The affine synthesis operator Sc = P j>0 P k∈Zd cj,kψj,k is shown to map the mixed-norm sequence space `(`) surjectively onto L(R), 1 ≤ p < ∞, under mild conditions on the synthesizer ψ ∈ L(R) (say, having a radially decreasing L majorant near infinity) and assuming R Rd ψ dx = 1. Here ψj,k(x) = | det aj |ψ(ajx− k), for some dilation matrices aj that expand. Therefore the standard norm on f ∈ L...

A quasiconvex function f being given, does there exist an increasing and continuous k which makes $$k\circ f$$ convex? How to build such a k? Some words on least convex (concave) functions. The ratio of two positive numbers is neither locally convexifiable nor concavifiable. Finally, some considerations the approximation preorder from finite number observations revealed preference problem are d...

Spaces of convex and concave functions appear naturally in theory applications. For example, regression log-concave density estimation are important topics nonparametric statistics. In stochastic portfolio theory, on the unit simplex measure concentration capital, their gradient maps define novel investment strategies. The may also be regarded as optimal transport simplex. this paper we constru...

Energetic proton acceleration from concave targets, the fronts of which were irradiated with 40 fs laser pulses with an intensity of 10 W/cm, has been studied as a function of the depth of the concave shape. Three kinds of targets, a triangular concave target, a circular concave target and a parabolic concave target are considered. When the depth of the concave shape was varied, the peak proton...

This paper presents a duality theory for solving concave minimization problem and nonconvex quadratic programming problem subjected to nonlinear inequality constraints. By use of the canonical dual transformation developed recently, two canonical dual problems are formulated, respectively. These two dual problems are perfectly dual to the primal problems with zero duality gap. It is proved that...