The principal theorem of this thesis is a theorem by Peano on the existence of a solution to a certain integral equation. The two primary notions underlying this theorem are uniform convergence and equi-continuity. Theorems related to these two topics are proved in Chapter II. In Chapter III we state and prove a classical existence and uniqueness theorem for an integral equation. In Chapter IV we consider the approximation on certain functions by means of elementary expressions involving "bent line" functions. The last chapter, Chapter V, is the proof of the theorem by Peano mentioned above. Also included in this chapter is an example in which the integral equation has more than one solution. The first chapter sets forth basic definitions and theorems with which the reader should be acquainted.

L’œuvre de Kierkegaard se présente sous une forme poétique, non seulement par les fictions qu’il produit, mais encore par les pseudonymes auxquels il donne la parole et qui confèrent aux textes les plus conceptuels l’apparence fictive d’un discours subjectif. La forme poétique n’est donc pas un jeu arbitraire. Elle répond aux exigences de la pensée de l’existence : une pensée subjective, car l’on n’existe pas dans l’abstraction, où il s’agit de se comprendre soi-même dans l’existence. Une pensée existentielle n’est pas un savoir objectif qui peut être transmis directement : elle nécessite une communication indirecte. Tel est le rôle de la forme poétique. Son emploi est donc essentiellement philosophique, et ne fait pas de Kierkegaard un poète. Du poète, il s’agit, au contraire, de dénoncer l’illusion, en particulier celle du romantique. Confondant la possibilité et la réalité, le poète plane au-dessus de sa propre existence. Il faut alors de l’ironie pour libérer l’individu d’une telle illusion et l’amener au commencement de la vie personnelle, d’une existence éthique. C’est pourquoi la forme poétique est, ici, ironique ; il s’agit de parler la même langue que ceux à qui l’on s’adresse, un langage esthétique, afin de les amener à une pensée véritable d’eux-même : tromper en vue du vrai. Fondée philosophiquement pour utiliser la possibilité, qui est sa forme, en vue de la réalité, qui est son horizon éthique, la poétique kierkegaardienne peut ainsi présenter à l’individu les déterminations dialectiques de l’existence, et l’ouvrir au passage de la possibilité à la réalité : un saut qualitatif, une décision qui n’appartient qu’à lui. Grâce à la forme poétique, la pensée subjective se fait maïeutique ; l’auteur s’efface pour laisser la place à celui dont parle la fiction et à qui elle s’adresse, celui que l’auteur veut éveiller à lui-même : l’individu singulier. / Kierkegaard uses a poetic form in its works, not only by the fictions he composes but also by the pseudonyms he makes speak, who give to the most conceptual texts the fictional appearance of a subjective speech. Thus, the poetic form is not an arbitrary game. It is an answer to the requirements of the thinking of existence, a subjective thinking, for one does not exist in abstraction : be understandable oneself in one’s own existence. An existential thought is not an objective knowledge, which can be given directly : it requires an indirect communication. Such is the role of the poetic form. It is essentially a philosophic employment, and does not make a poet of Kierkegaard. On the contrary, his works tend to denounce the poet’s delusion, especially of the Romantic. The poet confuses possibility with reality, and glide above his own existence. Irony is then needed to free the subject from his delusion, and lead him to the beginning of his personal life, an ethical existence. That’s why the poetic form of Kierkegaard’s works is ironic in itself, for it is to speak the langage of those whom the speech speaks to, an aesthetic langage, in order to lead them to a true thinking of themselves : deceive toward the truth. Philosophically founded to use possibility, which is its form, with the reality in mind, which is its ethical horizon, the kierkegaardian poetic is enabled to present to the individual the dialectical determinations of existence, and show him the passage from possibility to reality : a qualitative leap, as his own decision. Through the poetic, the subjective thinking appears to be maïeutics. The author disappears to hand over the place to the one whom the fiction talks about and whom it speaks to, the one who the author wants to awaken within himself : the Individual.

Thesis (M.A.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The purpose of this thesis is to discover the meaning of, and relationship among, what Kierkegaard refers to in his writings as the aesthetic, the ethical and the religious spheres of existence. The sources consulted cover the majority of Kierkegaard's pseudonymous writings. In the first chapter it is shown that Kierkegaard developed the concept of spheres of existence in an effort to show that philosophical categories must be derived from the structure of existence rather than the structure of thought. Contrary to Hegel, Kierkegaard maintains that in existence thought and being can never be identified, but are dialectically related in the sense of being in dialogue with each other. It is the principle of mediation to which Kierkegaard most objects. The consequence of the identification of thought and being is to put them into an immediate relationship to each other and thereby remove from thought its traditional philosophical function of elucidating and directing being. Kierkegaard uses the word existence to refer to the giveness of being, the facticity of the individual. It is in recognizing that the Hegelian attitude toward the dialectical character of existence represents a possible mode of consciousness and that his own attitude represents an opposing mode that Kierkegaard distinguishes between the aesthetic and the ethical spheres of existence. The third sphere of existence, the religious, arises from the possibility that consciousness may relate itself to that which underlies existence, i.e. God. The identification of the spheres of existence with the self-conscious development of human subjectivity is further supported by Kierkegaard's discussion of the self in Sickness Unto Death. Kierkegaard maintains that if one is to secure a position in the flux that is existence, consciousness must cease to be passive and establish itself through resolution. Hence a sphere of existence is defined not only by its moce of consciousness but by its telos. In the second chapter it is shown that the aesthetic consciousness is an immediate, non-reflexive consciousness which has its telos in the external world. It reveals itself as an essentially unstable and unfree consciousness in that it is vulnerable to events over which it has no control. This vulnerability is the sign of despair, which is the occasion for consciousness to heal itself in self-choosing or abdicate its task to exercise itself as free spirit in the dialogue of thought and being. In the phenomenon of irony Kierkegaard finds an illustration of what he calls "boundary zones" to the spheres of existence, by which he means the consciousness of the ideal and all it involves without the choice of it. In the "boundary zone" there is no telos in the proper sense as consciousness entertains the telos of both spheres it bounds. In the third chapter ethical consciousness is seen to be a reflexive, self-choosing consciousness. The self that is chosen is personal existence, which reveals itself as given, in virtue of which one has a history and because of which one must repent. The ethical telos is the eternal validity of the self, which reveals itself as the universal human. Kierkegaard characterizes the ethical choice as absolute, and thus, even though the choice is of subjectivity, the qualification of absolute rules out the possibility of capricious and anarchic subjectivity. such an absolute choice, Kierkegaard believes, must give continuity to the self and must recognize its relation or dependence on something other than itself as it immediately is. With the subjectivity of choice arises the danger of temptation in the form of the possibility of a teleological suspension of the ethical. With this possibility arises the awareness that the self did not create itself but was created by Another, to Whom consciousness may establish a relationship. At this point consciousness may again enter a "boundary zone" of existence as the humorous consciousness, prior to the decision to relate itself to God. In the fourth chapter it is seen that consciousness, in its awareness of itself as dependent is also aware of itself as separated from that on which it defends, and hence that it can assume two attitudes toward this separation, that of resignation and that of faith. When the religious consciousness is characterized by resignation, Kierkegaard calls it religiousness A. When it is characterized by faith, he calls it religiousness B. In religiousness A the dialectical character of existence becomes fully explicit and consciousness becomes a sufferin; consciousness because the continuity it desires cannot be achieved in existence. Hence, in religiousness A consciousness resigns itself to a life of strife. In religiousness A consciousness has arrived as close to the truth as it is able through its own effort. Religiousness B is possible only if the condition for truth is given by God. The condition is faith, not as an exercise of thought, but as a mode of being. The temporality and finitude that characterized personal existence and separate it from its eternal happiness are made compatible with the religious telos in the person of Christ. That is, Christ is the only true mediction. However, Kierkegaard emphasizes that belief in this mediation is possible only at the offense of thought. In the last chapter it is asserted that the significance of Kierkegaard's conception of spheres of existence is that existence is not absurd, and that while man is not self-creating, he is self-choosing. / 2031-01-01

After a chapter analyzing Heidegger's Dasein Analytik as it is delineated in Sein und Zeit, in using, in large measure, an author coming from the anglo-american tradition, the A begins a quasi-commentary analysis of the second chapter of Heidegger's Die Grundprobleme der Phänomenologie, heretofore GP or (The Basic Problems of Phenomenology). This quasi-commentary method of analysis is required due to the informal nature of presentation, insofar as this GP text is a transcription of Heidegger's 1927 summer course at Marburg. The A's chapter 3 analyzes the essence and existence distinction as it is found (or it's equivalent in Scotus's case) in Aquinas, Scotus and Suarez. In terms of inspiration it soon becomes clear – even on a vocabulary level - that Heidegger's views are heavily influenced by Suarez and his doctrines, particularly from his Disputationes Metaphysicae, DM. Whereas Heidegger pretends to analyze Aquinas, Scotus and Suarez, each in his own right, the reality is that Suarez is the 'guiding light' throughout these three central, chapter 2 subsection GP analyses, (Alpha = Aquinas, Beta = Scotus and Gamma = Suarez). An obvious sign of this is Heidegger's bringing Giles of Rome and his famous duae res version of the essence and existence distinction into the Aquinas analysis. Although he got the idea from Suarez, Heidegger is slightly more affirmative than Suarez himself in attributing this at first startling version to Aquinas. (In a word, holding to the real distinction means being an Aegidian and Aquinas is said to hold to the real distinction.) The A makes extensive use of contemporary Aquinas analysis to show that the essence and existence distinction doctrine that emerges from Aquinas's Aristotle commentaries is far from resembling Giles's. Via analysis of Metaphysics, V, 7, two Quodlibetal questions and Book II of the Posterior Analytics commentary (Lectios 1-10), a simpler doctrine emerges as to what we are doing when we predicate existence and essence of material substances. Not only is this not a duae res doctrine but one that can be explained without talking about real distinctions at all! (Heidegger's views on Scotus and Suarez are at once penetrating and much more predictable.) The A next presents a chapter on Heidegger and Luther, showing the centrality of the theme 'betrayal of the tradition' in both figures. In a final chapter, the A examines Heidegger's 1929 analysis of what the subject matter of metaphysics is, from his Die Grundbegriffe der Metaphysik (The Fundamental Concepts of Metaphysics). Heidegger claims that, for the medieval, ontotheological tradition, the oldest and most sacred, i.e., God, is the subject matter of metaphysics. (This includes Heidegger's accusation that medieval ontology is faith buttressed.) Using a contemporary phenomenologist's and a medievalist's analysis, the A tries to show that Aquinas's commentary on Aristotle's Metaphysics reveals the subject matter of metaphysics not to be 'God', but ens commune. This philosophical conclusion is of course consequential for Heidegger's accusation that medieval ontology is faith supported. The A concludes that an examination of Aquinas's Aristotle commentaries would have led to other conclusions than Heidegger's on what the subject matter of metaphysics is as well as on Aquinas's views on predicating essence and existence.

Systems of semilinear parabolic differential equations arise in the modelling of many chemical and biological systems. We consider m component systems of the form ut = DΔu + f (t, x, u) ∂uk/∂η =0 k =1, ...m where u(t, x)=(uk(t, x))mk=1 is an unknown vector valued function and each u0k is zero outside Ωσ(k), D = diag(dk)is an m × m positive definite diagonal matrix, f : R × Rn× Rm → Rm, u0 is a componentwise nonnegative function, and each Ωi is a bounded domain in Rn where ∂Ωi is a C2+αmanifold such that Ωi lies locally on one side of ∂Ωi and has unit outward normal η. Most physical processes give rise to systems for which f =(fk) is locally Lipschitz in u uniformly for (x, t) ∈ Ω Ã— [0,T ] and f (·, ·, ·) ∈ L∞(Ω Ã— [0,T ) × U ) for bounded U and the initial data u0 is continuous and nonnegative on Ω. The primary results of this dissertation are three-fold. The work began with a proof of the well posedness for the system . Then we obtained a global existence result if f is polynomially bounded, quaipositive and satisfies a linearly intermediate sums condition. Finally, we show that systems of reaction-diffusion equations with large diffusion coeffcients exist globally with relatively weak assumptions on the vector field f.

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Largement mises en question dans la Bulle in agro dominico, les notions de créé et d'incréé trouvent cependant chez Eckhart une résonance profondément chrétienne. Le Maître y fonde une théologie et une mystique trinitaires qui orientent son anthropologie vers la filiation divine de l'homme à partir de l'actualisation de l'image du Verbe dans l'âme. Ainsi le motif de l'incarnation apparaît-il au cœur de la pensée d'Eckhart : "Pourquoi Dieu s'est-il fait homme ? Pour que Dieu naisse dans l'âme et que l'âme naisse en Dieu". En effet, le sens véritable de l'homme réside dans cette filiation. En elle, son désir de Dieu comme faim de l'être, trouve un accomplissement véritable. Car ce désir s'exprime comme celui d'un retour au Principe incréé, à cette origine dont la création constitue une sortie : ouverture vers Dieu, il est ce qui paradoxalement dit le manque et la plénitude. Le créé et l'incréé chez Eckhart s'articulent autour des notions de réminiscence et de désir. En effet, c'est en se souvenant de la grande noblesse que Dieu a mise dans son fond (3ème point du programme de prédication d'Eckhart), en expérimentant cette Présence divine au plus intime d'elle-même que l'âme éprouve le désir du retour à l'incréé, à ce fond sans fond, libre et dégagé du créé, par où elle expérimente la naissance éternelle du Verbe en elle / Eckhart's works are in german and latin : the latin ones show the basis doctrinal of sermons and treatises. His work's evolution is used for funding our reflexion as the Meister expresses in it his speculative genious. This clearly appears through his genuine mystical experience of the non-dividing which will arouse a lot of lacks of sympathy, as the papal condemnation testifies against some of Eckart's propositions (11 as rash and the remainder as heretical). The experience of the introvertive mystic includes a state of consciousness in which there is both a sense of illumination and an absence of distinction between subject and object ; that is, the contemplative is not having an experience like that of ordinary perception, where the thing perceived can be distinguished from the

In this work the problematic issue of price determination in economic theory is re-examined. In the first chapter a state-of-the-art survey regarding the existence of equilibrium and the structure of the equilibrium set in price-setting games is provided. In chapter two a new core concept, the Bertrand core, is introduced and characterized. In chapter three a revealed preference perspective upon the Nash equilibria in price-setting games is provided. In chapter four, the issue of Bayesian equilibrium existence is addressed when traders have incomplete information regarding each others' types. Finally, a summary of possible future avenues for research in this area is provided.