As discussed in class on 1/27/06, this is a nonhomogeneous constant-coefficient partial differential equation (PDE) of the form aux + buy = f(x, y), where a = b = 1. In particular, this question asks us to solve the Cauchy problem – one which is defined on the entire real line. Using the method presented in class, it is a straightforward process to determine the general solution u(x, y). First,...

Scars are a result of the natural healing process that occurs when the skin repairs itself after wounds, trauma, burns, surgical incision, or disease. Normal skin tissue is replaced with scar tissue to close open wounds and prevent infection. Scars can be painful, cause itching, and limit mobility. Many scars are primarily a cosmetic concern, but their presence may have a significant negative i...

1. Let z ∈ R, and consider the function fz : R→ R x 7→ x+ z We have fz is Borel-measurable since for all c ∈ R, {x ∈ R|fz(x) ≤ c} = {x ∈ R|x+ z ≤ c} = (−∞, c− z) ∈ B. We also observe that if E ⊆ R, then f−1 z (E) = {x ∈ R|x + z ∈ E} = {−z + (x + z)|x + z ∈ E} = −z + E. Thus we have: if E is a Borel set, then f−1 −y (E) = y + E is a Borel set. Conversely, if y + E is a Borel set, then −y + (y + ...

FCSM Statistical Policy Seminar Session Title: Integrating Electronic Systems for Disseminating Statistics Paper Title: Interacting with Tabular Data Through the World Wide Web Paper Authors: Carol A. Hert, Syracuse University; Gary Marchionini, Univ. of North Carolina; Elizabeth D. Liddy, Syracuse University; Ben Shneiderman, University of Maryland Paper Presented by: Carol A. Hert hert_c@bls....

A previously unpublished ultralow–dispersion spectrum of Sanduleak -69 202, the stellar progenitor of SN 1987A, is presented and the uncertain presupernova evolution of Sanduleak -69 202 is discussed. Subject headings: Supernovae: individual (SN 1987A) — techniques: ultralow– dispersion spectra — Large Magellanic Cloud — supergiants — stars: Sanduleak -69 202

http://www.sciencemag.org/cgi/content/full/303/5655/202 version of this article at: including high-resolution figures, can be found in the online Updated information and services, http://www.sciencemag.org/cgi/content/full/303/5655/202/DC1 can be found at: Supporting Online Material found at: can be related to this article A list of selected additional articles on the Science Web sites http://w...

OBJECTIVE The primary objective was to assess the long-term effectiveness of balloon catheter sinusotomy. METHODS Patients who had sinus ostia dilated with balloon catheters were prospectively evaluated 1 year after surgery with nasal endoscopy, a CT scan, and the Sino-Nasal Outcome Test (SNOT-20). RESULTS Sixty-six patients (202 sinuses) were examined. One hundred seventy-two of 202 sinus ...