A flexible multiscale and directional representation for images is proposed. The scheme combines directional filter banks with the Laplacian pyramid to provides a sparse representation for twodimensional piecewise smooth signals resembling images. The underlying expansion is a frame and can be designed to be a tight frame. Pyramidal directional filter banks provide an effective method to implem...

In the presence of a confining potential V, eigenfunctions continuous Schrödinger operator ?? + V decay exponentially with rate governed by part which is above corresponding eigenvalue; this can be quantified method Agmon. Analogous localization properties also established for eigenvectors discrete matrix. This note shows, perhaps surprisingly, that one replace matrix any real symmetric Z-matri...

Abstract We consider the four neutrino oscillation that accommodate all data. range of corresponding mixing parameters by result experiments. Implicaion search for mass square difference and are discussed. determine possible values effective majorana $|&lt;m&gt;|=|{\sum }_{j}U_{ej}^{2}m_{j}|$ |&lt;<mml:mi...

We use the numerical S-matrix bootstrap method to obtain bounds on two leading Wilson coefficients of chiral lagrangian controlling low-energy dynamics massless pions thus providing a proof concept that can be used derive non-perturbative EFTs in more than spacetime dimensions.