Any nonlinear equation of the form y′′ = ∑N n=0 an(z)y n has a (generally branched) solution with leading order behaviour proportional to (z − z0) about a point z0, where the coefficients an are analytic at z0 and aN (z0) 6= 0. We consider the subclass of equations for which each possible leading order term of this form corresponds to a one-parameter family of solutions represented near z0 by a...

An experimental set-up of the method of caustics was proposed for the accurate evaluation of stress intensity factor. The stress intensity factor evaluation was based on a new formula which was based on the caustic shape area. The new formula was based on the shape area of the caustics. The stress optical constants were evaluated according to the new formula of the stress intensity factor. The ...

Let (f, g) be a pair of complex analytic functions on a singular analytic space X. We give “the correct” definition of the relative polar curve of (f, g), and we give a very formal generalization of Lê’s attaching result, which relates the relative polar curve to the relative cohomology of the Milnor fiber modulo a hyperplane slice. We also give the technical arguments which allow one to work w...

Let X be a Banach space and Z a nonempty closed subset of X. Let J :Z → R be a lower semicontinuous function bounded from below. This paper is concerned with the perturbed optimization problem infz∈Z{J (z)+ ‖x − z‖}, denoted by (x, J )-inf for x ∈X. In the case when X is compactly fully 2-convex, it is proved in the present paper that the set of all points x in X for which there does not exist ...

Martı́n González-Alonso and Michael J. Ramsey-Musolf Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, USA (Received 25 December 2012; published 14 March 2013) We study the impact of a leptophobic Z0 gauge boson on the C1q and C2q parameters that describe the low-energy, pari...

Given a probability measure μ with infinite support on the unit circle ∂D = {z : |z| = 1}, we consider a sequence of paraorthogonal polynomials hn(z, λ) vanishing at z = λ where λ ∈ ∂D is fixed. We prove that for any fixed z0 6∈ supp(dμ) distinct from λ, we can find an explicit ρ > 0 independent of n such that either hn or hn+1 (or both) has no zero inside the disk B(z0, ρ), with the possible e...

Let X be a Banach space and Z a nonempty closed subset of X. Let J :Z → R be an upper semicontinuous function bounded from above. This paper is concerned with the perturbed optimization problem supz∈Z{J (z)+ ‖x − z‖}, which is denoted by (x, J )-sup. We shall prove in the present paper that if Z is a closed boundedly relatively weakly compact nonempty subset, then the set of all x ∈X for which ...

We calculate the rate of production ofW+Υ and Z0+Υ at the Tevatron. We find the cross sections at a center-of-mass energy of 1.8 TeV to be roughly 450 pb for W+Υ and 150 pb for Z0+Υ. The dominant production mechanism involves the binding of a color-octet bb̄ pair into a P-wave bottomonium state which subsequently decays into Υ. The purely leptonic decay modes of Υ, W, and Z0 provide signatures w...

In this paper we derive quantitative uniqueness estimates at infinity for solutions to an elliptic equation with unbounded drift in the plane. More precisely, let u be a real solution to ∆u + W · ∇u = 0 in R2, where W is real vector and ‖W‖Lp(R2) ≤ K for 2 ≤ p <∞. Assume that ‖u‖L∞(R2) ≤ C0 and satisfies certain a priori assumption at 0. Then u satisfies the following asymptotic estimates at R ...

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary point z0 of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away from z0 cannot vanish to infinite order at z0 unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the...