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.

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.

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate another agent to misrepresent his preference and, after an appropriate redistribution of their shares, each obtain a strictly preferred share. We characterize all bribe-proof rules as the class of efficient, strategy-proof, and weak replacement monotonic rules. In addition, we identify the functional form of all bribe-proof and tops-only rules.

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.

Growth, habit formation, and catching-up\ with the Joneses

When habits are introduced multiplicatively in a capital accumulation model, the consumers' objective function might fail to be concave. In this paper we provide conditions aimed at guaranteeing the existence of interior solutions to the consumers' problem. We also characterize the equilibrium path of two growth models with multiplicative habits: the internal habit formation model, where individual habits coincide with own past consumption, and the external habit formation (or catching-up with the Joneses) model, where habits arise from the average past consumption in the economy. We show that the introduction of external habits makes the equilibrium path inefficient during the transition towards the balanced growth path. We characterize in this context the optimal tax policy.

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.

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

Turkey's accession to the EU: interests, ideas and path dependence

The paper is divided into four sections. The first offers a critical assessment of explanations of both rationalist and constructivist approaches currently dominating European studies and assesses the notion of path dependence. The second and third sections analyse the role of both material interests and polity ideas in EU enlargement to Turkey, and conclude that explanations exclusively based on either strategic calculations or values and identities have significant shortcomings. The fourth section examines the institutional path of Turkey's candidacy to show how the course of action begun at Helsinki restricted the range of possible and legitimate options three years later in Copenhagen.

Chain conditions for Leavitt path algebras

In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the algebras L(E)for which every corner is left (equivalently, right)artinian. They are also precisely the algebras L(E) for which every finitely generated left (equivalently, right) L(E)-module is artinian. In our second main result, we give necessary and sufficient conditions for every corner of L(E) to be left (equivalently, right) noetherian. They also turn out to be precisely those algebras L(E) for which every finitely generated left(equivalently, right) L(E)-module is noetherian. In both situations, isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x−1] are provided. Likewise, in both situations, equivalent graph theoretic conditions on E are presented.

The Difficult and tortuous path of agricultural cooperative networks in spain, 1890-1935

The rural associationism developed from the last decades of the XIX century could be consider as an answer of the agriculturists to the increasing integration of agriculture in the market, and to the effects of the Great Depression. In the case of Spain, the initiatives in this sense arose with certain delay in relation to the countries of Western Europe. The beginning of the Spanish cooperativism is closely bound to the Law of 1906. It granted the agrarian cooperatives with fiscal exemptions and other types of supports to the associates, although the process did not really accelerate until the promulgation of the law regulation in 1908.

The word problem distinguishes counter languages

Counter automata are more powerful versions of finite state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of Zn is accepted by a nondeterministic m-counter automaton if and only if m &= n.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

"Vie et Passion de Jésus-Christ" (Pathé, 1902-1905): hétérogénéité des "tableaux", déclinaison des motifs

Cette étude examine deux copies de la "Vie et Passion de Jésus Christ" conservées par la Cinémathèque suisse avec une première préoccupation de type philologique qui conduit à prendre la mesure de l'autonomisation de chacun des "tableaux" composant le film et de l'hétérogénéité de ce dernier. Puis les constats émis à propos du support matériel sont articulés avec une réflexion d'ordre esthétique qui dégage l'importance de l'"effet-tableau" inscrivant cette production filmique dans une généalogie plus large. Le cinéma étant alors le lieu de convergences entre diverses séries culturelles, l'article envisage les liens entre la production Pathé et une pratique jusqu'ici peu discutée dans ce contexte, celle du tableau vivant. This article is a study of two copies of the "Life and Passion of Jesus Christ" held at the Cinemathèque suisse. Our first, broadly philological, concern is to recognise the degree of autonomy of each of the "tableaus" that make up the film, thus establishing the latter's heterogeneous composition. Secondly, adopting a more aesthetic approach, we discuss the importance of the tableau-effect, placing this kind of film production in a wider genealogical context. Given that cinema was at the time a meeting place for different cultural sequences, this article the examines the links between Pathe films and the "tableau vivant", a practice that until now has been rarely discussed in this regard.