Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg-de Vries Equation

In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries equation. In particular, we derive sufficient conditions for such a solution to be orbitally stable in terms of the Hessian of the classical action of the corresponding traveling wave ordinary differential equation restricted to the manifold of periodic traveling wave solution. We show this condition is equivalent to the solution being spectrally stable with respect to perturbations of the same period in the case of the Korteweg-de Vries equation, and in neighborhoods of the homoclinic and equilibrium solutions in the case of a power-law nonlinearity.Comment: 24 page

Decreased risk of breast cancer associated with oral bisphosphonate therapy

Preclinical studies and adjuvant trials using bisphosphonates have found them to have an antitumor effect. Although major advances have been made in chemoprevention strategies with selective estrogen receptor modulators and aromatase inhibitors, their use has been fraught with significant adverse effects such as venous thromboembolic events and an increased risk for endometrial cancer. In this context, several recent observational studies have investigated a chemoprevention role for oral bisphosphonates in decreasing risk for breast cancer. This review will aim to summarize these studies and present a critical evaluation of the association between oral bisphosphonate use and breast cancer risk reduction. © 2012 Mathew and Brufsky, publisher and licensee Dove Medical Press Ltd

When the Trumpet Call is Unclear: A Rhetorical Analysis of the Speech That Launched the Jesus Seminar

Since the Jesus Seminar has become almost iconic in religious media coverage, it merits academic scrutiny. This article focuses on the Seminar\u27s inaugural address given by founder Robert Funk on March 21, 1985, at the Pacific School of Religion in Berkeley, California. In that address, Funk set forth the Seminar\u27s mission and method that has guided the association ever since. The main thesis of this article is that clues to the Seminar\u27s successes and failures may be found in Funk\u27s inaugural address, which may be uncovered through a text-in-context analysis of the speech

The Aaron Diamond Foundation AIDS Research in New York City

Case study examines a foundation that spent down its $200 million endowment over 10 years on programs in medical research, minority education, and culture in New York City

Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case

Extending previous results of Oh--Zumbrun and Johnson--Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling-wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions.Comment: Fixed minor typo

Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev-Petviashvili Equation

In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev-Petviashvili equation. By analyzing high and low frequency limits of the appropriate periodic Evans function, we derive an orientation index which yields sufficient conditions for such an instability to occur. This index is geometric in nature and applies to arbitrary periodic traveling waves with minor smoothness and convexity assumptions on the nonlinearity. Using the integrable structure of the ordinary differential equation governing the traveling wave profiles, we are then able to calculate the resulting orientation index for the elliptic function solutions of the Korteweg-de Vries and modified Korteweg-de Vries equations.Comment: 26 pages. Sign error corrected in Lemma 3. Statement of main theorem corrected. Exposition updated and references added