On the density of polyharmonic splines

This article treats the question of fundamentality of the translates of a polyharmonic spline kernel (also known as a surface spline) in the space of continuous functions on a compact set \Omega\subset \RR^d when the translates are restricted to $\Omega$. Fundamentality is not hard to demonstrate when a low degree polynomial may be added or when translates are permitted to lie outside of $\Omega$; the challenge of this problem stems from the presence of the boundary, for which all successful approximation schemes require an added polynomial. When $\Omega$ is the unit ball, we demonstrate that translates of polyharmonic splines are fundamental by considering two related problems: the fundamentality in the space of functions vanishing at the boundary and fundamentality of the restricted kernel in the space of continuous function on the sphere. This gives rise to a new approximation scheme composed of two parts: one which approximates purely on $\partial \Omega$, and a second part involving a shift invariant approximant of a function vanishing outside of a neighborhood $\Omega$.Comment: 17 page

Movements of the world: The sources of transcendental philosophy

A great difference is made to contemporary accounts of transcendental philosophy if the question is raised as to how far down its inquiries into the sources of cognitions extend. It is true that the transcendental deduction is designed to reset the orbit of metaphysics around experiences rather than things; and although there are exceptions, neither Kant nor his successor transcendentalists ceased to extend the inquiry into the ultimate grounds of cognition insofar as these are made possible not by objectives, but by what exceeds their being, that is, their formation. Indeed, it is in thinking sources, in descendence, that transcendental philosophy most achieves its objects

Criteria to scrutinize new rights: protecting rights against artificial proliferation

Human and fundamental rights are powerful legal means to protect and promote human dignity. On the one hand, the recognition of implicit and new rights appears unavoidable and desirable as history and its evolving circumstances permanently present new challenges to human dignity. On the other hand, an artificial proliferation of rights can weaken rights’ legal and political worth. The rights system cannot expand limitless, hence criteria to test new rights must be construed in the search of adequate parameters to update the system. These criteria should reveal the presence of substantial fundamentality in rights not explicitly or formally enshrined in the constitutional text. The testing path of new rights is conceived as a discursive process which reinforces the mutual relation between rights and democracy

A Theory of Domestic Violence in International Law

This thesis is born of the question: why do women suffer domestic violence disproportionately to any other group? Why does it continue, in the same form, with the same degree of pain, without rebate? And, if the same harm occurs over and over again, consistent through generations and uniform across borders, why then has the international community not yet developed effective means to address it? This thesis attempts to find a legal answer. This is prefaced, however, by the acknowledgement that the law is only one tool in an array of mechanisms, such as health, economics, and politics, which, if properly combined, could alleviate the pain and difficulties experienced by many victims of domestic violence. The area of law to which I look is international human rights law. My initial motivation for considering public international law arose from the repetition of similar forms of domestic violence around the globe. All over the world women suffer the same type of violence at the hands of their intimate partners and they endure the same feelings of helplessness and isolation when looking to the state for protection. If such violence is universal, it seems then, so too should be the solution. I propose in this thesis that international law, if properly fashioned, can be used effectively as part of this solution. In particular, I maintain that the authoritative enunciation of a norm against domestic violence in international law can improve the way states address domestic violence. I do not propose that individual abusers should be tried by international law. My focus instead is on the extent to which states fail consistently to alleviate domestic violence. This is important because many legal systems appreciate neither the exigency of extreme forms of domestic violence, nor the extent to which women as a group are disproportionately victims of this violence. The result of this lack of appreciation is an almost universal failure to police, prevent and punish domestic violence effectively.3 Due to the socialized normalcy of domestic violence, very few cases are reported or actually prosecuted. Where prosecutions do proceed, victims will often drop their complaints either because they have reconciled with, or because they fear recrimination from, their abuser. Given the disjuncture between the reality of domestic violence and the inefficacy of many legal systems to address it, a revision of the law vis-à-vis domestic violence is needed. Both national and international legal systems are in need of change. This thesis proposes that the international community should adopt a clear and authoritative articulation of a legal right against extreme and systemic forms of domestic violence and a corresponding duty of states to help remedy such violence. This proposition is made on the basis that international law currently does not contain an effective articulation of this right, and that adopting effective global standards in international law for addressing such violence would help improve state enforcement of this right. Under the current state of international law, it is difficult to convince states to prioritize its resources and infrastructures to protect abused women. Articulating clear and effective global standards in international law for addressing extreme forms of domestic violence would provide an important and practical benchmark against which domestic state legislation could be evaluated and re-shaped. Formulating such global standards could place pressure on states to take basic remedial steps against such violence, such as enacting legislation that allows for restraining orders to be made at the same time as a maintenance order, or creating accessible shelters, which will accommodate the divergent needs of women, including their children

Constitutional rights norms in the European Union legal framework: an analysis of European Union citizenship as a constitutional right

The Court of Justice of the European Union (CJEU) continues to be subjected to a level of scrutiny that differs significantly from that received by domestic courts of constitutional relevance and status. This intense scrutiny is rooted in the wide range of cultural and legal understandings of the role of courts within specific legal systems and has resulted in the CJEU being labelled an activist court with a political agenda. This thesis contributes to legal scholarship and in part, political science, adding to the discourse surrounding the CJEU and its reasoning, by suggesting that a norm theoretical approach informs the Court’s jurisprudence and advances its role as the constitutional court of the European Union (EU). The CJEU, as a de facto constitutional court within the EU constitutional order, applies and interprets the norms of the Treaty on European Union and the Treaty on the Functioning of the European Union. These norms demonstrate the characteristics of constitutional rights norms, as discussed by Robert Alexy’s Theory of Constitutional Rights Norms. It is argued that understanding norms in this way enables a clear distinction between rules and principles as norm categories to be drawn. The thesis offers a structural analysis of the EU constitutional framework, highlighting specific norm characteristics as influential in the process of constitutionalisation. Treaty norms governing EU citizenship are analysed in this thesis from the perspective of constitutional rights norms, which enables these norms to be seen as open-textured, requiring rights and interests to be balanced where they conflict with other provisions. The radiating effect of these provisions gives constitutional relevance to secondary legislation, which is of particularly relevance in the context of EU law. The thesis makes the case for looking at EU citizenship, in its norm structure, as a constitutional principle, which requires the CJEU to apply and interpret the provision in specific ways that may then be construed as judicial activism. The thesis informs and enhances the highly relevant and topical discussion of EU citizen rights through a norm structural analysis of the Treaty provisions enshrining EU citizenship within the EU legal framework. The thesis suggests that such an evaluation enables a more objective consideration of EU citizenship as a constitutional right extending beyond subjective rights. Finally, it is argued in this thesis that understanding norm categories and their relevance within the EU constitutional framework enables the development` of a structured understanding of the Court’s jurisprudence based on legal theory

The Primacy of Ethics: Kant, Deleuze, Levinas

The Primacy of Ethics: Kant, Deleuze, Levina

ON THE EMERGENT ASPECTS OF QUANTUM MECHANICS IN RELATION TO THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES AND EMERGENT GRAVITY

This PhD thesis elaborates on a proposal made by the Dutch theoretical physicist G. 't Hooft (1999 Nobel prize in physics), to the effect that quantum mechanics is the emergent theory of some underlying, deterministic theory. According to this proposal, information-loss effects in the underlying deterministic theory lead to the arrangement of states of the latter into equivalence classes, that one identifies as quantum states of the emergent quantum mechanics. In brief, quantisation is dissipation, according to 't Hooft. In our thesis we present two mechanisms whereby quantum mechanics is explicitly seen to emerge, thus explicitly realising 't Hooft's proposal. The first mechanism makes use of Verlinde's approach to classical mechanics and general relativity via holographic screens. This technique, first presented in 2010 in order to understand the emergent nature of spacetime and gravity, is applied in our thesis to the case of quantum mechanics. The second mechanism presented to support 't Hooft's statement is based on a dictionary, also developed by the authors, between semiclassical quantum mechanics, on the one hand, and the classical theory of irreversible thermodynamics, on the other. This thermodynamical formalism, established by Nobel prize winners Onsager and Prigogine, can be easily mapped into that of semi-classical quantum mechanics.Acosta Iglesias, D. (2012). ON THE EMERGENT ASPECTS OF QUANTUM MECHANICS IN RELATION TO THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES AND EMERGENT GRAVITY [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/36530Palanci

Nietzsche's Meta-Existentialism

In this work, I offer a new interpretation of Nietzsche's existential philosophy. I argue that, methodologically, Nietzsche's existentialism is a consequence of making the typical existential position foundational, and then developing to the fullest the implications of this position. I call the resultant approach, "meta-existentialism." Further, I show that Nietzsche's meta-existential philosophy necessarily implicates his complex critique of metaphysics. In other words, his particular type of existentialism can be understood only by thoroughly investigating his criticism of metaphysical thought. Previous interpreters who have sought to portray Nietzsche as an existential thinker, such as Karl Jaspers, Walter Kaufmann and Robert Solomon, fail to seriously engage his critique of metaphysics. They set aside the latter issue, precisely in order to explicate his existentialism. My interpretation remedies this deficiency. This work also addresses those other commentators who do carefully consider Nietzsche's relation to metaphysics, although they do not interpret him as an existentialist. While poststructuralist thinkers, such as Eric Blondel, Sarah Kofman and Michel Haar, have argued that Nietzsche's thought exceeds the limits of metaphysics, other philosophers, such as Martin Heidegger, have claimed that Nietzsche remains trapped within its confines. My argument undercuts this debate by showing that Nietzsche provides an open-ended and ambiguous critique of metaphysics, in which the problem of metaphysics is never settled once and for all. By analyzing Nietzsche's central notion of "will to power" and the problem of "decadence," I show that an encounter with and an ever-renewed critique of metaphysics is essential to Nietzsche's meta-existentialism