Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

The philosophical foundations of classical "rDzogs chen" in Tibet : investigating the distinction between dualistic mind (sems) and primordial knowing (ye shes)

While the syncretistic Tibetan tradition known as rDzogs chen ("Great Perfection") has attracted considerable attention over the past few decades, its philosophical foundations remain largely unknown to those unacquainted with its primary sources. This thesis looks at the essentials of rDzogs chen philosophy through the lens of two principal distinctions that the tradition has considered indispensable for understanding its distinctive views and practices: dualistic mind (sems) versus primordial knowing (ye shes) and dharmakâya versus the 'ground of all' (kun gzhi) conditioned experience. Arguing that the distinctions provided classical rDzogs chen scholars with a crucial framework for (a) articulating the necessary conditions of nondual primordial knowing, the conditio sine qua non of rNying ma soteriology, and (b) schematizing the relationship between the exoteric and esoteric vehicles of Indian Buddhism within a unifying conception of the Buddhist path as the progressive disclosure of primordial knowing, the thesis shows how the rDzogs chen philosophy of mind has been integral to the tradition's complex soteriology. The thesis consists of two parts: (1) a detailed philosophical investigation of the distinctions and (2) an anthology of previously untranslated Tibetan materials on the distinctions accompanied by critical editions and introductions. The first part systematically invesigates the nature and scope of the distinctions and traces their evolution and complex relationships with Indian Buddhist Cittamâtra, Madhyamaka, Pramàriavàda, and Vajrayâna views. It concludes with an exploration of some soteriological implications of the mind/primordial knowing distinction that became central to rDzogs chen path hermeneutics in the classical period as authors of rDzogs chen path summaries used this distinction to reconcile progressivist sutric and non-progressivist tantric models of the Buddhist path. The translations and texts included in part two of the thesis consist of (a) a short treatise from Klong chen pa's Miscellaneous Writings entitled Sems dang ye shes kyi dris lan (Reply to Questions Concerning Mind and Primordial Knowing), (b) selected passages on the distinctions from this author's monumental summary of the rDzogs chen snying thig system, the Theg mchog mdzod (Treasury of the Supreme Vehicle), and (c) an excerpt on rDzogs chen distinctions taken from 'Jigs med gling pa's (1729-1798) 18th century Klong chen sNying thig path summary entitled Treasury of Qualities (Yon tan mdzod) along with a word-by- word commentary by Yon tan rgya mtsho (b. 19th c.).

The “Death of environmentalism” debates: forging links between SEA and civil society discourses

Social and environmental accounting (SEA) is currently going through a period of critical selfanalysis.Challenging questions are being raised about how SEA should be defined, who should be doing the defining, and what the agenda should be. We attempt to engage and enrich these debates from both a process and content perspective by drawing on the political philosophy of agonistic pluralism and a set of debates within the environmental movement – “the death of environmentalism” debates. The contribution of the paper is twofold: to set forth the death of environmentalism debates in the accounting literature and, in doing so, to contextualize and theorize the contested nature of SEA using agonistic pluralism. In contrast to consensually oriented approaches to SEA, the desired outcome is not necessarily resolution of ideological differences but to imagine, develop, and support democratic processes wherein these differences can be recognized and engaged. We construe the “Death” debates as illustrative of the contestable practical and political issues facing both SEA and progressive social movements generally, demonstrating the context and content of the deliberations necessary in contemplating effective programs of engagement. The SEA community, and civil society groups, can benefit from the more overtly political perspective provided by agonistic pluralism. By surfacing and engaging with various antagonisms in this wider contested civic sphere, SEA can more effectively respond to, and move beyond, traditional politically conservative, managerialist approaches to sustainability.

International nursing : cultivating a culture of empowerment

International nursing has been a growing phenomenon throughout the globe. International nurses have been found to be an asset to healthcare organizations and an important part of the health care team. However, growing concern for the plight of international nurses facing obstacles such as professional stagnation and exploitation has spurred the development of strategies to mitigate and ameliorate the experiences of nurses working abroad. In this respect, the purpose of this study was to explore the management-influenced factors and the nurse team-influenced factors that promote the empowerment of the international nurse in the health care setting. The methodology used in this study was a systemic review. After a rigorous search for relevant empirical studies using OVID database, eight empirical research studies were selected using systematic review methodology to collect, analyze and synthesize data. The selected eight empirical studies were then subjected to a content analysis. The results suggested that the empowerment of an international nurse is inseparable from the empowerment of the health care organization. Based on the findings in this study, strategies to promote international nurses were found to mirror strategies evidenced to empower the nursing organization. Some of the management-influenced factors which were found to facilitate empowerment included a diversity rich work culture, transformational leadership at the management level, and a responsibility to foster the values of the organization. The team-influenced factors which were found to contribute to the empowerment of the international nurse included a united mutually-interdependent nurse team, shared accountability among the members of the nurse team, and the building of trust in work relationships. To conlude, this study indicates that efforts to empower international nurses without considering the work culture and the organization as a whole are futile because empowerment cannot take place in an environment that lacks antecedent conditions. Strategies to empower the international nurse should not focus on the deficits and special needs of the international nurse, but should focus on the similarities and commonalities of the nursing body. Empowerment of the international nurse mean open honest communication, supportive work environment, and a firm policy to quell disruptive elements that threaten the organization's values, mission, and philosophy of care.

On a series of Goldbach and Euler

Theorem 1 of Euler s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those examples of misuse of divergent series to obtain correct results so frequent during the seventeenth and eighteenth centuries. We examine this proof closelyand, with the help of some insight provided by a modern (and completely dierent) proof of the Goldbach-Euler Theorem, we present a rational reconstruction in terms which could be considered rigorous by modern Weierstrassian standards. At the same time, with a few ideas borrowed from nonstandard analysis we see how the same reconstruction can be also be considered rigorous by modern Robinsonian standards. This last approach, though, is completely in tune with Goldbach and Euler s proof. We hope to convince the reader then how, a few simple ideas from nonstandard analysis, vindicate Euler's work.

The modal nature of structures in ontic structural realism

Ontic structural realism is the view that structures are what is real in the first place in the domain of fundamental physics. The structures are usually conceived as including a primitive modality. However, it has not been spelled out as yet what exactly that modality amounts to. This paper proposes to fill this lacuna by arguing that the fundamental physical structures possess a causal essence, being powers. Applying the debate about causal vs. categorical properties in analytic metaphysics to ontic structural realism, I show that the standard argument against categorical and for causal properties holds for structures as well. Structural realism, as a position in the metaphysics of science that is a form of scientific realism, is committed to causal structures. The metaphysics of causal structures is supported by physics, and it can provide for a complete and coherent view of the world that includes all domains of empirical science.

The structural nature of perceptual experiences

Intuitively, we think of perception as providing us with direct cognitive access to physical objects and their properties. But this common sense picture of perception becomes problematic when we notice that perception is not always veridical. In fact, reflection on illusions and hallucinations seems to indicate that perception cannot be what it intuitively appears to be. This clash between intuition and reflection is what generates the puzzle of perception. The task and enterprise of unravelling this puzzle took, and still takes, centre stage in the philosophy of perception. The goal of my dissertation is to make a contribution to this enterprise by formulating and defending a new structural approach to perception and perceptual consciousness. The argument for my structural approach is developed in several steps. Firstly, I develop an empirically inspired causal argument against naïve and direct realist conceptions of perceptual consciousness. Basically, the argument says that perception and hallucination can have the same proximal causes and must thus belong to the same mental kind. I emphasise that this insight gives us good reasons to abandon what we are instinctively driven to believe - namely that perception is directly about the outside physical world. The causal argument essentially highlights that the information that the subject acquires in perceiving a worldly object is always indirect. To put it another way, the argument shows that what we, as perceivers, are immediately aware of, is not an aspect of the world but an aspect of our sensory response to it. A view like this is traditionally known as a Representative Theory of Perception. As a second step, emphasis is put on the task of defending and promoting a new structural version of the Representative Theory of Perception; one that is immune to some major objections that have been standardly levelled at other Representative Theories of Perception. As part of this defence and promotion, I argue that it is only the structural features of perceptual experiences that are fit to represent the empirical world. This line of thought is backed up by a detailed study of the intriguing phenomenon of synaesthesia. More precisely, I concentrate on empirical cases of synaesthetic experiences and argue that some of them provide support for a structural approach to perception. The general picture that emerges in this dissertation is a new perspective on perceptual consciousness that is structural through and through.

El tiempo de la matemática

Since the Old Order of the Time was subverted in Greece by establishing a New Order of the Space, the conjugation of Mathematics with temporality has been extremely problematic. Those have escaped from the temporary obligation both as delimiting their objects as assigning them their truth or falsehood. Nevertheless, the History of Mathematics seems to indicate that where truths of this science try to lead an independent existence apart from their creators, that is to say, in the context of their justification, time exerts its retaliations upon this escape.

Mathematics in Catalonia: 1996-2002

The aim of this article is to present the main conclusions of the Report on research in Catalonia for the area of mathematics**. The report was prepared by Joaquim Bruna, Marta Sanz, Joan de Solà-Morales and the author of this text, and published by the Institute for Catalan Studies in 1998. In the report, scientific activity in the area of mathematics was measured essentially by examining two parameters: papers published in specialised journals and doctoral theses read. It should be recognised that a considerable amount of activity in the field of mathematics consists of applying existing knowledge to the resolution of practical technological problems that arise in particular companies. This kind of scientific activity was not measured in any way in the report due to the difficulty of obtaining objective data. This article is divided into the following sections: human resources, scientific production, funding, research publications, research centres, and conclusions.