The Real 3x+1 Problem

In this work, we introduce another extension U of the 3n+1 function to the real line. We propose a conjecture about the U-trajectories that generalizes the famous 3n+1 (or Collatz) conjecture. We then prove our main result about the iterates of U (which is directly related to both of these conjectures). We also introduce the "flipped 3x+1" function \widetilde U and prove an analogous result for its trajectories. In the final section, we pose some interesting questions about the iterates of U (and \widetilde U), prove a couple of simple results about the iterates of U and \widetilde U, introduce other related functions and propose yet more conjectures and questions about their iterates. It's our hope that the results, conjectures and questions presented here will be not only relevant to the 3n+1 conjecture itself, but also of interest in their own right.Comment: 12 pages. Accepted for publication in Acta Arithmetica. Added more references. The published version is slightly differen

Further application of a semi-microscopic core-particle coupling method to the properties of Gd155,157, and Dy159

In a previous paper a semi-microscopic core-particle coupling method that includes the conventional strong coupling core-particle model as a limiting case, was applied to spectra and electromagnetic properties of several well-deformed odd nuclei. This work, coupled a large single-particle space to the ground state bands of the neighboring even cores. In this paper, we generalize the theory to include excited bands of the cores, such as beta and gamma bands, and thereby show that the resulting theory can account for the location and structure of all bands up to about 1.5 MeV.Comment: 15 pages including 9 figure(postscript), submitted to Phys.Rev.

Gap Domain Wall Fermions

I demonstrate that the chiral properties of Domain Wall Fermions (DWF) in the large to intermediate lattice spacing regime of QCD, 1 to 2 GeV, are significantly improved by adding to the action two standard Wilson fermions with supercritical mass equal to the negative DWF five dimensional mass. Using quenched DWF simulations I show that the eigenvalue spectrum of the transfer matrix Hamiltonian develops a substantial gap and that the residual mass decreases appreciatively. Furthermore, I confirm that topology changing remains active and that the hadron spectrum of the added Wilson fermions is above the lattice cutoff and therefore is irrelevant. I argue that this result should also hold for dynamical DWF and furthermore that it should improve the chiral properties of related fermion methods.Comment: 12 pages of text, 14 figures, added sect.6 on topology and reference

The Toric Phases of the Y^{p,q} Quivers

We construct all connected toric phases of the recently discovered $Y^{p,q}$ quivers and show their IR equivalence using Seiberg duality. We also compute the R and global U(1) charges for a generic toric phase of $Y^{p,q}$.Comment: 14 pages, 3 figure

Closed-Form Density of States and Localization Length for a Non-Hermitian Disordered System

We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schroedinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of the information transmission through non-linear optical fibers.Comment: 5 pages, 1 figur

Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter

We present the first evidence from lattice simulations that the magnetic monopoles in three dimensional compact quantum electrodynamics (cQED3) with N_f=2 and N_f= 4 four-component fermion flavors are in a plasma phase. The evidence is based mainly on the divergence of the monopole susceptibility (polarizability) with the lattice size at weak gauge couplings. A weak four-Fermi term added to the cQED3 action enabled simulations with massless fermions. The exact chiral symmetry of the interaction terms forbids symmetry breaking lattice discretization counterterms to appear in the theory's effective action. It is also shown that the scenario of a monopole plasma does not depend on the strength of the four-Fermi coupling. Other observables such as the densities of "isolated" dipoles and monopoles and the so-called specific heat show that a crossover from a dense monopole plasma to a dilute monopole gas occurs at strong couplings. The implications of our results on the stability of U(1) spin liquids in two spatial dimensions are also discussed.Comment: 20 pages, 9 figure

The impact of corporate philanthropy on reputation for corporate social performance

This study seeks to examine the mechanisms by which a corporation’s use of philanthropy affects its reputation for corporate social performance (CSP), which the authors conceive of as consisting of two dimensions: CSP awareness and CSP perception. Using signal detection theory (SDT), the authors model signal amplitude (the amount contributed), dispersion (number of areas supported), and consistency (presence of a corporate foundation) on CSP awareness and perception. Overall, this study finds that characteristics of firms' portfolio of philanthropic activities are a greater predictor of CSP awareness than of CSP perception. Awareness increases with signal amplitude, dispersion, and consistency. CSP perception is driven by awareness and corporate reputation. The authors’ contention that corporate philanthropy is a complex variable is upheld, as we find that CSP signal characteristics influence CSP awareness and perception independently and asymmetrically. The authors conclude by proposing avenues for future research

Broadband stimulated four-wave parametric conversion on a tantalum pentoxide photonic chip

We exploit the large third order nonlinear susceptibility (?(3) or “Chi 3”) of tantalum pentoxide (Ta2O5) planar waveguides and realize broadband optical parametric conversion on-chip. We use a co-linear pump-probe configuration and observe stimulated four wave parametric conversion when seeding either in the visible or the infrared. Pumping at 800 nm we observe parametric conversion over a broad spectral range with the parametric idler output spanning from 1200 nm to 1600 nm in infrared wavelengths and from 555 nm to 600 nm in visible wavelengths. Our demonstration of on-chip stimulated four wave parametric conversion introduces Ta2O5 as a novel material for broadband integrated nonlinear photonic circuit applications