New classes of diadic and triadic biorthogonal wavelets and wavelet-type frames in signal space are presented. The construction employs interpolatory filters with rational transfer functions that originate from continuous and discrete splines. These filters have linear phase. They are amenable either to fast cascading or parallel recursive implementation. The wavelets are applied to compression...

We develop a unifying perspective on several decompositions exhibiting directional parabolic scaling. In each decomposition, the individual atoms are highly anisotropic at fine scales, with effective support obeying the parabolic scaling principle length ≈ width. Our comparisons allow to extend Theorems known for one decomposition to others. We start from a Continuous Curvelet Transform f → Γf ...

In the pointfree topological context of locales and frames, real functions on a locale L are represented as localic morphisms S(L)→ L(R) (i.e. frame homomorphisms L(R) → S(L)) where S(L) stands for the frame of all sublocales of L and L(R) denotes the frame of reals. This is reminiscent of dealing with (not necessarily continuous) real functions X → R as with continuous functions D(X)→ R where ...

This paper presents a simplified approach for the design of semi-continuous composite beams in braced frames, where specific attention is given to the effect of joint rotational stiffness. A simple composite beam model is proposed incorporating the effects of semi-rigid end connections and the non-prismatic properties of a 'cracked' steel-concrete beam. This beam model is extended to a sub-fram...