Professor Rudolf Gorenflo and his Contribution to Fractional Calculus

MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo

Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Om naturens förvandlingar : Vetenskap, kunskap och frihet i Rudolf Steiners tidiga tänkande. Idéhistoriska perspektiv på Waldorfpedagogiken

TRANSFORMATIONS OF NATURE Science, Knowledge and Freedom in the Early Thinking of Rudolf Steiner. Perspectives on Waldorf Education in the light of the History of Ideas Waldorf Education is based on the worldview that Rudolf Steiner (1861-1925) developed to a wide-ranging anthroposophical movement in the first decades of the 20th century. This thesis takes as its departure the early thinking of Rudolf Steiner that precedes anthroposophy, and its main purpose is to uncover the tradition of ideas represented in Steiner´s early life and which, in different ways, have emerged in the practice of Waldorf Education. Through systematic analysis I attempt to bring to light different aspects of Steiner’s early thinking: his concept of science, his epistemological startingpoints and his philosophy of freedom. By departing from J. W. Goethe’s qualitative concept of science, Steiner strove in his early works to formulate a monistic worldview which appears to be closely related to the Romantic Movement and its philosophy of nature. Characteristic traits of his thinking are, on the one hand, a critique of a one-sided enlightenment and, on the other hand, an aspiration to see the world as a living organic unity. Human beings can, by developing our intuitive faculties, get a deeper understanding of the indissoluble relationship between man and nature. Against this background Steiner´s early thinking can be read as a special kind of romantic development narrative. Steiner’s early thinking also opens the way for romantic perspectives on Waldorf Education. It appears that many central aims and conceptions in Waldorf Education can be illuminated by the epistemological perspective upon which Steiner elaborated early in his life. An organic curriculum, phenomenological didactics and high ideal of freedom can be considered seen as educational applications of conceptions that played an important role in Goethe and his age. Thus, Waldorf Education provides in our contemporary society an exceptional set of educational values: a holistic education with romantic undertones.

Karl Gottschalk and Elisbeth nee Steinfeld with their son Rudolf Gottschalk (later Grahame) and son Fritz Gottschalk (Levy) of Lisbeth's first marriage.

Rudolf Gottschalk (later Grahame) on right; Fritz Gottschalk (Levy) on left

Karl Gottschalk and Elisbeth nee Steinfeld with their son Rudolf Gottschalk (later Grahame) and son Fritz Gottschalk (Levy) of Lisbeth's first marriage.

Rudolf Gottschalk (later Grahame) on right; Fritz Gottschalk (Levy) on left

Walter, Ilse, Freddy, Ursula, and Rudolf Gottschalk with Edith Braunschweig in costumes dancing to a minuet for the 80th birthday celebration of Henriette Gottschalk; Hannover, Germany. Portraits Children

On 5 Oct 1929 the family got together in Hannover to celebrate the 80th Birthday of Henrietta Gottschalk nee Rothschild where the children danced a minuet by Beethoven or Mozart; left to right: Grandniece Edith Braunschweig, Walter Gottschalk, Ilse Gottschalk, Freddy Gottschalk, Ursula Gottschalk, and Rudolf Gottschalk

Albert Einstein with his son-in-law Rudolf Kayser Portraits Groups; Men

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Studio portrait of Hilde Mosse, Marianne Ginsberg (Gilbert) and Rudolf Mosse sitting on a sled Portraits; Children

Verso: Handwritten postcard correspondence dated 1916 January 21

Dr. Simberg, Rudolf Mosse, Richard Israel and other unidentified men hunting with Count Czarnecki Portraits; Children

Jagd beim Grafen Czarnecki

Leo Baeck sitting on grass with Rudolf Seligsohn; Erzgebirge Portraits; Groups; Men

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Rudolf and Antoinette von Kahler in living room; Vienna-Doebling Architecture; Residences

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