ON ABEL CONVERGENT SERIES OF FUNCTIONS

In this paper, we are concerned with Abel uniform convergence and Abel pointwise convergence of series of real functions where a series of functions Σ fn is called Abel uniformly convergent to a function f if for each " > 0 there is a _ > 0 such that jfx(t) 􀀀 f(t)j < " for 1 􀀀 _ < x < 1 and 8t 2 X, and a series of functions Σ fn is called Abel pointwisely convergent to f if for each t 2 X and 8" > 0 there is a _("; t) such that for 1 􀀀 _ < x < 1 jfx(t) 􀀀 f(t)j < "

Analytical-approximate solution of Abel integral equations

It is known that Abel integral equation has a solution in a closed form, with a removable singularity.The presence of Volterra integrals with weak singularity is not always integrable for continuous differentiable class of functions.In this work we propose an analytical approximate method for the solution of Abel integral equations. We showed that the proposed method is exact for the known function in the cases of polynomials and irrational function of the form f(t)tα+1(a0+a1t+···+antn),0<α<1.For the derivation of the proposed method we expand the known function to the Taylor series around a singular points. Substituting this expansion into the solution of Abel equation we could remove the singularity. All evaluations of the integrals are calculated analytically. The obtained solution is a series that is uniformly convergence to the exact solution

Les aportacions de John F. Nash a l'economia : equilibri i negociació

John F. Nash va rebre el Premi Nobel d'Economia l'any 1994, juntament amb John C. Harsanyi i Reinhard Selten, «per les seves anàlisis de l'equilibri en la teoria dels jocs no cooperatius», i el Premi Abel de Matemàtiques l'any 2015, juntament amb Louis Nirenberg, «per les seves contribucions notables i fonamentals a la teoria d'equacions en derivades parcials no lineals i les seves aplicacions a l'anàlisi geomètrica». Aquest article presenta les dues contribucions més importants de Nash a l'economia: l'equilibri de Nash d'un joc no cooperatiu i la solució de Nash al problema de la negociació

‘The Water Lilies’ of the Orangerie, Ricoeur and the ‘flâneur’

«Le flâneur – Nympheas Orangerie» is the title that Olivier Abel (president of the Scientific Council of the Fonds Ricoeur) gave to one of his Entretien with Ricoeur. We can read the two pages of this dialogue in the booklet (Paul Ricoeur. Le tragique et la promesse) that accompanies the double DVD about the life and work of the French thinker: Paul Ricoeur. Philosophe de tous les dialogues2. The film language configures and refigures – with images, clips of interviews (of Ricoeur and his friends/interpreters), photos and video fragments – Ricoeur‘s entire journey, a journey that is symbolically presented in a circular manner. We do not know if this was really the intent of the authors (C. Reussner, O. Abel, F. Dosse). But in our eyes, focused on the Water Lilies of the Orangerie, the symbolic ‗circle‘ (‗symbolic‘ more than ‗hermeneutical‘ circle) is evident

Relating Church-Style and Curry-Style Subtyping

Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the context do not interact well with the logical relation proof of completeness or termination. This paper proposes a natural modification to the type syntax for F-Omega-Sub, adding variable's bound to the variable type constructor, thereby separating the computational behavior of the variable from the context. The algorithm for subtyping in F-Omega-Sub can then be given on types without context or kind information. As a consequence, the metatheory follows the general approach for type systems without computational information in the context, including a simple logical relation definition without Kripke-style indexing by context. This new presentation of the system is shown to be equivalent to the traditional presentation without bounds on the variable type constructor.Comment: In Proceedings ITRS 2010, arXiv:1101.410

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA

In a recent paper, [1], 2005, the indefinite integrals of a certain type are calculated using some linear homogeneous differential equations of second order with variable coefficients, associated with the integrals. In some simple cases, like the examples considered in this paper, the linear independent solutions of these differential equations are directly calculated relative to elementary functions. In more difficult cases, the power series method must be used. In such situations, it is advisable to use the algebraic symbolic calculus on computer. Examples of this type will be given in a subsequent paper. Because the main formula from which the integrals can be calculated is not rigorous proved in [1], we give here a correct proof based on the Abel-Liouville formula for the differential equations of second order. For completeness, we give here the proof for this formula and some of its applications, necessary to our work. Also, we included two examples.indefinite integrals, second order linear homogeneous differential equations, Abel-Liouville formula

Defending Steinbeck: Morality, Philosophy, and Sentimentality in East of Eden

John Steinbeck’s novel East of Eden was published in 1952. Intended to be his magnum opus, the book received largely mixed reviews upon its release. The New York Times called it, “Clumsy in structure and defaced by excessive melodramatics and much cheap sensationalism,” and literary critic Arthur Mizener claimed that, with this novel, “[Steinbeck’s] insight and talent cease to work and he writes like the author of any third-rate best-seller.” Steinbeck’s literary reputation has long-suffered from reviews such as these, as well as from the accusation that he is a sentimentalist with a penchant for moralizing ethos which endows his work with ephemeral value. My thesis uses East of Eden to defend Steinbeck’s literary reputation. By analyzing Steinbeck’s exploration of the universal theme of good and evil, as well as his assertion that man may choose his own morality, I argue that East of Eden is representative of Steinbeck’s best work and his true capability as a writer. I also contest the accusation that East of Eden is an imperfectly structured novel with an inconsistent theme; I inspect the character of Cathy Ames Trask and through her, argue that Steinbeck’s structure for the novel is very intentional, and that his development of Cathy is not a contradictory element. Finally, my thesis evaluates the above-mentioned motifs to argue that sentimentality is not a detrimental quality to Steinbeck’s work, and that deep human emotion, such as is found in East of Eden, should be celebrated, not disregarded as manipulative or unnecessary