Sökning: "sums of squares"
Hittade 5 avhandlingar innehållade orden sums of squares.
1. Cubical Intepretations of Type Theory
Sammanfattning : 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. LÄS MER
2. Combinatorial Methods in Complex Analysis
Sammanfattning : 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. LÄS MER
3. Quaternion Orders and Ternary Quadratic Forms Orders of Class Number One and Representations of Algebraic Integers by Quadratic Forms
Sammanfattning : 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. LÄS MER
4. Power ideals, Fröberg conjecture and Waring problems
Sammanfattning : 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. LÄS MER
5. Enumerative combinatorics related to partition shapes
Sammanfattning : 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. LÄS MER