Search for dissertations about: "sums of squares"

Found 5 swedish dissertations containing the words sums of squares.

2. 1. Cubical Intepretations of Type Theory

   Author : Simon Huber; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Dependent Type Theory; Univalence Axiom; Models of Type Theory; Identity Types; Cubical Sets;

   Abstract : The interpretation of types in intensional Martin-Löf type theory as spaces and their equalities as paths leads to a surprising new view on the identity type: not only are higher-dimensional equalities explained as homotopies, this view also is compatible with Voevodsky's univalence axiom which explains equality for type-theoretic universes as homotopy equivalences, and formally allows to identify isomorphic structures, a principle often informally used despite its incompatibility with set theory. While this interpretation in homotopy theory as well as the univalence axiom can be justified using a model of type theory in Kan simplicial sets, this model can, however, not be used to explain univalence computationally due to its inherent use of classical logic. READ MORE

4. 2. Combinatorial Methods in Complex Analysis

   Author : Per Alexandersson; Boris Shapiro; Alexandre Eremenko; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; combinatorics; Schrödinger equation; Toeplitz matrix; sums of squares; Schur polynomials; Mathematics; matematik;

   Abstract : The theme of this thesis is combinatorics, complex analysis and algebraic geometry. The thesis consists of six articles divided into four parts.Part A: Spectral properties of the Schrödinger equationThis part consists of Papers I-II, where we study a univariate Schrödinger equation with a complex polynomial potential. READ MORE

5. 3. Quaternion Orders and Ternary Quadratic Forms Orders of Class Number One and Representations of Algebraic Integers by Quadratic Forms

   Author : Elise Björkholdt; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; quaternion order; ternary quadratic form; class number; even Clifford algebra; quaternion algebra; embedding number; 11E12; 16H05; 11E20; 11E25; 11E88; even Clifford algebra;

   Abstract : Let R be the ring of integers in a totally real quadratic field K. The purpose of the thesis is to study totally definite quaternion R-orders and representations of elements in R by totally positive definite integral ternary quadratic forms. The thesis consists of three papers. READ MORE

6. 4. Power ideals, Fröberg conjecture and Waring problems

   Author : Alessandro Oneto; Boris Shapiro; Ralf Fröberg; Kristian Ranestad; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; power ideals; Hilbert function; fat points; Waring problem; matematik; Mathematics;

   Abstract : This thesis is divided into two chapters. First, we want to study particularclasses of power ideals, with particular attention to their relation with the Fröberg conjecture on the Hilbert series of generic ideals. READ MORE

7. 5. Enumerative combinatorics related to partition shapes

   Author : Jonas Sjöstrand; Anders Björner; Christian Krattenthaler; KTH; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; partition shape; sign-imbalance; Robinson-Schensted correspondence; chess tableau; restricted word; cylindrical lattice walk; Poincaré polynomial; Bruhat interval; rook polynomial; pattern avoidance; partitionsform; teckenobalans; Robinson-Schensted-korrespondens; schacktablå; begränsade ord; cylindriska latticestigar; poincarépolynom; bruhatintervall; tornpolynom; mönsterundvikande permutation; MATHEMATICS; MATEMATIK;

   Abstract : This thesis deals with enumerative combinatorics applied to three different objects related to partition shapes, namely tableaux, restricted words, and Bruhat intervals. The main scientific contributions are the following. READ MORE