On subset sums of r-sets

AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not divisible by q for each q⩾2. Let f(n,r) denote the maximum cardinality of an r-set A ⊂ {1,2,…,n} having no subset sum Σεiai(εi=0 or 1, aiϵA) equal to a power of two. In this paper estimates for f(n,r) are obtained. We prove that limr→∞αr=0, where αr=limn→∞f(n,r)n. This result verifies a conjecture of Erdős and Freiman (1990)

Implications of a DK Molecule at 2.32 GeV

We discuss the implications of a possible quasinuclear DK bound state at 2.32 GeV. Evidence for such a state was recently reported in D_s^+pi^o by the BaBar Collaboration. We first note that a conventional quark model c-sbar assignment is implausible, and then consider other options involving multiquark systems. An I=0 c sbar n nbar baryonium assignment is one possibility. We instead favor a DK meson molecule assignment, which can account for the mass and quantum numbers of this state. The higher-mass scalar c-sbar state expected at 2.48 GeV is predicted to have a very large DK coupling, which would encourage formation of an I=0 DK molecule. Isospin mixing is expected in hadron molecules, and a dominantly I=0 DK state with some I=1 admixture could explain both the narrow total width of the 2.32 GeV state as well as the observed decay to D_s^+ pi^o. Additional measurements that can be used to test this and related scenarios are discussed.Comment: 6 pages, 1 figur

The Ursinus Weekly, March 1, 1937

Alex Bartha\u27s steel pier orchestra will syncopate at April junior prom • Ditter attacks court reform in Sunday\u27s forum • Four schools to wrestle here Sat. • Directors meet, give Sheeder religion chair • Ozzie Werley\u27s thirteen pieces to play for sophs • Andrew Brodbeck, director of college, died Saturday • Roberts and Broidy get \u27Kind lady\u27 leads • Second yearly intramural night to be held week before Easter • Dean McConn named speaker at forum Sunday, March 7 • Professor Michael\u27s survey shows 48.1 percent of class of \u2736 prepared to teach employed as teachers • Elizabethtown falls to bear co-eds; girl debaters win over rivals by 2-1 decision • Two Ursinusites checkmate high school chess players • Germany going down hill say speakers in IRC • State official discloses hints on becoming teacher • Yost\u27s theatre party sees Nazimova in Ibsen\u27s Ghosts • Guest and Laughlin beaten in talk match • Musical talent of Ursinus present program for Y\u27s • Co-eds observe Color Day in presentation ceremony • Vaccaro\u27s only field goal of game beats Drexel in overtime • Matmen fall before strong G-burg foe • Girls down Rosemont and Moravian easily • Bob Keehn instrumental in accumulating winning points as cubs down Drexel, Hill School, and Norristown foes • Brodbeck is dorm B.B. champ; Boxing to start in near future • Day, Shreiner are tops in co-ed\u27s basketball league • Ken\u27s passers come close to beating out Leb. Val. • Ursinus students sojourn in Poconos over week-end • Girls to elect May queen Wed; May pageant tryouts next week • Dr. Carolus Harry speaks and asks Lutherans to conferencehttps://digitalcommons.ursinus.edu/weekly/1923/thumbnail.jp

The Ursinus Weekly, December 14, 1936

Jing addresses athletic meeting • Christmas observance includes church service in Bomberger and party in gym • Doc Winkler, campus personality, is dead • Meredith, former Washington state coach, speaks tonight • Costello and Tworzydlo on Little All-American • Boswell and Helffrich debate as Tau Kappa Alpha initiation • Campus groups entertain at informal Xmas parties • Angermann talks to Y\u27s on consumer cooperation • Old speaks at vespers in chapel; Snyder, Olp lead • Psych test results show frosh thirty points above average • Ruby nears completion as senior write-ups are due • Mr., Mrs. Burton report on Newark IRC convention • Brownback to be chairman • Dr. McClure speaks today • Lantern is published • Fraternity correction • Pre-meds to hear Sommers • Brodbeck is interdorm champ; Curtis gridders place second • Co-ed basketeers launch first practice of season • Freeland, Brodbeck ahead as basketball loop starts • Ursinus graduate of 1892 dies suddenly last week • Beta Sigs pledge Astheimer • Juniors win class hockeyhttps://digitalcommons.ursinus.edu/weekly/1916/thumbnail.jp

The Ursinus Weekly, March 8, 1937

Max McConn uses higher learning as forum topic • Lafayette, Gettysburg, Haverford meet here for Middle Atlantics, finish in that order • Fenton is selected to reign at May Day • Curtain Club brings Hedgerow here twice • Alspach goes on air for Ursinus as frat brothers listen in • Ursinus directors attend Andrew Brodbeck\u27s funeral • Physical ed. meeting tonight features two guest speakers • Prom committee invites chaperones, signs Bartha • Japanese evangelist speaks at Tuesday\u27s chapel service • Phi Alpha Psis give party for many alumni members • State legislator W. Hess \u2731, to address hist. so. sci. group • Journal of Higher Education runs article by registrar Sheeder on college policies • Brotherhood meets • Co-eds wage four debates with Kutztown, Leb. Val. • Belles ring bells and maul mincing males and tell tall tales to make sisters happy • Convention of Tau Kappa Alpha chapters to be held at G-burg • Men cancel New York trip; debate at home instead • Hell\u27s bells; An ode • Varsity drops final home game to Drexel; frosh come through again to snap victory • Swarthmore holds girls to close win • Intramural night changed to after spring vacation • Shreiner wins three during week to lead interdorm race • Foul-shooting contest starts this week for men basketeershttps://digitalcommons.ursinus.edu/weekly/1924/thumbnail.jp

The Ursinus Weekly, October 12, 1936

Many alumni return for Old Timers\u27 Day featuring football game and council dance • YM-YW fosters library; new project starts today • Frosh dine, dance in first social event as a class • Student activities council sets Halloween party date • Ursinus students pick Landon 2-1, in first Weekly straw vote • Ursinus to begin Feb. admissions • Large audience sees As Husbands Go, Curtain Club production by Rachel Crothers, in gym Friday night • Debate topic is regulation of industry by Congress • Finance committee receives Hench bequest; plans budget • Struck by hit-and-run driver, Seagrave\u27s condition is fair • The human adventure, 8-reel historical film, to be shown • Ruby dedicated to McClure • Ursinus grad is delegate to Harvard tercentenary • Sigma Nu\u27s give alumnae tea • Gardens planned for halls • First Lantern scheduled to appear at Christmas • Round table group discusses marketing of college annuities • Fegely is vespers speaker; quartet from Trappe sings • Boiler house painted • Grizzlies chalk up first victory of season; Red Devils succumb 7-0 before old timers • Bear cubs to open season Saturday against Malvern • Soccer team loses initial league tilt to Dickinson • Grizzlies to meet veteran F. & M. team at Lancaster • Interclass hockey starts Tuesday; playoff Thursday • Gridmen get training table • Hockeyites defeat alumnae • Intersorority council releases list for new women studentshttps://digitalcommons.ursinus.edu/weekly/1907/thumbnail.jp

The Ursinus Weekly, April 20, 1936

Dr. Penniman to be commencement speaker; baccalaureate sermon by Rev. P. Leinbach • Prom, play head junior week-end • Campus women select leaders • TKA meeting • Open house committee plans varied program • Dr. Yost Jr. notes changes in reviewing new Lantern • Worcester elected head of lettermen\u27s group • Men\u27s council postpones elections until early May • Paper staff members hear address by A. H. Hendricks • Ursinus plans annual high school track meet • Y.M. names Fenstermacher president for coming year • Council on student activities calls off May 8 Ruby dance • Yost to speak at vespers • Professor Young to speak on problems of Near East • Preparations for May Day to be completed this week • Correlation, subject of study of class in mathematics 16 • Glassmoyer announces Ruby to appear on campus May 15 • Paisley topic announced • Wildcats take first game from grizzlies • Track, field men practice intensively for first meet • Worster gets lone victory as netmen lose to Roses • Stine wins foul-shot contest; Derr leads for dorm plaque • Track and field records of past season are compiled • J.V\u27s to open versus Hill • Girls\u27 tennis dates fixed • Dramatist to address Y.W.https://digitalcommons.ursinus.edu/weekly/1958/thumbnail.jp

The Ursinus Weekly, February 1, 1937

Dr. Clawson wins chess tournament • Fraternity rushing begins Wednesday • Girls exercise doubtful options and invite men to annual Lorelei Friday night, Feb. 12 • Forum to hear talk on Hitler movements • Shelley and Lipkin to speak over radio in Penn debate • Dean W. Kline returns to college duties today • College and borough work for better sewage system • Women\u27s Club to purchase 612 as dorm for college • Current catalogue contains changes in many courses; new studies given in chem, physics, music and history • Library association gives 60 books, promotes fund for endowment • Hedgerow cast plays Shaw at Ursinus this Wednesday • N.Y.A. allotment for Ursinus is reduced by eight percent • Helfferich addresses Lions • Seniors at work on revelation of class bests and mosts • Ursinus Circle entertains girls of college at tea • Sheeder on college day programs at high schools • Frosh basketballers lose a heartbreaker • Wrestlers preparing for Temple match on Saturday • Hoopsters face still schedule for week; three tilts on deck • Saturday informal sports plan will begin this week in gymhttps://digitalcommons.ursinus.edu/weekly/1919/thumbnail.jp

The Ursinus Weekly, September 14, 1936

Directors elect D. L. Helffrich vice-president; add Rev. J. M. Niblo to board membership • Small bear squad reports to Mac • Freshman enrollment surpasses last year • Pneumonia attack proves fatal to Dr. J. M. Anders, senior board member, at his summer home in Maine • Death removes Dr. Goepp from the Ursinus faculty • Ursinus College buys A. D. Fetterolf home • Tests and counselors\u27 banquet open orientation week program • Prof. Carter returns to post after year\u27s leave of absence • Anders\u27 will provides for $15,000 bequest to Ursinus • Bailey married last June • Freshman handbook edited by F. Ditzel and K. Clouse • Twelve graduates secure teaching, coaching posts • Class authorizes staff to edit small 1937 Ruby • Ursinus to have N. Y. A. • Four religious conferences held here during summerhttps://digitalcommons.ursinus.edu/weekly/1903/thumbnail.jp

The Ursinus Weekly, January 11, 1937

$100,000 Ursinus scholarship fund planned by county committee in honor of Omwake • Junior week-end chairmen chosen • Winspear speaks at Sunday forum • Getting married to be presented on Feb. 3 • Fred Wrigley\u27s band at frat-sorority ball • Weekly board approves election of new reporters • Pancoast sets final date on$3.50 Ruby subscription • Ursinus Circle to give tea for girls on Wednesday afternoon • Alumnus kills fox on campus; Poum quits chase, is foxed • Fenton and Roberts scholarships are established at high schools • McClure addresses chamber of commerce at Souderton • Directors discuss retirement annuity plan at fall meeting • Barnard represents Ursinus at social studies convention • Roving reporter interviews male students on pertinent topics; poll discloses Simon and Rogers most popular actresses and Camels the favored cigarette • New radio program affords opportunity for college talent • Bear basketeers swamped in first league games by strong F. & M. & G-burg teams • Grizzly grapplers ready for Penn on Saturday • Cubs to meet Brown Prep in season\u27s opener Wed. • Grizzlies meet Lebanon Valley Wednesday; Albright Saturday • Brodbeck gets undisputed lead of inter-dorm basketball loop • Banquet for hockey team • Council on activities sets evening for annual Lorelei • Roller skating party held tonight by Phys. Ed Club • Frosh elect Dave Hartman to men\u27s student council • May pageant deadline sethttps://digitalcommons.ursinus.edu/weekly/1917/thumbnail.jp