The Cournot-Theocharis Problem Reconsidered

In 1959 Theocharis [10] showed that with linear demand and constant marginal costs Cournot equilibrium is destabilized when the competitors become more than three. With three competitors the Cournot equilibrium point becomes neutrally stable, so, even then, any perturbation throws the system into an endless oscillation. Theocharis's argument was in fact proposed already in 1939 by Palander [4]. None of these authors considered the global dynamics of the system, which necessarily becomes nonlinear when consideration is taken of the facts that prices, supply quantities, and profits of active firms cannot be negative. In the present paper we address the global dynamics.The authors 1 and 3 are partially supported by the grant FS 00684/PI/04 from Fundación Séneca (Comunidad Autónoma de la Región de Murcia, Spain

Periodicity and chaos on a modified Samuelson model

Several discrete time nonlinear growth models with complicated dynamical behavior have been introduced in the literature. In this paper we propuse a modified Samuelson model and we study its dynamical behavior depending on several parameters, which turn out to be the same as the logistic family. Moreover in the base situation the dynamical behavior only depends on the initial values of supply and demand

Aplicación de técnicas de b-learning en el proceso de evaluación continúa en el ámbito universitario

[SPA] La implantación del EEES supone un importante cambio conceptual en el proceso de aprendizaje sobre todo en el ámbito universitario. El profesor deja de ser un mero transmisor de conocimientos y pasa a ser el eje fundamental y organizador en el proceso cognitivo. En este marco el uso de las nuevas tecnologías de la información constituye una herramienta básica para el profesor. En este trabajo analizamos la combinación de técnicas de b-learning aplicadas al seguimiento del trabajo continuo del alumno. Nuestro objetivo es analizar la inclusión de técnicas b-learning en el proceso de aprendizaje así como establecer una comparativa entre las actividades integradas en el proceso de evaluación continua realizadas de forma presencial frente a las no presenciales. Para ello realizaremos el análisis específico de los datos de participación de los alumnos en cada una de las actividades así como de las valoraciones realizadas por los mismos estudiantes. Las conclusiones que se obtienen advierten que para los alumnos una adecuada autogestión y programación del tiempo disponible es un elemento fundamental para el desarrollo y realización de las actividades virtuales. Asimismo el diseño de las actividades virtuales y especialmente la programación de las mismas por parte del profesor constituye un elemento clave para el seguimiento del alumno.[ENG] The implementation of the EHEA is a major conceptual change in the learning process especially at the university level. The teacher is no longer a mere transmitter of knowledge and becomes the cornerstone and organizer in the cognitive process. In this framework the use of new information technologies is an essential tool for the teacher. Our goal in this work is to analyse the combination of b-learning techniques applied to the continuous monitoring of student work. We establish a comparison between the integrated activities in the process of continuous assessment performed in the classroom versus on-line activities. The results are based on the objective data of student participation as well as the assessments made by the students. The conclusions obtained from the analysis warn that it is necessary proper management and programming of their own time by students for success especially in virtual activities. In order to get it, a proper organization by students and design activities and scheduling them by the teacher is required

El problema de Markus-Yamabe en el Duopolio de Cournot

La dinámica de un duopolio de Cournot puede ser modelizada mediante una función antitriangular en dos dimensiones, es decir, una función de la forma F(x, y) = (f(y), g(x)), donde f y g, (las funciones de reacción), son funciones unidimensionales continuas, y x e y son las cantidades que producen dos empresas rivales. Las propiedades dinámicas de estas funciones de Cournot están relacionadas con la dinámica de funciones unidimensionales. En este trabajo probamos que el problema de Markus-Yamabe tiene respuesta afirmativa para funciones antitriangulares (o de Cournot), esto es, si (x0, y0) es un punto de equilibrio del juego duopolista, y los valores propios de la matriz DF(x, y) tienen valor absoluto menor que 1 para cualquier par (x, y), entonces se alcanza (x0, y0) mediante iteraciones de la función F, cualesquiera que sean las cantidades x e y de partida

Attracting complex networks

Real phenomena from different areas of Life Sciences can be described by complex networks, whose structure is usually determining their intrinsic dynamics. On the other hand, Dynamical Systems Theory is a powerful tool for the study of evolution processes in real situations. The concept of global attractor is the central one in this theory. In the last decades there has been an intensive research in the geometrical characterization of global attractors. However, there still exists a weak connection between the asymptotic dynamics of a complex network and the structure of associated global attractors. In this paper we show that, in order to analyze the long-time behavior of the dynamics on a complex network, it is the topological and geometrical structure of the attractor the subject to take into account. In fact, given a complex network, a global attractor can be understood as the new attracting complex network which is really describing and determining the forwards dynamics of the phenomena. We illustrate our discussion with models of differential equations related to mutualistic complex networks in Economy and Ecology

Evaluation of appendicitis risk prediction models in adults with suspected appendicitis

Background Appendicitis is the most common general surgical emergency worldwide, but its diagnosis remains challenging. The aim of this study was to determine whether existing risk prediction models can reliably identify patients presenting to hospital in the UK with acute right iliac fossa (RIF) pain who are at low risk of appendicitis. Methods A systematic search was completed to identify all existing appendicitis risk prediction models. Models were validated using UK data from an international prospective cohort study that captured consecutive patients aged 16–45 years presenting to hospital with acute RIF in March to June 2017. The main outcome was best achievable model specificity (proportion of patients who did not have appendicitis correctly classified as low risk) whilst maintaining a failure rate below 5 per cent (proportion of patients identified as low risk who actually had appendicitis). Results Some 5345 patients across 154 UK hospitals were identified, of which two‐thirds (3613 of 5345, 67·6 per cent) were women. Women were more than twice as likely to undergo surgery with removal of a histologically normal appendix (272 of 964, 28·2 per cent) than men (120 of 993, 12·1 per cent) (relative risk 2·33, 95 per cent c.i. 1·92 to 2·84; P < 0·001). Of 15 validated risk prediction models, the Adult Appendicitis Score performed best (cut‐off score 8 or less, specificity 63·1 per cent, failure rate 3·7 per cent). The Appendicitis Inflammatory Response Score performed best for men (cut‐off score 2 or less, specificity 24·7 per cent, failure rate 2·4 per cent). Conclusion Women in the UK had a disproportionate risk of admission without surgical intervention and had high rates of normal appendicectomy. Risk prediction models to support shared decision‐making by identifying adults in the UK at low risk of appendicitis were identified

On topological sequence entropy and chaotic maps on inverse limit spaces

The aim of this paper is to prove the following results: a continuous map f : [0; 1] ! [0; 1] is chaotic if the shift map of : lim ([0; 1]; f) ! lim ([0; 1]; f) is chaotic. However, this result fails, in general, for arbitrary compact metric spaces. f : lim ([0; 1]; f) ! lim ([0; 1]; f) is chaotic i there exists an increasing sequence of positive integers A such that the topological sequence entropy hA( f ) > 0. Finally, for any A there exists a chaotic continuous map fA : [0; 1] ! [0; 1] such that hA( fA) = 0:This paper has been partially supported by the grant PB/2/FS/97 (Fundación Séneca, Comunidad Autónoma de Murcia). I wish to thank the referee for the proof of Proposition 2.1 and the comments that helped me to improve the paper

New results on entropy, sequence entropy and related topics / José Salvador Cánovas Peña ; directores Francisco Balibrea Gallego, Victor Jiménez López.

Resúmen en castellano.Tesis-Universidad de Murcia.Consulte la tesis en: BCA. GENERAL. ARCHIVO UNIVERSITARIO. T.M-2093

Computing explicitly topological sequence entropy: the unimodal case

There are many tools todeal with the idea of "complex dynamical behaviour" for the family C(I) of continuous maps on a conpact interval I. Among them topological entropy enjoys a steady popularity, one of the reasons being that it can be used as an indicator of the "size" of this dynamical complexity which, contrary o measure-theoretic approaches, is preserved under topological conjugacy.This paper has been partially supported by the DGICYT grant P95-1004, the DGISEC grant PB98-0374-C03-01 and the Fundación Séneca (Comunidad Autónoma de Murcia) grant PB/2/FS/97

Commutativity and non-commutativity of the topological sequence entropy

In this paper we study the commutativity property for topological sequence entropy. We prove that if $X$ is a compact metric space and $f,g: X\rightarrow X$ are continuous maps then $h _A(f\circ g)=h_A(g\circ f)$ for every increasing sequence $A$ if $X=[0,1]$, and construct a counterexample for the general case. In the interim, we also show that the equality $h_A(f)=h_A(f\vert _{\cap _{n\ge 0}f^n(X)})$ is true if $X=[0,1]$ but does not necessarily hold if $X$ is an arbitrary compact metric space.This paper has been partially supported by the D.G.C.Y.T. grant PB95-1004 and the grants COM-20/96 MAT and PB/2/fs/97 (Fundación Séneca, Comunidad Autónoma de Murcia