A Discrete Fourier Kernel and Fraenkel's Tiling Conjecture

The set B_{p,r}^q:=\{\floor{nq/p+r} \colon n\in Z \} with integers p, q, r) is a Beatty set with density p/q. We derive a formula for the Fourier transform \hat{B_{p,r}^q}(j):=\sum_{n=1}^p e^{-2 \pi i j \floor{nq/p+r} / q}. A. S. Fraenkel conjectured that there is essentially one way to partition the integers into m>2 Beatty sets with distinct densities. We conjecture a generalization of this, and use Fourier methods to prove several special cases of our generalized conjecture.Comment: 24 pages, 6 figures (now with minor revisions and clarifications

Self-Matching Properties of Beatty Sequences

We study the selfmatching properties of Beatty sequences, in particular of the graph of the function $\lfloor j\beta\rfloor$ against $j$ for every quadratic unit $\beta\in(0,1)$. We show that translation in the argument by an element $G_i$ of generalized Fibonacci sequence causes almost always the translation of the value of function by $G_{i-1}$. More precisely, for fixed $i\in\N$, we have $\bigl\lfloor \beta(j+G_i)\bigr\rfloor = \lfloor \beta j\rfloor +G_{i-1}$, where $j\notin U_i$. We determine the set $U_i$ of mismatches and show that it has a low frequency, namely $\beta^i$.Comment: 7 page

Insufficient discriminant validity:a comment on Bove, Pervan, Beatty and Shiu (2009)

Bove, Pervan, Beatty, and Shiu [Bove, LL, Pervan, SJ, Beatty, SE, Shiu, E. Service worker role in encouraging customer organizational citizenship behaviors. J Bus Res 2009;62(7):698–705.] develop and test a latent variable model of the role of service workers in encouraging customers' organizational citizenship behaviors. However, Bove et al. [Bove, LL, Pervan, SJ, Beatty, SE, Shiu, E. Service worker role in encouraging customer organizational citizenship behaviors. J Bus Res 2009;62(7):698–705.] claim support for hypothesized relationships between constructs that, due to insufficient discriminant validity regarding certain constructs, may be inaccurate. This research comment discusses what discriminant validity represents, procedures for establishing discriminant validity, and presents an example of inaccurate discriminant validity assessment based upon the work of Bove et al. [Bove, LL, Pervan, SJ, Beatty, SE, Shiu, E. Service worker role in encouraging customer organizational citizenship behaviors. J Bus Res 2009;62(7):698–705.]. Solutions to discriminant validity problems and a five-step procedure for assessing discriminant validity then conclude the paper. This comment hopes to motivate a review of discriminant validity issues and offers assistance to future researchers conducting latent variable analysis

Richard B. Bullock v. The Utah Department of Transportation : Brief of Appellee

RICHARD B. BULLOCK, Plaintiff and Appellant, vs. THE STATE OF UTAH DEPARTMENT OF TRANSPORTATION; EUGENE H. FINDLAY, CRAIG ZWICK, P.K. MOHANTY, DEAN W. HOLBROOK, ALAN W. DEARDON, J. VANCE BEATTY, FAYE B. BEATTY, THE ESTATE OF REED A. BULLOCK, DECEASED, CLEO H. BULLOCK, CLEO H. BULLOCK, INDIVIDUALLY, AND DOES 1 THROUGH 50, INCLUSIVE, Defendants and Appellees. Case No. 970582-CA Priority Number 1

Editorial Board

Editor-in Chief Jessica J. Penkal Executive Editor Michael Manning Managing Editors Jeffrey D. Perkins Christopher C. Stoneback Intake Editors Charlotte S. Beatty Megan Heahlke Staff Daniel Browder Brad J. Brown Jeffrey T. Dickson Nicole Ducheneaux Moriah Gillis Jason A. Johns Elizabeth Lowrance Kimberly McKelvey Faculty Advisor J. Martin Burk

Editorial Board

Editor-in-Chief Thomas W. Korver Assistant Editors-in Chief J. Wayne Capp Mark J. Luebeck Executive Editor Benjamin T. Cory Managing Editors Kathryn J. Bell James E. Dallner Intake Editors Cassie Coleman J. Winston Irwin Symposium Editor Lisa M. Polk Staff Charlotte S. Beatty Megan Heahlke Michael Manning Jessica Penkal Jeffrey D. Perkins Christopher S. Stoneback Matthew C. Thuesen Faculty Advisor J. Martin Burk

Editorial Board

Editor-in Chief Shelton C. Williams Associate Editors Richard L. Beatty Gary L. Davis Bruce L. Ennis Paul K. Keller Alden Pedersen Lawrence H. Sverdrup Staff Douglas D. Dasinger Harry B. Endsley III John R. Gordon Larry Petersen J. Dwaine Royball Sidney J. Strong William K. Wilburn Faculty Advisor Larry M. Eliso

Editorial Board

Editors-in Chief Hertha L. Lund Stephanie C. Stimpson Articles Editors Brendan R. Beatty Greg E. Overturf Citations Editors Tiffany B. Lonnevik Lisa A. Rodeghiero Managing Editor Robert J. Guite Staff Abbott Cooper Christopher J. Flann Sean S. Frampton Jamie J. Gaghwiler James M. Hughes Jason P. Loble Robert C. Lukes M. Scott Regan Jon. O. Shields David M. Wagner Faculty Advisor Carl Tobia

Editorial Board

Editors-in Chief James E. Conwell Page Carroccia Dringman Articles Editors Patrick N. Dringman Alice J. Hinshaw Citations Editors Timothy S. Hamill Cynthia K. Staley Business Manager Ann M. Monaghan Staff Brenden R. Beatty Mark Diefenderfer Robert J. Guite Tiffany B. Lonnevik Hertha L. Lunch Greg E. Overturf Lisa A. Rodeghiero Stephanie C. Simpson James T. Towe Faculty Advisor Carl Tobia

Pupillometric measurement of operator workload

Pupillometry as a method of measuring workload is described. Pupillometric measures provide an indication of momentary fluctuations in central nervous system excitability that occur as cognitive operations are performed; the magnitude of these changes may serve as a sensitive indicator of the workload imposed by cognitive tasks