Characterisations of elementary pseudo-caps and good eggs

In this note, we use the theory of Desarguesian spreads to investigate good eggs. Thas showed that an egg in $\mathrm{PG}(4n-1, q)$, $q$ odd, with two good elements is elementary. By a short combinatorial argument, we show that a similar statement holds for large pseudo-caps, in odd and even characteristic. As a corollary, this improves and extends the result of Thas, Thas and Van Maldeghem (2006) where one needs at least 4 good elements of an egg in even characteristic to obtain the same conclusion. We rephrase this corollary to obtain a characterisation of the generalised quadrangle $T_3(\mathcal{O})$ of Tits. Lavrauw (2005) characterises elementary eggs in odd characteristic as those good eggs containing a space that contains at least 5 elements of the egg, but not the good element. We provide an adaptation of this characterisation for weak eggs in odd and even characteristic. As a corollary, we obtain a direct geometric proof for the theorem of Lavrauw

Central aspects of skew translation quadrangles, I

Except for the Hermitian buildings $\mathcal{H}(4,q^2)$, up to a combination of duality, translation duality or Payne integration, every known finite building of type $\mathbb{B}_2$ satisfies a set of general synthetic properties, usually put together in the term "skew translation generalized quadrangle" (STGQ). In this series of papers, we classify finite skew translation generalized quadrangles. In the first installment of the series, as corollaries of the machinery we develop in the present paper, (a) we obtain the surprising result that any skew translation quadrangle of odd order $(s,s)$ is a symplectic quadrangle; (b) we determine all skew translation quadrangles with distinct elation groups (a problem posed by Payne in a less general setting); (c) we develop a structure theory for root-elations of skew translation quadrangles which will also be used in further parts, and which essentially tells us that a very general class of skew translation quadrangles admits the theoretical maximal number of root-elations for each member, and hence all members are "central" (the main property needed to control STGQs, as which will be shown throughout); (d) we solve the Main Parameter Conjecture for a class of STGQs containing the class of the previous item, and which conjecturally coincides with the class of all STGQs.Comment: 66 pages; submitted (December 2013

Central aspects of skew translation quadrangles, 1

Modulo a combination of duality, translation duality or Payne integration, every known finite generalized quadrangle except for the Hermitian quadrangles H(4, q2), is an elation generalized quadrangle for which the elation point is a center of symmetry-that is, is a "skew translation generalized quadrangle" (STGQ). In this series of papers, we classify and characterize STGQs. In the first installment of the series, (1) we obtain the rather surprising result that any skew translation quadrangle of finite odd order (s, s) is a symplectic quadrangle; (2) we determine all finite skew translation quadrangles with distinct elation groups (a problem posed by Payne in a less general setting); (3) we develop a structure theory for root elations of skew translation quadrangles which will also be used in further parts, and which essentially tells us that a very general class of skew translation quadrangles admits the theoretical maximal number of root elations for each member, and hence, all members are "central" (the main property needed to control STGQs, as which will be shown throughout); and (4) we show that finite "generic STGQs," a class of STGQs which generalizes the class of the previous item (but does not contain it by definition), have the expected parameters. We conjecture that the classes of (3) and (4) contain all STGQs

Finite semifields and nonsingular tensors

In this article, we give an overview of the classification results in the theory of finite semifields (note that this is not intended as a survey of finite semifields including a complete state of the art (see also Remark 1.10)) and elaborate on the approach using nonsingular tensors based on Liebler (Geom Dedicata 11(4):455-464, 1981)

Generalized and Higher Dimensional Apollonian Packings

In this thesis, we show that circle, sphere, and higher dimensional sphere packings may be realized as subsets of the boundary of hyperbolic space, subject to certain symmetry conditions based on a discrete group of motions of the hyperbolic space. This leads to developing and applying counting methods which admit rigorous upper and lower bounds on the Hausdorff (or Besikovitch) dimension of the residual set of several generalized Apollonian circle packings. We find that this dimension (which also coincides with the critical exponent of a zeta-type function) of each packing is strictly greater than that of the Apollonian packing, supporting the unsolved conjecture that, among the many possible disk tilings of the plane, the Apollonian packing has the smallest possible residual set dimension. The obtained rigorous bounds are also consistent with the heuristic estimates calculated herein

Ancient Maya Commerce: Multidisciplinary Research at Chunchucmil

Ancient Maya Commerce presents nearly two decades of multidisciplinary research at Chunchucmil, Yucatan, Mexico—a thriving Classic period Maya center organized around commercial exchange rather than agriculture. An urban center without a king and unable to sustain agrarian independence, Chunchucmil is a rare example of a Maya city in which economics, not political rituals, served as the engine of growth. Trade was the raison d’être of the city itself. Using a variety of evidence—archaeological, botanical, geomorphological, and soil-based—contributors show how the city was a major center for both short- and long-distance trade, integrating the Guatemalan highlands, the Gulf of Mexico, and the interior of the northern Maya lowlands. By placing Chunchucmil into the broader context of emerging research at other Maya cities, the book reorients the understanding of ancient Maya economies. The book is accompanied by a highly detailed digital map that reveals the dense population of the city and the hundreds of streets its inhabitants constructed to make the city navigable, shifting the knowledge of urbanism among the ancient Maya. Ancient Maya Commerce is a pioneering, thoroughly documented case study of a premodern market center and makes a strong case for the importance of early market economies in the Maya region. It will be a valuable addition to the literature for Mayanists, Mesoamericanists, economic anthropologists, and environmental archaeologists.https://uknowledge.uky.edu/anthro_book/1000/thumbnail.jp

Ancient Maya Commerce

Nearly two decades of research at Chunchucmil, Yucatan, Mexico documented a thriving city of 40,000 people without the powerful kings and massive temples seen at other Maya centers. What brought people to this area, the driest in the Maya world, and how did they survive? Ancient Maya Commerce provides a pioneering study in economic anthropology, making the strongest case yet that ancient Maya economies were quite complex, containing markets in addition to other forms of exchange. Multiple lines of evidence including household archaeology, regional survey, paleo-ecology and soil chemistry show that Chunchucmil was a major center for both short and long distance trade, integrating the Guatemalan highlands, the Gulf of Mexico and the interior of the northern Maya lowlands. By placing Chunchucmil into the broader context of emerging research at other Maya cities, this book helps reorient our understanding of ancient Maya economies, foregrounding the increasingly important role of commerce

The Bristol Bay Environment A Background Study of Available Knowledge

The State of AlaskaTABLE OF CONTENTS Section Title Page I INTRODUCTION ] PURPOSE AND SCOPE 1 GENERAL LOCATION AND 3 SETTING II GEOMORPHOLOGY 7 INTRODUCTION 7 ONSHORE AREAS 15 OFFSHORE AREAS 18 REFERENCES CITED 24 III PHYSICAL OCEANOGRAPHY 27 INTRODUCTION 27 CIRCULATION 32 TIDES AND TIDAL CURRENTS 35 SUMMER WATER TYPES 41 SEA ICE AND WINTER 56 CONDITIONS WAVES 59 REFERENCES CITED 62 iii IV CLIMATE 65 INTRODUCTION 65 DATA SOURCES 66 REGIONAL WEATHER PATTERNS 66 TEMPERATURE 75 PRECIPITATION 95 DETAILED WEATHER 108 CONDITIONS SURFACE WINDS 108 ICE CONDITIONS 129 SOLAR RADIATION 134 LENGTH OF DAYLIGHT 135 EFFECT OF WEATHER ON 137 MAN'S ACTIVITIES REFERENCES CITED 149 V GEOLOGY 150 BEDROCK GEOLOGY 150 ONSHORE SURFICIAL 177 GEOLOGY CONTEMPORARY MARINE 189 SEDIMENTS MINERALS 200 iv OIL AND GAS 215 OTHER ENERGY RESOURCES 234 VOLCANISM 243 SEISMICITY 255 COASTAL PROCESSES AND 264 EROSION REFERENCES CITED 268 VI HYDROLOGY 278 INTRODUCTION 278 SURFACE WATER 278 GROUND WATER 295 REFERENCES CITED 300 VII BIOTA OF BRISTOL BAY 301 MARINE BACTERIA 301 PLANKTON 301 MARINE MACROPHYTES 318 BENTHIC AND INTERTIDAL 321 INVERTEBRATES PELAGIC FAUNA 381 TERRESTRIAL BIOTA 504 V ECOLOGICAL SYSTEMS AND 522 MECHANISMS REFERENCES CITED 536 VIII SOCIOECONOMICS 557 GENERAL DESCRIPTION OF 557 THE STUDY REGION POPULATION AND EDUCATION 592 LABOR FORCE AND 618 EMPLOYMENT INCOME AND COST OF 637 LIVING HOUSING AND PUBLIC 656 SERVICES INDUSTRIAL ACTIVITY 668 TRANSPORTATION FACILITIES 700 AND COSTS LAND USE AND LAND STATUS 724 REFERENCES CITED 744 IX POTENTIAL CONFLICTS OF 7 51 RESOURCE USE EFFECT,S OF THE ENVIRONMENT 7 51 ON RESOURCE USE EFFECTS OF RESOURCE USE ON 771 THE ENVIRONMENT vi EFFECTS OF PETROLEUM 800 DEVELOPMENT ON OTHER RESOURCE USE EFFECTS OF RESOURCE USE 804 ON THE SOCIOECONOMIC CHARACTER OF THE AREA DEVELOPMENT SCENARIO 811 REFERENCES CITED 820 X DATA GAPS 827 INTRODUCTION 827 GEOMORPHOLOGY 827 OCEANOGRAPHY 828 CLIMATE 831 GEOLOGY 832 HYDROLOGY 834 BIOLOGY 835 SOCIOECONOMIC 839 REFERENCES CITED 841 XI ALTERNATIVE METHODS FOR 843 PETROLEUM DEVELOPMENT INTRODUCTION 843 EXPLORATION 845 DEVELOPMENT 848 CONCLUSIONS 855 REFERENCES CITED 85

Proceedings of the tenth international conference Models in developing mathematics education: September 11 - 17, 2009, Dresden, Saxony, Germany

This volume contains the papers presented at the International Conference on “Models in Developing Mathematics Education” held from September 11-17, 2009 at The University of Applied Sciences, Dresden, Germany. The Conference was organized jointly by The University of Applied Sciences and The Mathematics Education into the 21st Century Project - a non-commercial international educational project founded in 1986. The Mathematics Education into the 21st Century Project is dedicated to the improvement of mathematics education world-wide through the publication and dissemination of innovative ideas. Many prominent mathematics educators have supported and contributed to the project, including the late Hans Freudental, Andrejs Dunkels and Hilary Shuard, as well as Bruce Meserve and Marilyn Suydam, Alan Osborne and Margaret Kasten, Mogens Niss, Tibor Nemetz, Ubi D’Ambrosio, Brian Wilson, Tatsuro Miwa, Henry Pollack, Werner Blum, Roberto Baldino, Waclaw Zawadowski, and many others throughout the world. Information on our project and its future work can be found on Our Project Home Page http://math.unipa.it/~grim/21project.htm It has been our pleasure to edit all of the papers for these Proceedings. Not all papers are about research in mathematics education, a number of them report on innovative experiences in the classroom and on new technology. We believe that “mathematics education” is fundamentally a “practicum” and in order to be “successful” all new materials, new ideas and new research must be tested and implemented in the classroom, the real “chalk face” of our discipline, and of our profession as mathematics educators. These Proceedings begin with a Plenary Paper and then the contributions of the Principal Authors in alphabetical name order. We sincerely thank all of the contributors for their time and creative effort. It is clear from the variety and quality of the papers that the conference has attracted many innovative mathematics educators from around the world. These Proceedings will therefore be useful in reviewing past work and looking ahead to the future