We consider a family of smooth maps on an infinite cylinder which have invariant curves that are nowhere smooth. Most points on such a curve are buried deep within its spiked structure, and the outermost exposed points of the curve constitute an invariant subset which we call the "facade" of the curve. We find that for surprisingly many of the maps in the family, all points in the facades of th...

A function F on the space of n × n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument. Spectral functions are just symmetric functions of the eigenvalues. We show that a spectral function is twice (continuously) differentiable at a matrix if and only if the corresponding symmetric function is twice (continuously) differentiable at the vector of eige...

in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p

Any sufficiently often differentiable curve in the orbit space of a compact Lie group representation can be lifted to a once differentiable curve into the representation space. Smooth curves can even be lifted to a once differentiable curves which are orthogonal to the orbits.

The problem considered is as follows: given C ⊂ R and F : C → R differentiable, find f : C → R differentiable such that ‖∇f(x)‖−1∇f(x) = ‖F (x)‖−1F (x) for all x ∈ C. Conditions for f to be pseudoconvex or convex are given. The results are applied to the differentiable case of the revealed preference problem.

Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex–differentiable structure on that same space. Complex–differentiable structures on a given real manifold are often not unique. This letter is devoted to analysing the dependence of the notion of a quantum on the complex–differentiable structure chosen on classic...