CURRICULUM VITAE: Milford H. Wolpoff
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Arxiv:1707.09546V1 [Math.GN] 29 Jul 2017 Ru,Sprbegop Rcmatgop Suoopc G Pseudocompact Group, Precompact Group, Separable Group, 54B15
THE SEPARABLE QUOTIENT PROBLEM FOR TOPOLOGICAL GROUPS ARKADY G. LEIDERMAN, SIDNEY A. MORRIS, AND MIKHAIL G. TKACHENKO Abstract. The famous Banach-Mazur problem, which asks if every infinite- dimensional Banach space has an infinite-dimensional separable quotient Ba- nach space, has remained unsolved for 85 years, though it has been answered in the affirmative for reflexive Banach spaces and even Banach spaces which are duals. The analogous problem for locally convex spaces has been answered in the negative, but has been shown to be true for large classes of locally convex spaces including all non-normable Fr´echet spaces. In this paper the analogous problem for topological groups is investigated. Indeed there are four natural analogues: Does every non-totally disconnected topological group have a sep- arable quotient group which is (i) non-trivial; (ii) infinite; (iii) metrizable; (iv) infinite metrizable. All four questions are answered here in the negative. How- ever, positive answers are proved for important classes of topological groups including (a) all compact groups; (b) all locally compact abelian groups; (c) all σ-compact locally compact groups; (d) all abelian pro-Lie groups; (e) all σ-compact pro-Lie groups; (f) all pseudocompact groups. Negative answers are proved for precompact groups. 1. Introduction It is natural to attempt to describe all objects of a certain kind in terms of basic building blocks of that kind. For example one may try to describe general Banach spaces in terms of separable Banach spaces. Recall that a topological space is said to be separable if it has a countable dense subset. -
Hands-On Human Evolution: a Laboratory Based Approach
Hands-on Human Evolution: A Laboratory Based Approach Developed by Margarita Hernandez Center for Precollegiate Education and Training Author: Margarita Hernandez Curriculum Team: Julie Bokor, Sven Engling A huge thank you to….. Contents: 4. Author’s note 5. Introduction 6. Tips about the curriculum 8. Lesson Summaries 9. Lesson Sequencing Guide 10. Vocabulary 11. Next Generation Sunshine State Standards- Science 12. Background information 13. Lessons 122. Resources 123. Content Assessment 129. Content Area Expert Evaluation 131. Teacher Feedback Form 134. Student Feedback Form Lesson 1: Hominid Evolution Lab 19. Lesson 1 . Student Lab Pages . Student Lab Key . Human Evolution Phylogeny . Lab Station Numbers . Skeletal Pictures Lesson 2: Chromosomal Comparison Lab 48. Lesson 2 . Student Activity Pages . Student Lab Key Lesson 3: Naledi Jigsaw 77. Lesson 3 Author’s note Introduction Page The validity and importance of the theory of biological evolution runs strong throughout the topic of biology. Evolution serves as a foundation to many biological concepts by tying together the different tenants of biology, like ecology, anatomy, genetics, zoology, and taxonomy. It is for this reason that evolution plays a prominent role in the state and national standards and deserves thorough coverage in a classroom. A prime example of evolution can be seen in our own ancestral history, and this unit provides students with an excellent opportunity to consider the multiple lines of evidence that support hominid evolution. By allowing students the chance to uncover the supporting evidence for evolution themselves, they discover the ways the theory of evolution is supported by multiple sources. It is our hope that the opportunity to handle our ancestors’ bone casts and examine real molecular data, in an inquiry based environment, will pique the interest of students, ultimately leading them to conclude that the evidence they have gathered thoroughly supports the theory of evolution. -
Manifestations of Nonlinear Roundness in Analysis, Discrete Geometry And
MANIFESTATIONS OF NON LINEAR ROUNDNESS IN ANALYSIS, DISCRETE GEOMETRY AND TOPOLOGY STRATOS PRASSIDIS AND ANTHONY WESTON Abstract. Some forty years ago Per Enflo introduced the nonlinear notions of roundness and generalized roundness for general metric spaces in order to study (a) uniform homeomorphisms between (quasi-) Banach spaces, and (b) Hilbert's Fifth Problem in the context of non locally compact topological groups (see [23], [24], [25], and [26]). Since then the concepts of roundness and generalized roundess have proven to be particularly useful and durable across a number of important mathematical fields such as coarse geometry, discrete geometry, functional analysis and topology. The purpose of this article is to take a retrospective look at some notable applications of versions of nonlinear roundness across such fields, to draw some hitherto unpublished connections between such results, and to highlight some very intriguing open problems. 1. Nonlinear Roundness | Introduction and Background Nonlinear notions of roundness and generalized roundness (see Definition 1.1) were introduced by Enflo in the late 1960s in a series of concise but elegant papers [23], [24], [25] and [26]. The purpose of Enflo’s programme of study in these papers was to investigate Hilbert's fifth problem in the context of non locally compact topological groups and to address the nonlinear classification of topological vector spaces up to uniform homeomorphism. Therein, Enflo used both roundness and generalized roundness in order to expose decisive estimates on the distortion of certain nonlinear maps between metric spaces. Later, within the context of Banach spaces, it became clear that roundness could be viewed as a natural precursor of Rademacher type. -
Bacterial Diversity and Function Within an Epigenic Cave System and Implications for Other Limestone Cave Systems
University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2015 Bacterial diversity and function within an epigenic cave system and implications for other limestone cave systems Kathleen Merritt Brannen-Donnelly University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Biogeochemistry Commons, Environmental Microbiology and Microbial Ecology Commons, and the Geology Commons Recommended Citation Brannen-Donnelly, Kathleen Merritt, "Bacterial diversity and function within an epigenic cave system and implications for other limestone cave systems. " PhD diss., University of Tennessee, 2015. https://trace.tennessee.edu/utk_graddiss/3543 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Kathleen Merritt Brannen-Donnelly entitled "Bacterial diversity and function within an epigenic cave system and implications for other limestone cave systems." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, -
L. Maligranda REVIEW of the BOOK by ROMAN
Математичнi Студiї. Т.46, №2 Matematychni Studii. V.46, No.2 УДК 51 L. Maligranda REVIEW OF THE BOOK BY ROMAN DUDA, “PEARLS FROM A LOST CITY. THE LVOV SCHOOL OF MATHEMATICS” L. Maligranda. Review of the book by Roman Duda, “Pearls from a lost city. The Lvov school of mathematics”, Mat. Stud. 46 (2016), 203–216. This review is an extended version of my two short reviews of Duda's book that were published in MathSciNet and Mathematical Intelligencer. Here it is written about the Lvov School of Mathematics in greater detail, which I could not do in the short reviews. There are facts described in the book as well as some information the books lacks as, for instance, the information about the planned print in Mathematical Monographs of the second volume of Banach's book and also books by Mazur, Schauder and Tarski. My two short reviews of Duda’s book were published in MathSciNet [16] and Mathematical Intelligencer [17]. Here I write about the Lvov School of Mathematics in greater detail, which was not possible in the short reviews. I will present the facts described in the book as well as some information the books lacks as, for instance, the information about the planned print in Mathematical Monographs of the second volume of Banach’s book and also books by Mazur, Schauder and Tarski. So let us start with a discussion about Duda’s book. In 1795 Poland was partioned among Austria, Russia and Prussia (Germany was not yet unified) and at the end of 1918 Poland became an independent country. -
L. Maligranda REVIEW of the BOOK BY
Математичнi Студiї. Т.50, №1 Matematychni Studii. V.50, No.1 УДК 51 L. Maligranda REVIEW OF THE BOOK BY MARIUSZ URBANEK, “GENIALNI – LWOWSKA SZKOL A MATEMATYCZNA” (POLISH) [GENIUSES – THE LVOV SCHOOL OF MATHEMATICS] L. Maligranda. Review of the book by Mariusz Urbanek, “Genialni – Lwowska Szko la Matema- tyczna” (Polish) [Geniuses – the Lvov school of mathematics], Wydawnictwo Iskry, Warsaw 2014, 283 pp. ISBN: 978-83-244-0381-3 , Mat. Stud. 50 (2018), 105–112. This review is an extended version of my short review of Urbanek's book that was published in MathSciNet. Here it is written about his book in greater detail, which was not possible in the short review. I will present facts described in the book as well as some false information there. My short review of Urbanek’s book was published in MathSciNet [24]. Here I write about his book in greater detail. Mariusz Urbanek, writer and journalist, author of many books devoted to poets, politicians and other figures of public life, decided to delve also in the world of mathematicians. He has written a book on the phenomenon in the history of Polish science called the Lvov School of Mathematics. Let us add that at the same time there were also the Warsaw School of Mathematics and the Krakow School of Mathematics, and the three formed together the Polish School of Mathematics. The Lvov School of Mathematics was a group of mathematicians in the Polish city of Lvov (Lw´ow,in Polish; now the city is in Ukraine) in the period 1920–1945 under the leadership of Stefan Banach and Hugo Steinhaus, who worked together and often came to the Scottish Caf´e (Kawiarnia Szkocka) to discuss mathematical problems. -
Juvenile Hominoid Cranium from the Terminal Miocene of Yunnan, China
Article Geology November 2013 Vol.58 No.31: 37713779 doi: 10.1007/s11434-013-6021-x Juvenile hominoid cranium from the terminal Miocene of Yunnan, China JI XuePing1,2, JABLONSKI Nina G3, SU Denise F4, DENG ChengLong5, FLYNN Lawrence J6, YOU YouShan7 & KELLEY Jay8* 1 Department of Paleoanthropology, Yunnan Institute of Cultural Relics and Archaeology, Kunming 650118, China; 2 Yunnan Key Laboratory for Paleobiology, Yunnan University, Kunming 650091, China; 3 Department of Anthropology, The Pennsylvania State University, University Park, PA 16802, USA; 4 Department of Paleobotany and Paleoecology, Cleveland Museum of Natural History, Cleveland, OH 44106, USA; 5 State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China; 6 Peabody Museum of Archaeology and Ethnology, Harvard University, Cambridge, MA 02138, USA; 7 Zhaotong Institute of Cultural Relics, Zhaotong 657000, China; 8 Institute of Human Origins and School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, USA Received May 28, 2013; accepted July 8, 2013; published online August 7, 2013 Fossil apes are known from several late Miocene localities in Yunnan Province, southwestern China, principally from Shihuiba (Lufeng) and the Yuanmou Basin, and represent three species of Lufengpithecus. They mostly comprise large samples of isolated teeth, but there are also several partial or complete adult crania from Shihuiba and a single juvenile cranium from Yuanmou. Here we describe a new, relatively complete and largely undistorted juvenile cranium from the terminal Miocene locality of Shuitangba, also in Yunnan. It is only the second ape juvenile cranium recovered from the Miocene of Eurasia and it is provisionally assigned to the species present at Shihuiba, Lufengpithecus lufengensis. -
Alternative Models for Evaluating Variation and Sexual Dimorphism in Fossil Hominoid Samples Jeremiah E
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 140:253–264 (2009) Beyond Gorilla and Pongo: Alternative Models for Evaluating Variation and Sexual Dimorphism in Fossil Hominoid Samples Jeremiah E. Scott,1* Caitlin M. Schrein,1 and Jay Kelley2 1School of Human Evolution and Social Change, Institute of Human Origins, Arizona State University, Tempe, AZ 85287-4101 2Department of Oral Biology, College of Dentistry, University of Illinois at Chicago, Chicago, IL 60612 KEY WORDS bootstrap; dental variation; Lufengpithecus; Ouranopithecus; Sivapithecus ABSTRACT Sexual size dimorphism in the postca- cies. Using these samples, we also evaluated molar dimor- nine dentition of the late Miocene hominoid Lufengpithe- phism and taxonomic composition in two other Miocene cus lufengensis exceeds that in Pongo pygmaeus, demon- ape samples—Ouranopithecus macedoniensis from strating that the maximum degree of molar size dimor- Greece, specimens of which can be sexed based on associ- phism in apes is not represented among the extant ated canines and P3s, and the Sivapithecus sample from Hominoidea. It has not been established, however, that Haritalyangar, India. Ouranopithecus is more dimorphic the molars of Pongo are more dimorphic than those of than the extant taxa but is similar to Lufengpithecus, any other living primate. In this study, we used resam- demonstrating that the level of molar dimorphism pling-based methods to compare molar dimorphism in required for the Greek fossil sample under the single-spe- Gorilla, Pongo,andLufengpithecus to that in the papio- cies taxonomy is not unprecedented when the compara- nin Mandrillus leucophaeus to test two hypotheses: tive framework is expanded to include extinct primates. (1) Pongo possesses the most size-dimorphic molars In contrast, the Haritalyangar Sivapithecus sample, if among living primates and (2) molar size dimorphism in it represents a single species, exhibits substantially Lufengpithecus is greater than that in the most dimorphic greater molar dimorphism than does Lufengpithecus. -
Per Enflo to Return to Chagrin Series for Mozart Concertos on January 21 by Daniel Hathaway
Per Enflo to return to Chagrin Series for Mozart concertos on January 21 by Daniel Hathaway Most of us feel fortunate if we can make a dent in a single professional career. Thus it’s inspiring that Per Enflo has distinguished himself both as a theoretical mathematician and a concert pianist. His interest in those parallel but distinct disciplines dates from his childhood in Sweden, where he first showed an aptitude for mathematics and played his first full recital on a professional concert series at the age of 11. As a mathematician, Enflo has cracked several seemingly unsolvable problems in functional analysis while teaching at Berkeley, Stanford, the École Polytechnique in Paris, and the Royal Institute of Technology in Stockholm. In 1989, he was appointed one of three “University Professors” at Kent State. In addition to teaching mathematics, he also worked on such cross-disciplinary issues as the zebra mussel invasion and the phosphorus loading of Lake Erie, anthropology and human evolution, and acoustics and noise reduction. Upon retirement in 2012, he moved back to Sweden, but still makes regular appearances in the States. This weekend, Enflo will return to Northeast Ohio to play Mozart’s 17th and 21st Concertos with the Cleveland Virtuosi on the Chagrin Concert Series at Valley Lutheran Church in Chagrin Falls. The free 3:00 pm concert on Sunday, January 21 will be led by Enflo’s frequent collaborator, violinist and series artistic director Hristo Popov. I recently spoke with Per Enflo in a telephone conversation from his home in Östervåla near Uppsala and began by asking him how he spends his time these days. -
New Middle Pleistocene Hominin Cranium from Gruta Da Aroeira (Portugal)
New Middle Pleistocene hominin cranium from Gruta da Aroeira (Portugal) Joan Dauraa, Montserrat Sanzb,c, Juan Luis Arsuagab,c,1, Dirk L. Hoffmannd, Rolf M. Quamc,e,f, María Cruz Ortegab,c, Elena Santosb,c,g, Sandra Gómezh, Angel Rubioi, Lucía Villaescusah, Pedro Soutoj,k, João Mauricioj,k, Filipa Rodriguesj,k, Artur Ferreiraj, Paulo Godinhoj, Erik Trinkausl, and João Zilhãoa,m,n aUNIARQ-Centro de Arqueologia da Universidade de Lisboa, Faculdade de Letras, Universidade de Lisboa, 1600-214 Lisbon, Portugal; bDepartamento de Paleontología, Facultad de Ciencias Geológicas, Universidad Complutense de Madrid, 28040 Madrid, Spain; cCentro Universidad Complutense de Madrid-Instituto de Salud Carlos III de Investigación sobre la Evolución y Comportamiento Humanos, 28029 Madrid, Spain; dDepartment of Human Evolution, Max Planck Institute for Evolutionary Anthropology, 04103 Leipzig, Germany; eDepartment of Anthropology, Binghamton University-State University of New York, Binghamton, NY 13902; fDivision of Anthropology, American Museum of Natural History, New York, NY 10024; gLaboratorio de Evolución Humana, Universidad de Burgos, 09001 Burgos, Spain; hGrup de Recerca del Quaternari - Seminari d’Estudis i Recerques Prehistòriques, Department of History and Archaeology, University of Barcelona, 08007 Barcelona, Spain; iLaboratorio de Antropología, Departamento de Medicina Legal, Toxicología y Antropología Física, Facultad de Medicina, Universidad de Granada, 18010 Granada, Spain; jCrivarque - Estudos de Impacto e Trabalhos Geo-Arqueológicos Lda, -
Age at First Molar Emergence in Early Miocene Afropithecus Turkanensis
Journal of Human Evolution 44 (2003) 307–329 Age at first molar emergence in early Miocene Afropithecus turkanensis and life-history evolution in the Hominoidea Jay Kelley1*, Tanya M. Smith2 1 Department of Oral Biology (m/c 690), College of Dentistry, University of Illinois at Chicago, 801 S. Paulina, Chicago, IL 60612, USA 2 Interdepartmental Doctoral Program in Anthropological Sciences, Stony Brook University, Stony Brook, NY 11794, USA Received 12 July 2002; accepted 7 January 2003 Abstract Among primates, age at first molar emergence is correlated with a variety of life history traits. Age at first molar emergence can therefore be used to broadly infer the life histories of fossil primate species. One method of determining age at first molar emergence is to determine the age at death of fossil individuals that were in the process of erupting their first molars. This was done for an infant partial mandible of Afropithecus turkanensis (KNM-MO 26) from the w17.5 Ma site of Moruorot in Kenya. A range of estimates of age at death was calculated for this individual using the permanent lateral incisor germ preserved in its crypt, by combining the number and periodicity of lateral enamel perikymata with estimates of the duration of cuspal enamel formation and the duration of the postnatal delay in the inception of crown mineralization. Perikymata periodicity was determined using daily cross striations between adjacent Retzius lines in thin sections of two A. turkanensis molars from the nearby site of Kalodirr. Based on the position of the KNM-MO 26 M1 in relation to the mandibular alveolar margin, it had not yet undergone gingival emergence. -
Religion 3 Second Edition Cabasilas, Lindsay Jones Nicholas Editor in Chief
ENCYCLOPEDIA OF RELIGION 3 SECOND EDITION CABASILAS, LINDSAY JONES NICHOLAS EDITOR IN CHIEF CYRUS II MACMILLAN REFERENCE USA An imprint of Thomson Gale, a part of The Thomson Corporation THOMSON THOMSON GAL•• E Encyclopedia of Religion. Second Edition Lindsay Jones, Editor in Chief © 2005 Thomson Gale, a part of The For permission to use material from this Since this page cannot legibly accommodate Thomson Corporation. product, submit your request via Web at all copyright notices, the acknowledgments http://www.gale-edit.com/permissions. or you constitute an extension of the copyright Thomson, Star Logo and Macmillan Reference may download our Permissions Request form notice. USA are trademarks and Gale is a registered and submit your request by fax or mail to: trademark used herein under license. While every effort has been made to Permissions ensure the reliability of the information pre- For more information, contact Thomson Gale sented in this publication, Thomson Gale Macmillan Reference USA 27500 Drake Rd. does not guarantee the accuracy of the data An imprint of Thomson Gale Farmington Hills, MI 48331-3535 contained herein. Thomson Gale accepts no 27500 Drake Rd. Permissions Hotline: payment for listing; and inclusion in the pub- Farmington, Hills, MI 48331-3535 248-699-8006 or 800-877-4253 ext. 8006 lication of any organization, agency, institu- Or you can visit our Internet site at Fax: 248-699-8074 or 800-762-4058 tion, publication, service, or individual does http://www.gale.com not imply endorsement of the editors or pub- lisher. Errors brought to the attention of the ALL RIGHTS RESERVED publisher and verified to the satisfaction of No part of this work covered by the copyright the publisher will be corrected in future hereon may be reproduced or used in any editions.