Rain Forest and of small patches of Scrub reveals the effects of human intervention (BARRETO, H. L. de Mello 1); consequently, all the formations have to be regarded as secon¬dary, though some of them probably include relicts of the primitive climax (WARMING, E. 2). On close examination, the Scrub cannot be considered as the climax, because of the following facts: 1. In the zone of Rain-Forest stretches of forest are present in very varied topographic conditions and the reconstitution of the associations show that man has destroyed an ecological unit (fig. 2). 2. In the zone of Scrub the characteristic patches are small. The banks of rivers and brooks, the valleys and ravine and whatever the soil has retained some humidity, is being invaded fry Rain Forest, which seems to be growing under optimum conditions. The Scrub is thus limited to small belts on the calcareous mountains and on sandy soils with alcaline depths (pH abo¬ve 7) which do not retain enough moisture for the Rain Forest that is progres¬sively restricting the area occupied by Scrub. In view of the topographic and present climatic conditions the Rain Forest must consequently be regarded as the regional climax. The presence of ecologically contradictory elements and associations shows that the real problem is that of the fluctuations of the climate of Passos or even of Minas Geraes during the quaternary and recent periods (DAN-SEREAU, P. : 3), a subject on which little is known and which is tied to the evolution of the climate of Brazil (OLIVEIRA, E. : 4) . The transformation of Scrub into Rain Forest has been - observed by the author before, in other parts of Brazil (VELOSO, PL P.: 5) . It seems probable that the Rio Grande has also greatly influenced the change of the regional vegetation, by invading areas of Scrub and dislocating the limit of the Pluvial climate towards the Canastra Range, though there are remnants of Scrub (postclimax) transfor¬med into secondary open country (disclimax, fig. 5) by human devastation and the setting of fire to the land. VEGETATION GROUPS OF THE PLUVIAL TYPE. The map of the region also shows that at the present time the small patches of forest (whether devasted or intact) occupy the least accessible places, such as valleys, peaks and abrupt slopes (fig. 2). Even these are now being destroyed, so that in the near future this forested region will be en¬tirely reduced to poor pasture land unless energetic measures of conservation are undertaken in time. The Special Service for Prophylaxis against Yellow Fever installed two of their four Stations for the Capture of Mosquitos in this area, one of them at Batatal and the other at Cachoeira, which have separate formations each of them composed of several associations. Other vegetation formations were also analysed, from the synecological point of view, so as to ascertain of which degree of succession their associations belong. These phytosociological sur¬veys give an idea of the principal characteristics of each station. BATATAL FORMATION. The abrupt nature of the valley has rendered this location inappropriate for agricultural purposes since colonial times. The relict of the primitive forest climax saved by this circumstance has expanded gradually to zones whose paedologic conditions favour the eatablishment of mesophilous species. The aerial photograph shows two small stretches of forest, one apparently primi¬tive, the other composed of associations belonging to the subclimax of the subsere. CACHOEIRA FORMATION. Aerial photographs show that this station is crossed by a small river, which divides it into two separate parts. The first, which presents ecological conditions similar, though not identical to those of Batatal, is favoured by topography and apparently remains primitive forest. Though the topography of the other, on the whole, favours the establishment of groups belonging to the normal sere of the climax, is has been partly devastated recently and the aspect of the associations has been completely modified. It was is this part that the four posts for the capturing of mosquitos were set up. The first forest is favoured by deposition of organic matter, washed out from the nearby devasted areas by torrential rains, and thus provides, an appropriate HABITAT for the climax species with certain hygrophilous trends of the ecological quasiclimax type. This association seems to have reached a biological equilibrium, as the dominates. Gallesia gorarema and Cariniana legalis (fig. 10), present an optimum vitality with a vigorous habit and a normal evolutionary cycle. The Cariniantum legalis Gallesiosum equilibrium, corresponds however, to a provisory association, because if the moving of soil by torrential rains should cease it would become possible…

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Consumers' behavior and the Bertrand paradox: an ACE approach

We analyze the classical Bertrand model when consumers exhibit some strategic behavior in deciding from which seller they will buy. We use two related but different tools. Both consider a probabilistic learning (or evolutionary) mechanism, and in the two of them consumers' behavior in uences the competition between the sellers. The results obtained show that, in general, developing some sort of loyalty is a good strategy for the buyers as it works in their best interest. First, we consider a learning procedure described by a deterministic dynamic system and, using strong simplifying assumptions, we can produce a description of the process behavior. Second, we use nite automata to represent the strategies played by the agents and an adaptive process based on genetic algorithms to simulate the stochastic process of learning. By doing so we can relax some of the strong assumptions used in the rst approach and still obtain the same basic results. It is suggested that the limitations of the rst approach (analytical) provide a good motivation for the second approach (Agent-Based). Indeed, although both approaches address the same problem, the use of Agent-Based computational techniques allows us to relax hypothesis and overcome the limitations of the analytical approach.

Implementation of the ordinal shapley value for a three-agent economy

We propose a simple mechanism that implements the Ordinal Shapley Value (Pérez-Castrillo and Wettstein [2005]) for economies with three or less agents.

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.

The Instrumental voter goes to the news-agent: demand for information, election closeness, and the media

This paper studies the impact of instrumental voting on information demand and mass media behaviour during electoral campaigns. If voters act instrumentally then information demand should increase with the closeness of an election. Mass media are modeled as profit-maximizing firms that take into account information demand, the value of customers to advertisers and the marginal cost of customers. Information supply should be larger in electoral constituencies where the contest is expected to be closer, there is a higher population density, and customers are on average more profitable for advertisers. The impact of electorate size is theoretically undetermined. These conclusions are then tested with comfortable results on data from the 1997 general election in Britain.

An ordinal shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Market Competition and Lower Tier Incentives

The relationship between competition and performance-related pay has been analysed in single-principal-single-agent models. While this approach yields good predictions for managerial pay schemes, the predictions fail to apply for employees at lower tiers of a firm's hierarchy. In this paper, a principal-multi-agent model of incentive pay is developed which makes it possible to analyze the effect of changes in the competitiveness of markets on lower tier incentive payment schemes. The results explain why the payment schemes of agents located at low and mid tiers are less sensitive to changes in competition when aggregated firm data is used. JEL classification numbers: D82, J21, L13, L22. Keywords: Cournot competition, Contract delegation, Moral hazard, Entry, Market size, Wage cost.

Las ideas de Marx llegan a la corriente principal de la economía

The paper first sets out simplified versions of recent mainstream papers which explain the rise of democracy in 19th century Europe and its instabliity in Latin America. Then it attempts to convince Marxists of the importance of these works for Marxist thought.