Discriminators of quadratic polynomials

Given $f \in \mathbb{Z}[x]$ and $n \in \mathbb{Z^{+}}$, the \emph{discriminator} $D_f(n)$ is the smallest positive integer $m$ such that $f(1), \ldots, f(n)$ are distinct mod $m$. In a recent paper, Z.-W. Sun proved that $D_f(n) = d^{\lceil \log_d n \rceil}$ if $f(x) = x(dx - 1)$ for $d \in \{2, 3\}$. We extend this result to $d = 2^r$ for any $r \in \mathbb{Z}^{+}$ and find that $D_f(n) = 2^{\lceil \log_2 n \rceil}$ in this case. We also provide more general statements for $d = p^r$, where $p$ is a prime. In addition, we present a potential method for generating prime numbers with discriminators of polynomials which do not always take prime values. Finally, we describe some general statements and possible topics for study about the discriminator of an arbitrary polynomial with integer coefficients.Comment: 8 page

Jill M. Baltazar Deichmann, AIA, NCARB / Master of Architecture, 2002

North Grant Park - Maggie Daley Park | Chicago, IL | Architectural Design, Code Consulting, 06/2010-12/2014 Primera Engineers, Ltd. Is part of the consultant team led by Michael Van Valkenburgh Associates Inc. of New York, selected by the Chicago Park District to design the major reconstruction of the 20-acre North Grant Park/Maggie Daley Park located near Chicago\u27s lakefront and major tourism centers of Millennium and Grant Parks. This project consists of the reinvention of the park space with a change in topography, pathways and planting. the project also introduces a children\u27s exploration center and play area, a rock climbing wall, and an ice track skating ribbon. The buildings and pavilions include a new food/retail concession kiosk, new utility building housing the ice ribbon mechanical equipment, and renovations to the existing field house mechanical room. The project provides an added unique element as the park itself is located atop the existing underground East Monroe Parking Garage. Primera provided all architectural, code consulting, mechanical, lighting controls design, electrical, plumbing, and fire protection engineering for the park and added buildings and pavilions.https://openscholarship.wustl.edu/wia_profiles/1027/thumbnail.jp

Dig Into Local Black History

Introduction to Dr. Louis Eugene King, African-American anthropologist with the Civilian Conservation Corps and the National Park Service at Gettysbur

Robert M. Ward Photograph Collection - Accession 502

The Robert M. Ward Photograph Collection consists of approximately 400 prints and 900 negatives from the photographs that he took in the 1940s, 1950s, and 1960s. Most of the events and individuals pictured are from the York County, SC area and include the Latta House in York, South Carolina, downtown Rock Hill, parades, baseball, military, aviation, sports, and other York County buildings and scenes. Also included are photographs of Landsford Canal State Park, York Technical College, Winthrop University, Catawba Indian chieftain King Haigler’s memorial, Andrew Jackson State Park, Kings Mountain State Park, Hall of Fame Golfer Sam Snead\u27s visit to Rock Hill, SC, and Charleston, South Carolina. The collection also contains newspaper articles from the York Observer, dated from 1988 to 1992, which helped to identify some of the people and events in the pictures.https://digitalcommons.winthrop.edu/manuscriptcollection_findingaids/1241/thumbnail.jp

Archaeological Survey for Proposed Improvements to Chippekokee Park and a Proposed Cycling and Walking Path in Vincennes, Knox County, Indiana

Abstracts are made available for research purposes. To view the full report, please contact the staff of the Glenn A. Black Laboratory of Archaeology (www.gbl.indiana.edu).At the request of Vincennes Parks & Recreation Department, the Glenn A. Black Laboratory of Archaeology, Indiana University (GBL) conducted Phase la archaeological reconnaissance surveys for proposed improvements to Chippekokee Park and a cycling and walking path connecting the vicinity of Kimmell Park and Chippekokee Park to Gregg Park in Vincennes, Knox County, Indiana. The improvement impact areas within Chippekokee Park consist of a 30 m x 50 m area at the northeast end of the park and a 65 m x 48 m area at the southeast end of the park. Approximately 1.19 acres were surveyed. The purposes of survey were I) to identify and document all of the cultural resources in the project area, 2) to evaluate any sites found with regard to their eligibility for inclusion on the National Register of Historic Places (NRHP) and the Indiana Register of Historic Sites and Structures (IRHSS), and 3) to make recommendations for the protection of significant and potentially significant sites. Fieldwork was conducted April 25, 2000 by GBL archaeologists Devin W. Fishel, Scott J. Shirar, and Brian W. Troyer. No cultural materials were discovered within the proposed project areas. Cultural resource clearance is therefore recommended for the proposed improvements to Chippekokee Park and the proposed cycling and walking path provided that all earth-moving activities are restricted to the currently defined project area boundaries

Average features of the muon component of EAS or = 10(17) eV

Three 10 sq m liquid scintillators were situated at approximately 0 m, 150 m and 250 m from the center of the Haverah Park array. The detectors were shielded by lead/barytes giving muon detection thresholds of 317 MeV, 431 MeV and 488 MeV respectively. During part of the operational period the 431 MeV threshold was lowered to 313 MeV for comparison purposes. For risetime measurement fast phototubes were used and the 10% to 70% amplitude time interval was parameterized by T sub 70. A muon lateral density distribution of the form rho mu (R theta) = krho(500)0.94 1/R(1 + R/490)-eta has been fitted to the data for 120 m R 600 m and 0.27 (500) 2.55. The shower size parameter (500) is the water Cerenkov response at 500 m from the core of the extensive air showers (EAS) and is relatable to the primary energy. The results show general consistency