353 research outputs found
Orthogonal Macroelement Scaling Vectors and Wavelets in 1-D
We develop a {\em macroelement} based technique for constructing orthogonal univariate multiwavelets. We illustrate the technique with two examples. In the first example we provide a new construction of the symmetric, orthogonal, continuous scaling vector given in \cite{GHM}. In the second example, we construct a continuous orthogonal scaling vector with three components. The components of this scaling vector are symmetric or antisymmetric and provide approximation order 3, (equivalently, the components of are orthogonal to polynomials of degree 2 or less.) We believe this second example to be new
Minimum Riesz energy problems for a condenser with "touching plates"
Minimum Riesz energy problems in the presence of an external field are
analyzed for a condenser with touching plates. We obtain sufficient and/or
necessary conditions for the solvability of these problems in both the
unconstrained and the constrained settings, investigate the properties of
minimizers, and prove their uniqueness. Furthermore, characterization theorems
in terms of variational inequalities for the weighted potentials are
established. The results obtained are illustrated by several examples.Comment: 32 pages, 1 figur
Energy bounds for codes and designs in Hamming spaces
We obtain universal bounds on the energy of codes and for designs in Hamming
spaces. Our bounds hold for a large class of potential functions, allow unified
treatment, and can be viewed as a generalization of the Levenshtein bounds for
maximal codes.Comment: 25 page
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