For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including eecient numerical estimates if the number L of decomposition levels is small, as well as growth estima...

Metal tellurides attract recent attention because of their promising applications as effective catalysts for the oxygen evolution reaction (OER). However, inappropriate adsorption energy between OER intermediates and telluride leads to an unsatisfactory electrocatalytic intrinsic activity. Herein, we adopt a unique in-situ cathodic electrochemical activation process facilitate surface self-reco...

We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system [17]. Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though the construction of the new ...

Through a two-step solvothermal method, different molar ratios of BiPO4 were grown in situ on the surface oxygen-vacancy-rich BiOBr (Ov-BiOBr), successfully constructing BiPO4/Ov-BiOBr heterojunction composite material. By novel type I high-low junction between semiconductor and Ov-BiOBr, stronger oxidative holes or reductive electrons retained, thereby improving redox performance photocatalyst...

The size of convective cores remains uncertain, despite its substantial influence on stellar evolution, and thus ages. seismic modeling young subgiants can be used to obtain indirect constraints the core structure during main sequence, thanks high probing potential mixed modes. We selected subgiant KIC10273246, observed by Kepler, based mixed-mode properties. thoroughly modeled this star, with ...

We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlevé equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridon...

We construct bivariate biorthogonal cosine wavelets on a twooverlapping rectangular grid with bell functions not necessary of tensor product type. The biorthogonal system as well as frame and Riesz basis conditions are given explicitly. Our methods are based on the properties of bivariate total folding and unfolding operators.

abstract We give a formula for the duals of the mask associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.