In this paper, we develop Terence Tao’s harmonic analysis method and apply it to restricted sumsets. The well known Cauchy-Davenport theorem asserts that if ∅ 6= A,B ⊆ Z/pZ with p a prime, then |A+ B| > min{p, |A|+ |B| − 1}, where A + B = {a + b : a ∈ A, b ∈ B}. In 2005, Terence Tao gave a harmonic analysis proof of the Cauchy-Davenport theorem, by applying a new form of the uncertainty princip...

In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space E, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of R, and we discuss their extension to E. We introduce the notion of E-metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of con...

Kronrod extensions to two classes of Gauss and Lobatto integration rules for the evaluation of Cauchy principal value integrals are derived. Since in one frequently occurring case, the Kronrod extension involves evaluating the derivative of the integrand, a new extension is introduced using n + 2 points which requires only values of the integrand. However, this new rule does not exist for all n...

s of MMA2013 & AMOE2013, May 27–30, 2013, Tartu, Estonia c © 2013 University of Tartu A CONFORMAL MAPPING METHOD IN INVERSE OBSTACLE SCATTERING RAINER KRESS Institut für Numerische und Angewandte Mathematik, Universität Göttingen Lotzestraße 16–18, 37083 Göttingen, Germany E-mail: [email protected] In a series of papers Akduman [1], Haddar [2] and Kress [5] have employed a conformal ...

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat’s principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a class...

This paper is the continuation of the work ”On an inverse problem for finite-difference operators of second order” ([1]). We consider the Cauchy problem for the Toda lattice in the case when the corresponding L-operator is a Jacobi matrix with bounded elements, whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum. Usin...

This paper is the continuation of the work ”On an inverse problem for finite-difference operators of second order” ([1]). We consider the Cauchy problem for the Toda lattice in the case when the corresponding L-operator is a Jacobi matrix with bounded elements, whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum. Usin...

Γ-ultrametric spaces are spaces which satisfy all the axioms of an ultrametric space except that the distance function takes values in a complete lattice Γ instead of R≥0. Γ-ultrametric spaces have been extensively studied as a way to weaken the notion of an ultrametric space while still providing enough structure to be useful (see for example [17], [18], [8]). The many uses of Γ-ultrametric sp...