Essays about: "Integral Equation"

Showing result 1 - 5 of 26 essays containing the words Integral Equation.

  1. 1. Development of a cable analysis theory based on integral equation derivation

    University essay from Luleå tekniska universitet/Institutionen för teknikvetenskap och matematik

    Author : Sandra Larsson; [2023]
    Keywords : ;

    Abstract : Electrification of transportation is a major subject of research today, especially in air travel. The increasing number of electronics and cables also increases the interference between them. From this, interest grew to increase the accuracy of electromagnetic modeling of cables. READ MORE

  3. 2. Adjoint-based Formulation for Shape Optimization Problems in Computational Fluid Dynamics

    University essay from KTH/Matematik (Avd.)

    Author : Anton Scotte; [2023]
    Keywords : ;

    Abstract : A continuous adjoint formulation for exterior optimization of Dirichlet data on the boundary for potential flow applications has been developed in this thesis. This has been performed by utilizing boundary integral methods for both the primal problem (Laplace’s equation) and for the corresponding adjoint equation (Poisson’s equation) on the unit disc. READ MORE

  4. 3. Investigation of soliton equations with integral operators and their dynamics

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Ruben Vikars Hall; Carl Svennerstedt; [2023]
    Keywords : Soliton; Calogero-Moser-Sutherland system; Lax pair; Hilbert transform; Szegö projection; Benjamin-Ono equation; Non-chiral Intermediate long-wave equation; Szegö equation;

    Abstract : We present Lax pairs and functions called Lax functions corresponding to Calogero- Moser-Sutherland (CMS) systems. We present the Benjamin-Ono (BO) equation and a pole ansatz to the BO equation, constructed from a specific type of Lax function called a special Lax function corresponding to Rational and Trigonometric CMS systems. READ MORE

  5. 4. The Riemann Hypothesis and the Distribution of Primes

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : David Appelgren; Leo Tikkanen; [2023]
    Keywords : Riemann; Riemann Hypothesis; Zeta Function; Prime Number Theorem;

    Abstract : The aim of this thesis is to examine the connection between the Riemannhypothesis and the distribution of prime numbers. We first derive theanalytic continuation of the zeta function and prove some of its propertiesusing a functional equation. READ MORE

  6. 5. The Riemann Zeta Function and Prime Numbers

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Oskar Rune; Linus Envall; [2023]
    Keywords : ;

    Abstract : This thesis is the result of a literature study regarding the relationship between the Riemann zeta function and prime numbers. We introduce the $\zeta$ function, discussing its properties. Then, starting from Riemann's original series, we derive the Euler product formula and functional equation for $\zeta$. READ MORE