Sökning: "real zeros"

Visar resultat 1 - 5 av 15 avhandlingar innehållade orden real zeros.

1. 1. Polynomial Sequences Generated by Linear Recurrences : Location and Reality of Zeros

   Författare :Innocent Ndikubwayo; Boris Shapiro; Rikard Bögvad; Tamás Forgacs; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; real-rooted polynomials; generating functions; discriminants; Tran s conjecture; Toeplitz matrices; Mathematics; matematik;

   Sammanfattning : In this thesis, we study the problem of location of the zeros of individual polynomials in sequences of polynomials generated by linear recurrence relations.In paper I, we establish the necessary and sufficient conditions that guarantee hyperbolicity of all the polynomials generated by a three-term recurrence of length 2, whose coefficients are arbitrary real polynomials. LÄS MER

3. 2. Topics in polynomial sequences defined by linear recurrences

   Författare :INNOCENT NDIKUBWAYO; Boris Shapiro; Rikard Bøgvad; Tamás Forgács; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; recurrence relation; q-discriminant; generating function; polynomial sequence; support; real zeros; matematik; Mathematics;

   Sammanfattning : This licentiate consists of two papers treating polynomial sequences defined by linear recurrences.In paper I, we establish necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence {P_i} generated by a three-term recurrence relation P_i(x)+ Q_1(x)P_{i-1}(x) +Q_2(x) P_{i-2}(x)=0 with the standard initial conditions P_{0}(x)=1, P_{-1}(x)=0, where Q_1(x) and Q_2(x) are arbitrary real polynomials. LÄS MER

4. 3. Tropical aspects of real polynomials and hypergeometric functions

   Författare :Jens Forsgård; Boris Shapiro; Grigory Mikhalkin; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Amoeba; Tropical Geometry; Hypergeometric function; Geometry of zeros; Discriminant; Mathematics; matematik;

   Sammanfattning : The present thesis has three main topics: geometry of coamoebas, hypergeometric functions, and geometry of zeros.First, we study the coamoeba of a Laurent polynomial f in n complex variables. We define a simpler object, which we call the lopsided coamoeba, and associate to the lopsided coamoeba an order map. LÄS MER

5. 4. Combinatorics and zeros of multivariate polynomials

   Författare :Nima Amini; Petter Bränden; Jim Haglund; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

   Sammanfattning : This thesis consists of five papers in algebraic and enumerative combinatorics. The objects at the heart of the thesis are combinatorial polynomials in one or more variables. We study their zeros, coefficients and special evaluations. Hyperbolic polynomials may be viewed as multivariate generalizations of real-rooted polynomials in one variable. LÄS MER

7. 5. Some new results concerning general weighted regular Sturm-Liouville problems

   Författare :Mervis Kikonko; Lars-Erik Persson; Peter Wall; Angelo B. Mingarelli; Alexey Karapetyants; Luleå tekniska universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Partial differential equations; Sturm-Liouville problem; Right-definite; left-definite; non-definite; indefinite; Dirichlet problem; spectrum; eigenvalues; non-real eigenvalues; Richardson number; Richardson index; turning point; Mathematics; Matematik;

   Sammanfattning : In this PhD thesis we study some weighted regular Sturm-Liouville problems in which the weight function takes on both positive and negative signs in an appropriate interval [a,b]. With such  problems there is the possible existence of non-real eigenvalues, unlike in the definite case (i.e. LÄS MER