Separation for the biharmonic differential operator in the Hilbert space associated with the existence and uniqueness theorem

AbstractIn this paper, we have studied the separation for the following biharmonic differential operator:Au=ΔΔu+V(x)u(x),x∈Rn, in the Hilbert space H=L2(Rn,H1) with the operator potential V(x)∈C1(Rn,L(H1)), where L(H1) is the space of all bounded linear operators on the Hilbert space H1 and ΔΔu is the biharmonic differential operator, while Δu=∑i=1n∂2u∂xi2 is the Laplace operator in Rn. Moreover, we have studied the existence and uniqueness of the solution of the biharmonic differential equationAu=ΔΔu+V(x)u(x)=f(x) in the Hilbert space H, where f(x)∈H

LA TEORIA KANTIANA DELLA MOTIVAZIONE MORALE NELLA 'FONDAZIONE DELLA METAFISICA DEI COSTUMI'. UN'ANALISI STORICO-CRITICA

The Thesis \uabLa teoria kantiana della motivazione morale nella Fondazione della metafisica dei costumi. Un\u2019analisi storico-critica\ubb aims to reconstruct Kant\u2019s theory of moral motivation as it is formulated in Groundwork of the Metaphysics of Morals. This Ph.D. Thesis is predominantly a commentary on the passages from Kant\u2019s Groundwork that are relevant to understanding his account of moral motivation. At the same time, as a background to the work, it considers the whole Kantian corpus with its differing theories of moral motivation. The Thesis includes four chapters, each devoted to the analysis of one of four conceptual areas of the Groundwork\u2019s theory of moral motivation: (1) practical reason, will and their reciprocal relationship, (2) will and good will, (3) the feeling and Triebfeder of respect, and (4) the Highest Good. The contemporary debate on Kant\u2019s moral motivation focuses on two opposite interpretations of it: viz., the affectivist and the intellectualist one. In order to choose between these interpretations, the letter of the Kantian texts must be thoroughly analyzed and their theoretical plausibility must be assessed. In the Introduction and in the first chapter I study Kant\u2019s theory of what a human action is and I give an interpretation of Kant\u2019s use of the adverb unmittelbar, which leads me to view Kant\u2019s theory of moral motivation as an affective one. In the remainder of the work I give further grounds to this interpretation by means of a detailed analysis of the text supported by a contextual theoretical study. Furthermore, the first chapter includes (a) the definition of practical reason and will as functions of the human mind, (b) the consequent identification of the laws according to which a rational being has the power of acting as the linking element between these functions and the human faculty of reason and (c) the examination of the secondary literature\u2019s positions about which kind of laws are the ones of human actions. I also provide an answer to the latter question, specifically addressing the issue of distinguishing the formal structure of these laws from their normative validity. The second chapter\u2019s first purpose is to understand the extent of philosophical and psychological possible knowledge about will and good will. To achieve this, I study the concept of moral experience as it appears in the Critique of Practical Reason. The second chapter also investigates Lust and Unlust, since I argue that they deeply mark Kantian conception of both sensible perception and moral motivation. Finally, in the chapter\u2019s conclusion I analyze the teleological argument of the Groundwork\u2019s first section, its structure, its role in the entire work, and the relevance it assumes by taking into account the systematic function of the Kantian notion of character. The third chapter presents a study on the different meanings that Kant\u2019s notion of respect assumes throughout the Groundwork, in the second Critique and in the Doctrine of Virtue. This analysis focuses in particular on the Kantian terms Bewegungsgrund and Triebfeder. The conclusion I draw from it is an assessment of Kant\u2019s peculiar form of a priori affectivism. The final chapter\u2019s arguments stem from the conclusions I drew in Chapter two concerning the relevance of teleology with regard to Kantian theory of morality and moral motivation. Besides commenting on the two explicitly numbered propositions about duty in Section one of the Groundwork (GMS, AA 04: 399.35-400.03 and GMS, AA 04: 400.17-19), I identify the first one, which has not been explicitly mentioned by Kant. The first proposition states the inclusion of the concept of good will in that of duty (GMS, AA 04: 397.06-08). This leads to the analysis of the meaning of Kant\u2019s definition of good will as good in itself, and, at the same time, not corresponding to the whole and Highest Good. I finally study the alleged inconsistency and irrelevancy of Kant\u2019s conception of the Highest Good in the framework of his theory of moral motivation, and I refute it: I eventually prove exactly the opposite, i.e. I point out the great importance and the coherent role that the Highest Good plays in Kant\u2019s theory of moral motivation

Inhibitors of spinal cord regeneration: strategies to determine the contribution of class-3 semaphorins to the inhibitory properties of the glial scar

Verhaagen, J. [Promotor]Niclou, S.P. [Copromotor