The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precisions assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to appl...

Introduction. Solving boundary value problems for partial differential operators by integral equation methods is not a new idea. However, the classical way to do it consists in representing the unknown solution as a potential of the type that will lead to an integral equation of the second kind. Then, Fredholm's theorems can be used. Thus, the Dirichlet problem is usually solved with the help o...

Szegos inequality concerning the second eigenvalue of a homogeneous, free membrane is extended to the case of an inhomogeneous free membrane. With the help of a variational principle and the conformal mapping technic upper bounds are constructed for the sum VjU2 + V j ^ > where ^ and ^ denote the second and third eigenvalue. These bounds only depend on the total mass of the domain and on a simp...

We study hydrodynamic oscillations of a cylindrical Bose gas above the BoseEinstein transition temperature using the hydrodynamic equations derived by Griffin, Wu and Stringari. This extends recent studies of a cylindrical Bosecondensed gas at T = 0. Explicit normal mode solutions are obtained for nonpropagating solutions. In the classical limit, the sound velocity is shown to be the same as a ...

Transverse coherence of Self-Ampli ed Spontaneous Emission (SASE) in high gain FELs is investigated through a three-dimensional eigenmode analysis. It is the rst time such an analysis could be carried out to account for the e ects of emittance and betatron focusing. In addition to the variational solution [1] found for the fundamental mode, E00, similar solutions are derived here for two higher...

We present applications of variational – wavelet approach to three different models of nonlinear beam motions with underlying collective behaviour: Vlasov-MaxwellPoisson systems, envelope dynamics, beam-beam model. We have the representation for dynamical variables as a multiresolution (multiscales) expansion via high-localized nonlinear eigenmodes in the base of compactly supported wavelet bas...

We consider a 5-axis CNC machine whose tool axis maintains a fixed angle with respect to the surface normal as the machine tool cuts a given path on a smooth surface. The tool axis a(ξ) lies on a cone of constant angle ψ about the surface normal n(ξ) at each point of the path, but its azimuthal position on this cone remains indeterminate. Geometrically speaking, given a curve n(ξ) on the unit s...

We study the following quasilinear problem with nonlinear boundary conditions −∆pu = λa(x)|u|p−2u+ k(x)|u|q−2u− h(x)|u|s−2u, in Ω, |∇u|p−2∇u · η + b(x)|u|p−2u = 0 on ∂Ω, where Ω is an unbounded domain in RN with a noncompact and smooth boundary ∂Ω, η denotes the unit outward normal vector on ∂Ω, ∆pu = div(|∇u|p−2∇u) is the p-Laplacian, a, k, h and b are nonnegative essentially bounded functions...

We consider problems of approximate inference in which the query of interest is given by a complex formula (such as a formula in disjunctive formal form (DNF)) over a joint distribution given by a graphical model. We give a general reduction showing that (approximate) marginal inference for a class of distributions yields approximate inference for DNF queries, and extend our techniques to accom...

In this paper, we propose bipartite polar classification to augment an input unorganized point set P with two disjoint groups of points distributed around the ambient space of P to assist the task of surface reconstruction. The goal of bipartite polar classification is to obtain a space partitioning of P by assigning pairs of Voronoi poles into two mutually invisible sets lying in the opposite ...