Rotationally symmetric p -harmonic maps fromD2toS2

Rotationally Symmetric Harmonic Diffeomorphisms between Surfaces

and Applied Analysis 3 We will prove this theorem by contradiction. The idea is similar to the proof of Theorem 1. Suppose ψ is a rotationally symmetric harmonic diffeomorphism from P(a) onto D∗ with the metric σ 2 d|u|, with the form ψ = g(r)e, then substituting ψ, σ 2 to u, σ in (2), respectively, we can get

Rotationally Symmetric Rose Links

This paper is an introduction to rose links and some of their properties. We used a series of invariants to distinguish some rose links that are rotationally symmetric. We were able to distinguish all 3-component rose links and narrow the bounds on possible distinct 4 and 5-component rose links to between 2 and 8, and 2 and 16, respectively. An algorithm for drawing rose links and a table of ro...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Quasi-symmetric functions and mod p multiple harmonic sums

We present a number of results about (finite) multiple harmonic sums modulo a prime, which provide interesting parallels to known results about multiple zeta values (i.e., infinite multiple harmonic series). In particular, we prove a “duality” result for mod p harmonic sums similar to (but distinct from) that for multiple zeta values. We also exploit the Hopf algebra structure of the quasi-symm...

Polarization aberrations. 1. Rotationally symmetric optical systems.

The polarization in isotropic radially symmetric lens and mirror systems in the paraxial approximation is examined. Polarized aberrations are variations in the phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear diattenuat...