Sökning: "special polynomials"

Visar resultat 1 - 5 av 24 avhandlingar innehållade orden special polynomials.

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

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

   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

3. 2. A combinatorial description of certain polynomials related to the XYZ spin chain

   Författare :Linnea Hietala; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; six-vertex model; eight-vertex SOS model; three-color model; domain wall boundary conditions; reflecting end; partition function; determinant formula; XYZ spin chain; alternating sign matrices; polynomials; positive coefficients;

   Sammanfattning : The aim of this thesis is to study the connection between the three-color model and the polynomials q_n(z) of Bazhanov and Mangazeev. To give some background, we describe some exactly solvable, quantum integrable lattice models and their connections to each other and to other models. LÄS MER

4. 3. Quantum many-body systems exactly solved by special functions

   Författare :Martin Hallnäs; Edwin Langmann; Pavel Winternitz; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Quantum many-body systems; integrable systems; special functions; Mathematical physics; Matematisk fysik;

   Sammanfattning : This thesis concerns two types of quantum many-body systems in one dimension exactly solved by special functions: firstly, systems with interactions localised at points and solved by the (coordinate) Bethe ansatz; secondly, systems of Calogero-Sutherland type, as well as certain recently introduced deformations thereof, with eigenfunctions given by natural many-variable generalisations of classical (orthogonal) polynomials. The thesis is divided into two parts. LÄS MER

5. 4. The Symmetric Meixner-Pollaczek polynomials

   Författare :Tsehaye Araaya; Sten Kaijser; Svante Janson; Hjalmar Rosengren; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; Meixner-Pollaczek polynomial; Orthogonal polynomial; Polynomial operator; Inner product; Umbral calculus; Sheffer polynomial; Convolution type polynomial; Connection and linearization problem; 33C45; 05A40; 33D45; Matematisk analys; Mathematical analysis; Analys; matematik; Mathematics;

   Sammanfattning : The Symmetric Meixner-Pollaczek polynomials are considered. We denote these polynomials in this thesis by pn(λ)(x) instead of the standard notation pn(λ) (x/2, π/2), where λ > 0. LÄS MER

7. 5. Combinatorics of solvable lattice models with a reflecting end

   Författare :Linnea Hietala; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; mathematics; mathematical physics; six-vertex model; eight-vertex SOS model; three-color model; reflecting end; domain wall boundary conditions; partition function; determinant formula; XYZ spin chain; alternating sign matrices; special polynomials; positive coefficients;

   Sammanfattning : I den här avhandlingen studerar vi några exakt lösbara, kvantintegrerbara gittermodeller. Izergin bevisade en determinantformel för partitionsfunktionen till sexvertexmodellen på ett gitter av storlek n × n med Korepins domänväggrandvillkor (domain wall boundary conditions – DWBC). LÄS MER