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    Epistel an Franz Jacobi

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    EPISTEL AN FRANZ JACOBI Epistel an Franz Jacobi ([1]) Titelseite ([1]) Nehmet die Lehre an, wie einen grossen Schatz Silber ... ([2]) Text ([3]

    q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers

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    We introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order q-differential operator having the q-classical polynomials as eigenfunctions in terms of other even order operators, which we explicitly construct in this work. The results here obtained can be viewed as the q-version of those given by Everitt et al. and by the first author, whilst the combinatorics of this new set of numbers is a q-version of the Jacobi–Stirling numbers given by Gelineau and the second author

    Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations

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    We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present paper is to show existence, uniqueness and a (locally in time) diffeomorphism property of the solution: the solution trajectory of the system is a diffeomorphism as a function of the initial momentum. This result enables us to implement a stochastic version of the classical method of characteristics for the Hamilton-Jacobi equations. An –in itself interesting– auxiliary result are pointwise a.s. estimates for iterated stochastic integrals driven by a vector of not necessarily independent jump-type semimartingales

    A discontinuous Galerkin moving mesh method for Hamilton-Jacobi equations

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    In this paper we consider the numerical solution of first-order Hamilton-Jacobi equations using the combination of a discontinuous Galerkin finite element method and an adaptive rr-refinement (mesh movement) strategy. Particular attention is given to the choice of an appropriate adaptivity criterion when the solution becomes discontinuous. Numerical examples in one and two dimensions are presented to demonstrate the effectiveness of the adaptive procedure

    Erbauliche Erörterung der Frage: Sollte der Mensch auch wohl verdienen, daß Gott Achtung für ihn hätte, und selbige durch Gnadenwerke bezeugte?

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    Autopsie nach Ex. der ULB Sachsen-AnhaltVorlageform des Erscheinungsvermerks: Leipzig, Bey Carl Ludwig Jacobi, 1754

    Fortsetzung und Beschluß des Versuches vom Ursprung der Abgötterey

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    Autopsie nach dem Exemplar der ULB HalleVorlage des Erscheinungsvermerks: Leipzig, Verlegts Carl Ludwig Jacobi, 1758.Druckerm
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