1. We consider differential topology to be the study of differentiable manifolds and differentiable maps. Then, naturally, manifolds are considered equivalent if they are diffeomorphic, i.e., there exists a differentiable map from one to the other with a differentiable inverse. For convenience, differentiable means C; in the problems we consider, C' would serve as well. The notions of different...

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...