Sökning: "power series algebra"

Visar resultat 1 - 5 av 10 avhandlingar innehållade orden power series algebra.

  1. 1. Waring-type problems for polynomials Algebra meets Geometry

    Detta är en avhandling från Stockholm : Department of Mathematics, Stockholm University

    Författare :Alessandro Oneto; Stockholms universitet.; [2016]
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; polynomials; Waring problems; Hilbert series; fat points; power ideals; secant varieties; matematik; Mathematics;

    Sammanfattning : In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. LÄS MER

  2. 2. Around power ideals From Fröberg's conjecture to zonotopal algebra

    Detta är en avhandling från Stockholm : Department of Mathematics, Stockholm University

    Författare :Gleb Nenashev; Stockholms universitet.; [2018]
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; matematik; Mathematics;

    Sammanfattning : In this thesis we study power algebras, which are quotient of polynomial rings by power ideals. We will study Hilbert series of such ideals and their other properties. We consider two important special cases, namely, zonotopal ideals and generic ideals. Such ideals have a lot combinatorial properties. LÄS MER

  3. 3. The Diamond Lemma for Power Series Algebras

    Detta är en avhandling från Umeå : Umeå universitet

    Författare :Lars Hellström; Umeå universitet.; [2002]
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; diamond lemma; power series algebra; Gröbner basis; embedding into skew fields; archimedean element in semigroup; q-deformed Heisenberg--Weyl algebra; polynomial degree; ring norm; Birkhoff orthogonality; filtered structure; Matematisk analys; MATHEMATICS Algebra; geometry and mathematical analysis Mathematical analysis; MATEMATIK Algebra; geometri och analys Analys; Mathematics; matematik;

    Sammanfattning : The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. LÄS MER

  4. 4. Constructive Newton–Puiseux Theorem, Sheaf Model of the Separable Closure and Dynamic Evaluation

    Detta är en avhandling från Göteborg : University of Gothenburg

    Författare :Bassel Mannaa; Göteborgs universitet.; Gothenburg University.; [2014]
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Newton–Puiseux; Algebraic curve; Sheaf model; Dynamic evaluation; Algebraic number; Grothendieck topos;

    Sammanfattning : Computing the Puiseux expansions of a plane algebraic curve defined by an affine equation over an algebraically closed field is a an important algorithm in algebraic geometry. This is the so-called Newton–Puiseux Theorem. The termination of this algorithm, however, is usually justified by non-constructive means. LÄS MER

  5. 5. Systems of Linear First Order Partial Differential Equations Admitting a Bilinear Multiplication of Solutions

    Detta är en avhandling från Matematiska institutionen

    Författare :Jens Jonasson; Linköpings universitet.; Linköpings universitet.; [2007]
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Cauchy–Riemann equations; holomorphic functions; algebra; MATHEMATICS; MATEMATIK;

    Sammanfattning : The Cauchy–Riemann equations admit a bilinear multiplication of solutions, since the product of two holomorphic functions is again holomorphic. This multiplication plays the role of a nonlinear superposition principle for solutions, allowing for construction of new solutions from already known ones, and it leads to the exceptional property of the Cauchy–Riemann equations that all solutions can locally be built from power series of a single solution z = x + iy ∈ C. LÄS MER