The object of this paper is to give new expressions for the wave field produced when a time harmonic point source is diffracted by a wedge with Dirichlet or Neumann boundary conditions on its faces. The representation of the total field is expressed in terms of quadratures of elementary functions, rather than Bessel functions, which is usual in the literature. An analogous expression is given f...

We show that the potential wells V (x) = x 10 + a x 8 + b x 6 + c x 4 + d x 2 + f /x 2 with a central spike possess arbitrary finite multiplets of elementary exact bound states. Their strong asymptotic growth implies an ambiguity in their PT symmetrically generalized quantization (via complex boundary conditions) but the three eligible recipes coincide at our exceptional solutions.

The boundary conditions of a non-trivial string background are classified. To this end we need traces on various spaces of conformal blocks, for which generalizations of the Verlinde formula are presented. CERN-TH/98-18 January 1998 —————— Slightly extended version of a talk given by C. Schweigert at the XXXI st International Symposium Ahrenshoop on the Theory of Elementary Particles (Buckow, G...

We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior regularity and rigidity properties, in a quantitative and qualitative way, and their (perhaps rather surprising) boundary behavior. We present at least a sketch of the proofs of these results, in a way that aims to be as elementary and self contained as possible, referring to the papers [CRS10, SV1...

The Topological Radon Theorem states that, for every continuous function from the boundary of a (d + 1)-dimensional simplex into Rn, there exist a pair of disjoint faces in the domain whose images intersect in Rn. The similarity between that result and the classical Borsuk-Ulam Theorem is unmistakeable, but a proof that the Topological Radon Theorem follows from Borsuk-Ulam is not immediate. In...

Let Gg,b be the set of all uni/trivalent graphs representing the combinatorial structures of pant decompositions of the oriented surface ⌃g,b of genus g with b boundary components. We describe the set Ag,b of all automorphisms of graphs in Gg,b showing that, up to suitable moves changing the graph within Gg,b, any such automorphism can be reduced to elementary switches of adjacent edges.

We prove that strict complementarity, primal and dual nondegeneracy of optimal solutions of convex optimization problems in conic form are generic properties. In this paper, we say generic to mean that the set of data possessing the desired property (or properties) has the same Hausdorr measure as the set of data that does not. Our proof is elementary and it employs an important result due to L...

We propose a new technique that provides a unified framework for modeling the collision dynamics of objects having arbitrary shape and rugosity. The technique assumes that boundary of the object is expressed by elementary segments with some random distribution of perturbation. Collision detection and treatment is done considering this conceptual representation. In order to efficiently detect co...

In this paper we focus on preprocessing for persistent homology computations. We adapt some techniques that were successfully used for standard homology computations. The main idea is to reduce the complex prior to generating its boundary matrix, which is costly to store and process. We discuss the following reduction methods: elementary collapses, coreductions (as defined by Mrozek and Batko),...

The notion of a hyperbolic group was introduced by Gromov [Gr]. Associated to any hyperbolic group, Γ, is its boundary, ∂Γ. This is a metrisable compactum on which Γ acts by homeomorphism. If Γ is non-elementary (i.e. not finite or virtually cyclic), then ∂Γ is perfect. The induced action of Γ on the space of distinct triples of ∂Γ is properly discontinuous and cocompact. The main result of thi...