On the number of Daubechies scaling functions and a conjecture of Chyzak et al.
Haar Type Orthonomal Wavelet Bases in R2.
Orthogonality Criteria for Compactly Supported Refinable Functions and Refinable Function Vectors.
Integral Self-Affine Tiles in ... Part II: Lattice Tilings.
Iterated function systems with a weak separation condition
Nonoverlapping contractive self-similar iterated function systems (IFS) have been studied in great detail via the open set condition. On the other hand much less is known about IFS with overlaps. To deal with such systems, a weak separation condition (WSC) has been introduced recently [LN1]; it is weaker than the open set condition and it includes many important overlapping cases. This paper has two purposes. First, we consider the class of self-similar measures generated by such IFS; we give a...
Coarse quantization for random interleaved sampling of bandlimited signals
The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let be a bandlimited signal that is sampled on a collection of interleaved grids { + } with offsets T n n = 1 N ⊂ [ 0 ,T ] . If the offsets are chosen independently and uniformly at random from [0] and if the sample values of are quantized with a first order Sigma-Delta algorithm, then with high probability the quantization error...
A stability theorem in nonlinear bilevel programming.
In this short paper, we are concerned with the stability of nonlinear bilevel programs. A stability problem is proven and an example is given to illustrate this theorem.
Coarse quantization for random interleaved sampling of bandlimited signals
The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let be a bandlimited signal that is sampled on a collection of interleaved grids { + } with offsets . If the offsets are chosen independently and uniformly at random from [0] and if the sample values of are quantized with a first order Sigma-Delta algorithm,...
Partitioning a planar graph without chordal 5-cycles into two forests
It was known that the vertex set of every planar graph can be partitioned into three forests. We prove that the vertex set of a planar graph without chordal 5-cycles can be partitioned into two forests. This extends a result obtained by Raspaud and Wang in 2008.
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