Orbit decidability and the conjugacy problem for some extensions of groups

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The generic Hanna Neumann conjecture and post correspondence problem

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The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

An Empirical Examination of the R&D Boundaries of the Firm - A Problem-Solving Perspective

We consider, both theoretically and empirically, how different organization modes are aligned to govern the efficient solving of technological problems. The data set is a sample from the Chinese consumer electronics industry. Following mainly the problem solving perspective (PSP) within the knowledge based view (KBV), we develop and test several PSP and KBV hypotheses, in conjunction with competing transaction cost economics (TCE) alternatives, in an examination of the determinants of the R&D organization mode. The results show that a firm’s existing knowledge base is the single most important explanatory variable. Problem complexity and decomposability are also found to be important, consistent with the theoretical predictions of the PSP, but it is suggested that these two dimensions need to be treated as separate variables. TCE hypotheses also receive some support, but the estimation results seem more supportive of the PSP and the KBV than the TCE.

Interlinkages and forecasting made possible by the use of the DECOIN analytical tool kit

This technical report is a document prepared as a deliverable [D4.3 Report of the Interlinkages and forecasting prototype tool] of a EU project – DECOIN Project No. 044428 - FP6-2005-SSP-5A. The text is divided into 4 sections: (1) this short introductory section explains the purpose of the report; (2) the second section provides a general discussion of a systemic problem found in existing quantitative analysis of sustainability. It addresses the epistemological implications of complexity, which entails the need of dealing with the existence of Multiple-Scales and non-equivalent narratives (multiple dimensions/attributes) to be used to define sustainability issues. There is an unavoidable tension between a “steady-state view” (= the perception of what is going on now – reflecting a PAST --& PRESENT view of the reality) versus an “evolutionary view” (= the unknown transformation that we have to expect in the process of becoming of the observed reality and in the observer – reflecting a PRESENT --& FUTURE view of the reality). The section ends by listing the implications of these points on the choice of integrated packages of sustainability indicators; (3) the third section illustrates the potentiality of the DECOIN toolkit for the study of sustainability trade-offs and linkages across indicators using quantitative examples taken from cases study of another EU project (SMILE). In particular, this section starts by addressing the existence of internal constraints to sustainability (economic versus social aspects). The narrative chosen for this discussion focuses on the dark side of ageing and immigration on the economic viability of social systems. Then the section continues by exploring external constraints to sustainability (economic development vs the environment). The narrative chosen for this discussion focuses on the dark side of current strategy of economic development based on externalization and the “bubbles-disease”; (4) the last section presents a critical appraisal of the quality of energy data found in energy statistics. It starts with a discussion of the general goal of statistical accounting. Then it introduces the concept of multipurpose grammars. The second part uses the experience made in the activities of the DECOIN project to answer the question: how useful are EUROSTAT energy statistics? The answer starts with an analysis of basic epistemological problems associated with accounting of energy. This discussion leads to the acknowledgment of an important epistemological problem: the unavoidable bifurcations in the mechanism of accounting needed to generate energy statistics. By using numerical example the text deals with the following issues: (i) the pitfalls of the actual system of accounting in energy statistics; (ii) a critical appraisal of the actual system of accounting in BP statistics; (iii) a critical appraisal of the actual system of accounting in Eurostat statistics. The section ends by proposing an innovative method to represent energy statistics which can result more useful for those willing develop sustainability indicators.

Symmetry for a Dirichlet-Neumann problem arising in water waves

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The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

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The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.