147 research outputs found
Cantor type functions in non-integer bases
Cantor's ternary function is generalized to arbitrary base-change functions
in non-integer bases. Some of them share the curious properties of Cantor's
function, while others behave quite differently
Closed subspaces, polynomial operators in the shift, and ARMA representations
AbstractThis paper is concerned with the representation of system behaviors by equations involving polynomial shift operators. In particular, the question of the elimination of latent (i.e., auxiliary) variables from an ARMA representation is considered for the case of multidimensional systems
A High Quartets Distance Construction
Given two binary trees on N labeled leaves, the quartet distance between the trees is the number of disagreeing quartets. By permuting the leaves at random, the expected quartet distance between the two trees is 23(N4) . However, no strongly explicit construction reaching this bound asymptotically was known. We consider complete, balanced binary trees on N=2n leaves, labeled by n bits long sequences. Ordering the leaves in one tree by the prefix order, and in the other tree by the suffix order, we show that the resulting quartet distance is (23+o(1))(N4) , and it always exceeds the 23(N4) bound
Nonlinear Neumann boundary stabilization of the wave equation using rotated multipliers
The rotated multipliers method is performed in the case of the boundary
stabilization by means of a(linear or non-linear) Neumann feedback. this method
leads to new geometrical cases concerning the "active" part of the boundary
where the feedback is apllied. Due to mixed boundary conditions, these cases
generate singularities. Under a simple geometrical conditon concerning the
orientation of boundary, we obtain a stabilization result in both cases.Comment: 17 pages, 9 figure
A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem
We consider a transmission wave equation in two embedded domains in ,
where the speed is in the inner domain and in the outer
domain. We prove a global Carleman inequality for this problem under the
hypothesis that the inner domain is strictly convex and . As a
consequence of this inequality, uniqueness and Lip- schitz stability are
obtained for the inverse problem of retrieving a stationary potential for the
wave equation with Dirichlet data and discontinuous principal coefficient from
a single time-dependent Neumann boundary measurement
Boundary stabilization of numerical approximations of the 1-D variable coefficients wave equation: A numerical viscosity approach
In this paper, we consider the boundary stabilization problem associated to the 1- d wave equation with both variable density and diffusion coefficients and to its finite difference semi-discretizations. It is well-known that, for the finite difference semi-discretization of the constant coefficients wave equation on uniform meshes (Tébou and Zuazua, Adv. Comput. Math. 26:337–365, 2007) or on somenon-uniform meshes (Marica and Zuazua, BCAM, 2013, preprint), the discrete decay rate fails to be uniform with respect to the mesh-size parameter. We prove that, under suitable regularity assumptions on the coefficients and after adding an appropriate artificial viscosity to the numerical scheme, the decay rate is uniform as the mesh-size tends to zero. This extends previous results in Tébou and Zuazua (Adv. Comput.Math. 26:337–365, 2007) on the constant coefficient wave equation. The methodology of proof consists in applying the classical multiplier technique at the discrete level, with a multiplier adapted to the variable coefficients
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