119,759 research outputs found

    Extremalis problĂ©mĂĄk többvĂĄltozĂłs Ă©s sĂșlyozott polinomokra = Extremal problems for multivariate and weighted polynomials

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    JĂłl ismert hogy a többvĂĄltozĂłs polinomok sƱrƱek a d-dimenziĂłs kompakt halmazokon folytonos fĂŒggvĂ©nyek terĂ©ben. A többvĂĄltozĂłs polinomok egy fontos rĂ©szhalmaza a homogĂ©n polinomok osztĂĄlya. Igy termĂ©szetesen felmerĂŒl az a kĂ©rdĂ©s, hogy igaz-e a sƱrĂŒsĂ©g a homogĂ©n polinomokra? Egy ismert sejtĂ©s szerint a konvex felĂŒleteken folytonos fĂŒggvĂ©nyek megközelĂ­thetƑek kĂ©t homogĂ©n polinom összegĂ©vel. A pĂĄlyĂĄzat keretĂ©ben kĂ©t fontos Ășj eredmĂ©ny szĂŒletett 1) igazoltuk a sejtĂ©st tetszƑleges sima ( egyĂ©rtelmĂŒ tĂĄmasz sikkal rendelkezƑ) konvex testeken egyenletes normĂĄban 2) igazoltuk a sejtĂ©st teljes ĂĄltalĂĄnossĂĄgban Lp normĂĄban Ezen kivĂŒl ĂĄltalĂĄnosĂ­tott Freud sĂșlyokra vonatkozĂł polinom-approximĂĄciĂłs problĂ©mĂĄkat vizsgĂĄltunk. Itt az ĂĄltalĂĄnosĂ­tĂĄs azt jelenti, hogy az eredeti Freud sĂșlyokat megszorozzuk olyan un. ĂĄltalĂĄnosĂ­tott polinomokkal, amelyeknek csak valĂłs gyökeik vannak. A klasszikus polinom-egyenlotlensĂ©gek analogonjait, valamint direkt Ă©s fordĂ­tott approximĂĄciĂłs tĂ©teleket bizonyĂ­tottunk. HibabecslĂ©seket adtunk fĂŒggvĂ©nyek sĂșlyozott approximĂĄciĂłjĂĄra Freud sĂșlyok esetĂ©n, olyan egĂ©sz fĂŒggvĂ©nyekkel törtĂ©no approximĂĄciĂł esetĂ©n, amelyek vĂ©ges, ill. vĂ©gtelen sok pontban interpolĂĄljĂĄk a fĂŒggvĂ©nyt. Ezek a hibabecslĂ©sek olyan sĂșlyozott folytonossĂĄgi modulusokat tartalmaznak, amelyeknĂ©l a polinom-surusĂ©g nem mindig garantĂĄlt | It is well known that multivariate polynomials are dense in the space of continuous functions on compact subsets of the d-dimensional space. An important family of multivariate polynomials is the space of all homogeneous polynomials. Thus it is natural to ask if the density holds for homogeneous polynomials. It has been conjectured that any function continuous on a convex surface can be approximated by sums of two homogeneous polynomials. In the framework of the present project the above conjecture was verified in two new important cases: 1) the conjecture was verified for uniform norm on arbitrary regular convex bodies, i.e., in case when the body possesses a unique tangent plane at each point of its boundary 2) the conjecture was verified in full generality in the Lp norm We also considered polynomial approximation problems on the real line with generalized Freud weights. The generalization means multiplying these weights by so-called generalized polynomials which have real roots only. Analogues of classical polynomial inequalities, as well as direct and converse approximation theorems were proved. We gave error estimates for the weighted approximation of functions with Freud-type weights, by entire functions interpolating at finitely or infinitely many points on the real line. The error estimates involve weighted moduli of continuity corresponding to general Freud-type weights for which the density of polynomials is not always guaranteed

    Colonial Trauma in Márquez and Rushdie’s Magical Realism

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    Gabriel García Márquez’s One Hundred Years of Solitude and Salman Rushdie’s Midnight’s Children are hallmarks of the genre of magical realism. A typically problematic genre in terms of classification, this article looks at magical realism from a Freudian perspective, with particular reference to Freud’s notion of The Uncanny. Freud’s notion of uncanniness deals in displacement; it is uncomfortable, haunting and cyclical. The dominant presence of such uncanny effects in magical realist literature, I argue, reveals the haunting presence of colonial trauma within the current postcolonial psyche

    Where did that come from? Countertransference and the Oedipal triangle in family therapy

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    Family systems therapists are uncomfortable using psychoanalytic terms. This reluctance restricts discussion of therapeutic process. How does one describe, for example, the therapist’s subjective experiences of the patient or family? Psychoanalysts call this countertransference yet there is no equivalent word commonly used in systemic practice. Therapists who avoid the word may also avoid the experience and thereby risk losing sight of fundamental clinical events

    Misusing Freud: Psychoanalysis and the Rise of Homosexual Conversion Therapy

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    Current ideas of conversion therapy often focus on extremist religious groups that wish to cleanse the world of what they view as an immoral abomination, homosexuality. However, conversion therapy started out as mostly scientific curiosity. Sigmund Freud’s psychoanalytic research on human sexuality helped set the standards on psychosexual study in the twentieth century. Unfortunately, his views on homosexuality became distorted in the 1950s when psychoanalysts and psychiatrists used his methods of therapy but ignored his conclusions on homosexuality and sexual nature itself. Such distortions led to the destruction of many lives within the homosexual community. Reparative therapy on homosexuals exploded into a crusade in the 1950s to attempt to cure what many psychoanalysts considered a pathological disease. But well before the post-World War II era, homosexuality was looked upon as abnormal or pathological. It began in the late-nineteenth century when those in the medical field started studying sexuality and understanding its relation to human behavior. Psychologists and psychiatrists like James Kiernan and Richard Von Kraft-Ebing defined sexual identity, and they used hypnosis to condition patients’ sexuality, which marked the beginning of the study of human sexuality at the turn of the twentieth century. It was when Sigmund Freud began to research sexuality as it related to behavior patterns and the makeup of the human psyche that the psychosexual field began to evolve

    Rapid polynomial approximation in L2L_2-spaces with Freud weights on the real line

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    The weights Wα(x)=exp⁥(−∣x∣α)W_\alpha(x)=\exp{(-|x|^{\alpha})} (α>1)(\alpha>1) form a subclass of Freud weights on the real line. Primarily from a functional analytic angle, we investigate the subspace of L2(R,Wα2(x) dx)L_2(\mathbb R, W_\alpha^2(x)\,dx) consisting of those elements that can be rapidly approximated by polynomials. This subspace has a natural Fr\'echet topology, in which it is isomorphic to the space of rapidly decreasing sequences. We show that it consists of smooth functions and obtain concrete results on its topology. For α=2\alpha=2 there is a complete and elementary description of this topological vector space in terms of the Schwartz functions.Comment: 18 page

    German-language culture and the Slav stranger within

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    The aim of this article is to delineate the symbolic position of the Slavonic, and in particular the Czech, in German-language Austrian culture of the period 1890–1940. My approach will be informed by psychoanalysis. A subsidiary aim is to try to demonstrate uses of psychoanalysis in the study of central European culture. What is at issue here is an historical set of social power relations that find their expression in culture, that is to say, in art and literature, and that can be interpreted by psychoanalysis. All too often psychoanalysis avoids the social and the political outside the framework of the individual and her or his predictable traumas emanating from domestic life.1 This article, however, constitutes an exercise in inter- and intra-cultural psychoanalysis: intra-cultural as an investigation of psychoanalytic dynamics within German-language culture; inter-cultural as an examination of the relationship between German-language and Slav cultures in psychoanalytic terms
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