In this paper we construct a one–parameter family of interpolating multigenerators which generalize the scalar generators constructed in [2] in a natural way. Furthermore we extend this approach to design a family of interpolating orthonormal multigenerators. The construction is based on the factorization techniques introduced in [21].

We describe several \wavelet transforms" which characterize smoothness spaces and for which the coe cients are obtained by sampling rather than integration. We use them to re-interpret the empirical wavelet transform, i.e. the common practice of applying pyramid lters to samples of a function.

Current SAT-based Model Checking is based on two major approaches: Interpolation-based (Imc) (global, with unrollings) and Property Directed Reachability/IC3 (Pdr) (local, without unrollings). Imc generates candidate invariants using interpolation over an unrolling of a system, without putting any restrictions on the SAT-solver’s search. Pdr generates candidate invariants by a local search over...

Bounded Model Checking (BMC) is well known for its simplicity and ability to find counterexamples. It is based on the idea of symbolically representing counterexamples in a transition system and then using a SAT solver to check for their existence or their absence. State-of-the-art BMC algorithms combine a direct translation to SAT with circuit-aware simplifications and work incrementally, shar...

A new class of biorthogonal wavelets—interpolating distributed approximating functional (DAF) wavelets are proposed as a powerful basis for scale-space functional analysis and approximation. The important advantage is that these wavelets can be designed with infinite smoothness in both time and frequency spaces, and have as well symmetric interpolating characteristics. Boundary adaptive wavelet...

In this paper a new model-based optimizing controller for a set of nonlinear systems is proposed. The nonlinear model set is based on a convex combination of two bounding linear models. An optimal control sequence is computed for each of the two bounding models. The proposed control algorithm is based on a convex combination of the two control sequences. A novel feature in these two optimizatio...

In many applications, wavelets are usually expected to have the following properties: compact support, orthogonality, linear-phase, regularity, and interpolation. To construct such wavelets, it is crucial designing scaling functions with the above properties. In twoand three-band cases, except for the Haar functions, there exists no scaling function with the above five properties. In -band case...

In this paper we study the existence and characterization of spaces which are images of minimal-norm projections that are required to interpolate at given functionals and satisfy additional shape-preserving requirements. We will call such spaces optimal interpolating spaces preserving shape. This investigation leads to concrete solutions in classical settings and, as examples, n will be determi...