G-invariant Szegő kernel asymptotics and CR reduction

Szegő-Widom asymptotics of Chebyshev polynomials on circular arcs

We review the main results of the seminal paper of Widom [2] on asymptotics of or-thogonal and Chebyshev polynomials associated with a set E (i.e., the monic polynomialsof degree at most n that minimize the sup-norm‖Tn‖E), where E is a system of Jordanregions and arcs. Thiran and Detaille [1], considered the Chebyshev polynomials Tn on acircular arc Aα and managed to fin...

Asymptotics, reduction and emergence

Stochastic Taylor expansions and heat kernel asymptotics

3 Stochastic Taylor expansions 5 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Brownian Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Exponential of a vector field . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Li...

BIOLOGICAL Cr(VI) REDUCTION

Scientific interest on chromium removal from water and wastewater has escalated recently. Chromium compounds exist in the environment naturally but are mostly found due to anthropogenic activities (tanning, paint, cement industries, etc.). Hexavalent chromium [Cr(VI)] is of major environmental importance because it is one of the most stable chromium forms found in the environment. It is soluble...

Kernel Asymptotics of Exotic Second-Order Operators

The Navier–Lamé operator of classical elasticity, μ∆v+(λ+μ)∇(∇·v), is the simplest example of a linear differential operator whose second-order terms involve a coupling among the components of a vector-valued function. Similar operators on Riemannian manifolds arise in conformal geometry and in quantum gravity. (In the latter context they have come to be called “nonminimal”, but “exotic” is pro...