DEFF Research Database (Denmark)
Bach-Nielsen, Carsten
2012-01-01
Om Villa d'Este, en renæssancehave ved Rom, der tematiserer Herkules' valg mellem dydens og lastens vej......Om Villa d'Este, en renæssancehave ved Rom, der tematiserer Herkules' valg mellem dydens og lastens vej...
Pedoe, Dan
1988-01-01
""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he
Indian Academy of Sciences (India)
of geometry he completely changed our way of thinking. Later geometers were to spend entire lifetimes trying ... dimensions up to and including three it is difficult to think of dimensions beyond except abstractly -in one's .... form I. gij ai aj is positive for any collection of numbers. (aI, ... , an). Moreover, the given form can easily ...
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...... matematik, geometri, og fysik til at forstå, hvad det er, der foregår....
Simplifying massive planar subdivisions
DEFF Research Database (Denmark)
Arge, Lars; Truelsen, Jakob; Yang, Jungwoo
2014-01-01
(SORT(N)) I/Os, where N is the size of the decomposition and SORT(N) is the number of I/Os need to sort in the standard external-memory model of computation. Previously, such an algorithm was only known for the special case of contour map simplification. Our algorithm is simple enough to be of practical......We present the first I/O- and practically-efficient algorithm for simplifying a planar subdivision, such that no point is moved more than a given distance εxy and such that neighbor relations between faces (homotopy) are preserved. Under some practically realistic assumptions, our algorithm uses...... interest. In fact, although more general, it is significantly simpler than the previous contour map simplification algorithm. We have implemented our algorithm and present results of experimenting with it on massive real-life data. The experiments confirm that the algorithm is efficient in practice...
Subdivision depth for triangular surfaces
Directory of Open Access Journals (Sweden)
G. Mustafa
2016-06-01
Full Text Available The aim of this attempt was to present an efficient algorithm for the evaluation of error bound of triangular subdivision surfaces. The error estimation technique is based on first order difference and this process is independent of parametrization. This technique can be easily generalized to higher arity triangular surfaces. The estimated error bound is expressed in-terms of initial control point sequence and constants. Here, we efficiently estimate error bound between triangular surface and its control polygon after k-fold subdivision and further extended to evaluate subdivision depth of the scheme.
Recursively-regular subdivisions and applications
Directory of Open Access Journals (Sweden)
Rafel Jaume
2016-05-01
Full Text Available We generalize regular subdivisions (polyhedral complexes resulting from the projection of the lower faces of a polyhedron introducing the class of recursively-regular subdivisions. Informally speaking, a recursively-regular subdivision is a subdivision that can be obtained by splitting some faces of a regular subdivision by other regular subdivisions (and continue recursively. We also define the finest regular coarsening and the regularity tree of a polyhedral complex. We prove that recursively-regular subdivisions are not necessarily connected by flips and that they are acyclic with respect to the in-front relation. We show that the finest regular coarsening of a subdivision can be efficiently computed, and that whether a subdivision is recursively regular can be efficiently decided. As an application, we also extend a theorem known since 1981 on illuminating space by cones and present connections of recursive regularity to tensegrity theory and graph-embedding problems.
Nanothermodynamics: a subdivision potential approach
Directory of Open Access Journals (Sweden)
R. Moussavi
2005-12-01
Full Text Available Classical thermodynamic laws and relations have been developed for macroscopic systems that satisfy the thermodynamic limit. These relations are challenged as the system size decreases to the scale of nano-systems, in which thermodynamic properties are overshadowed by system size, and the usual classical concepts of extensivity and intensivity are no longer valid. The challenges to the classical thermodynamics in relation to small systems are demonstrated, and via the approach introduced by Hill, the concept of sub-division potential is clarified in details. The fundamental thermodynamic relations are obtained using a rational-based method.
Effect of Watertight Subdivision on Subdivision Index for Medium Size Ro–Ro Passenger Ferries
Directory of Open Access Journals (Sweden)
M. Pawlowski
2017-09-01
Full Text Available Ro-pax vessels should fulfil the requirements of the current harmonised SOLAS Convention. The study analyses the effect of various ro-pax vessel subdivision arrangements on the subdivision index. A Polish ferry was chosen as a generic ship to perform the study. For illustration of damage survivability, the attained subdivision index A was calculated for a number of modified configurations. The arrangements included single and double sides above and below the car deck, with and without a double buoyant car deck. The conclusions of the study can be used in the design of new ro-pax vessels.
Planet map generation by tetrahedral subdivision
DEFF Research Database (Denmark)
Mogensen, Torben Ægidius
2010-01-01
We present a method for generating pseudo-random, zoomable planet maps for games and art. The method is based on spatial subdivision using tetrahedrons. This ensures planet maps without discontinuities caused by mapping a flat map onto a sphere. We compare the method to other map...
46 CFR 179.212 - Watertight bulkheads for subdivision.
2010-10-01
... (UNDER 100 GROSS TONS) SUBDIVISION, DAMAGE STABILITY, AND WATERTIGHT INTEGRITY Subdivision and Damage... passengers; or (2) Is constructed of wood on or after March 11, 2001, and operates in cold water. As an...
38 CFR 3.1002 - Political subdivisions of United States.
2010-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Political subdivisions of... Political subdivisions of United States. No part of any accrued benefits will be used to reimburse any political subdivision of the United States for expenses incurred in the last sickness or burial of any...
Fabrication of dielectric elastomer stack transducers (DEST) by liquid deposition modeling
Klug, Florian; Solano-Arana, Susana; Mößinger, Holger; Förster-Zügel, Florentine; Schlaak, Helmut F.
2017-04-01
Established fabrication methods for dielectric elastomer stack transducers (DEST) are mostly based on twodimensional thin-film technology. Because of this, DEST are based on simple two-dimensionally structured shapes. For certain applications, like valves or Braille displays, these structures are suited well enough. However, a more flexible fabrication method allows for more complex actuator designs, which would otherwise require extra processing steps. Fabrication methods with the possibility of three-dimensional structuring allow e.g. the integration of electrical connections, cavities, channels, sensor and other structural elements during the fabrication. This opens up new applications, as well as the opportunity for faster prototype production of individually designed DEST for a given application. In this work, a manufacturing system allowing three dimensional structuring is described. It enables the production of multilayer and three-dimensional structured DEST by liquid deposition modelling. The system is based on a custom made dual extruder, connected to a commercial threeaxis positioning system. It allows a computer controlled liquid deposition of two materials. After tuning the manufacturing parameters the production of thin layers with at thickness of less than 50 μm, as well as stacking electrode and dielectric materials is feasible. With this setup a first DEST with dielectric layer thickness less than 50 μm is build successfully and its performance is evaluated.
Rahvusooperi Estonia teatrihoone publikuruumide restaureerimistöödest / Liivi Künnapu
Künnapu, Liivi, 1953-
2006-01-01
Arhitektuuriajalooline ülevaade. 2005. a. restaureerimistöödest: garderoob-vestibüülist, peatrepist, ringfuajeedest, teatri- ja Valgest saalist, keldrikorruse ruumidest. Muinsuskaitse eritingimused, järelevalve: Liivi Künnapu. Projekteerijad: Peep Jänes, Indrek Suigussaar, AB Kolde Grupp. Sisekujundus: Juta Lember, Aulo Padar. Teostus: Koger ja Partnerid, projektijuht Indrek Võeras. Laemaali (E. Okas, E. Kits, R. Sagrits) restaureerimine, uuringud: KAR-Grupp. Akustik: Linda Madalik. Bibliogr. lk. 25. 8 vaadet
29 CFR 541.103 - Department or subdivision.
2010-07-01
... example, a large employer's human resources department might have subdivisions for labor relations, pensions and other benefits, equal employment opportunity, and personnel management, each of which has a...
Deep structure beneath Lake Ontario: Crustal-scale Grenville subdivisions
Forsyth, D. A.; Milkereit, B.; Zelt, Colin A.; White, D. J.; Easton, R. M.; Hutchinson, Deborah R.
1994-01-01
Lake Ontario marine seismic data reveal major Grenville crustal subdivisions beneath central and southern Lake Ontario separated by interpreted shear zones that extend to the lower crust. A shear zone bounded transition between the Elzevir and Frontenac terranes exposed north of Lake Ontario is linked to a seismically defined shear zone beneath central Lake Ontario by prominent aeromagnetic and gravity anomalies, easterly dipping wide-angle reflections, and fractures in Paleozoic strata. We suggest the central Lake Ontario zone represents crustal-scale deformation along an Elzevir–Frontenac boundary zone that extends from outcrop to the south shore of Lake Ontario.Seismic images from Lake Ontario and the exposed western Central Metasedimentary Belt are dominated by crustal-scale shear zones and reflection geometries featuring arcuate reflections truncated at their bases by apparent east-dipping linear reflections. The images show that zones analogous to the interpreted Grenville Front Tectonic Zone are also present within the Central Metasedimentary Belt and support models of northwest-directed crustal shortening for Grenvillian deep crustal deformation beneath most of southeastern Ontario.A Precambrian basement high, the Iroquoian high, is defined by a thinning of generally horizontal Paleozoic strata over a crestal area above the basement shear zone beneath central Lake Ontario. The Iroquoian high helps explain the peninsular extension into Lake Ontario forming Prince Edward County, the occurrence of Precambrian inlier outcrops in Prince Edward County, and Paleozoic fractures forming the Clarendon–Linden structure in New York.
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
20 CFR 404.1219 - Dissolution of political subdivision.
2010-04-01
... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Dissolution of political subdivision. 404... Agreements Is Obtained and Continues § 404.1219 Dissolution of political subdivision. If a political... satisfactory evidence of its dissolution or nonexistence. The evidence must establish that the entity is not...
Orienting the Neighborhood: A Subdivision Energy Analysis Tool; Preprint
Energy Technology Data Exchange (ETDEWEB)
Christensen, C.; Horowitz, S.
2008-07-01
This paper describes a new computerized Subdivision Energy Analysis Tool being developed to allow users to interactively design subdivision street layouts while receiving feedback about energy impacts based on user-specified building design variants and availability of roof surfaces for photovoltaic and solar water heating systems.
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
Key Technical Aspects Influencing the Accuracy of Tablet Subdivision.
Teixeira, Maíra T; Sá-Barreto, Lívia C L; Gratieri, Taís; Gelfuso, Guilherme M; Silva, Izabel C R; Cunha-Filho, Marcílio S S
2017-05-01
Tablet subdivision is a common practice used mainly for dose adjustment. The aim of this study was to investigate how the technical aspects of production as well as the method of tablets subdivision (employing a tablet splitter or a kitchen knife) influence the accuracy of this practice. Five drugs commonly used as subdivided tablets were selected. For each drug, the innovator drug product, a scored-generic and a non-scored generic were investigated totalizing fifteen drug products. Mechanical and physical tests, including image analysis, were performed. Additionally, comparisons were made between tablet subdivision method, score, shape, diluent composition and coating. Image analysis based on surface area was a useful tool as an alternative assay to evaluate the accuracy of tablet subdivision. The tablet splitter demonstrates an advantage relative to a knife as it showed better results in weight loss and friability tests. Oblong, coated and scored tablets had better results after subdivision than round, uncoated and non-scored tablets. The presence of elastic diluents such as starch and dibasic phosphate dehydrate conferred a more appropriate behaviour for the subdivision process than plastic materials such as microcrystalline cellulose and lactose. Finally, differences were observed between generics and their innovator products in all selected drugs with regard the quality control assays in divided tablet, which highlights the necessity of health regulations to consider subdivision performance at least in marketing authorization of generic products.
SIA matrices and non-negative stationary subdivision
Li, Xianjun
2012-01-01
This dissertation is concerned with SIA matrices and non-negative stationary subdivision, and is organized as follows: After an introducing chapter where some basic notation is given we describe, in Chapter 3, how non-negative subdivision is connected to a corresponding non-homogenous Markov process. The family of matrices A, built from the mask of the subdivision scheme, is introduced. Among other results, Lemma 3.1 and Lemma 3.2 relate the coefficients of the iterated masks to matrix produc...
Seis propostas deste milênio: as ideias de Calvino aplicadas na obra de Adriana Lisboa
Directory of Open Access Journals (Sweden)
João Paulo Lopes de Meira HERGESEL
2012-07-01
Full Text Available Segundo o escritor Italo Calvino, a leveza, a rapidez, a exatidão, a visibilidade, a multiplicidade e a consistência são seis virtudes que apenas a literatura pode salvar — essa teoria é abordada no livro Seis propostas para o próximo milênio. Este trabalho, que promove uma reunião da estilística com a linguística textual e com a linguística cognitiva, busca justificar a significância da utilização das propostas linguístico-estilísticas apresentadas por Calvino na produção de uma obra de cunho literário, tomando como objeto de estudo e exemplificação o conto Lady Anne, de Adriana Lisboa. Para além deste objetivo central, o artigo apresenta uma análise estilística detalhada da referida obra, que dá a conhecer o estilo literário dessa escritora da literatura contemporânea brasileira.
Rainbow game domination subdivision number of a graph
Directory of Open Access Journals (Sweden)
J. Amjadi
2014-09-01
Full Text Available The rainbow game domination subdivision number of a graph G is defined by the following game. Two players D and A, D playing first, alternately mark or subdivide an edge of G which is not yet marked nor subdivided. The game ends when all the edges of G are marked or subdivided and results in a new graph G'. . The purpose of D is to minimize the 2-rainbow dominating number \\gamma_{r2}(G' of G' while A tries to maximize it. If both A and D play according to their optimal strategies,\\gamma_{r2}(G' is well defined. We call this number the rainbow game domination subdivision number of G and denote it by \\gamma_{r2}(G' . In this paper we initiate the study of the rainbow game domination subdivision number of a graph and present sharp bounds on the rainbow game domination subdivision number of a tree.
Celestial Walk: A Terminating Oblivious Walk for Convex Subdivisions
Kuijper, Wouter; Ermolaev, Victor; Devillers, Olivier
2017-01-01
We present a new oblivious walking strategy for convex subdivisions. Our walk is faster than the straight walk and more generally applicable than the visibility walk. To prove termination of our walk we use a novel monotonically decreasing distance measure.
ORTHODONTIC TREATMENT ALTERNATIVE TO A CLASS III SUBDIVISION MALOCCLUSION
Janson, Guilherme; de Souza, José Eduardo Prado; Barros, Sérgio Estelita Cavalcante; Andrade, Pedro; Nakamura, Alexandre Yudi
2009-01-01
Class III malocclusions are considered one of the most complex and difficult orthodontic problems to diagnose and treat. Skeletal and/or dental asymmetries in patients presenting with Class III malocclusions can worsen the prognosis. Recognizing the dentoalveolar and skeletal characteristics of subdivision malocclusions and their treatment possibilities is essential for a favorable nonsurgical correction. Therefore, this article presents a nonsurgical asymmetric extraction approach to Class III subdivision malocclusion treatment which can significantly improve the occlusal and facial discrepancies. PMID:19668997
Guggenheimer, Heinrich W
1977-01-01
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
Rodger, Alison
1995-01-01
Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans
Roberts, Fred S.
The author cites work on visual perception which indicates that in order to study perception it is necessary to replace such classical geometrical notions as betweeness, straightness, perpendicularity, and parallelism with more general concepts. The term tolerance geometry is used for any geometry when primitive notions are obtained from the…
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Faulkner, T Ewan
2006-01-01
This text explores the methods of the projective geometry of the plane. Some knowledge of the elements of metrical and analytical geometry is assumed; a rigorous first chapter serves to prepare readers. Following an introduction to the methods of the symbolic notation, the text advances to a consideration of the theory of one-to-one correspondence. It derives the projective properties of the conic and discusses the representation of these properties by the general equation of the second degree. A study of the relationship between Euclidean and projective geometry concludes the presentation. Nu
Graustein, William C
2006-01-01
This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.Suitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz
2017-01-01
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
Divided Spheres Geodesics and the Orderly Subdivision of the Sphere
Popko, Edward S
2012-01-01
This well-illustrated book-in color throughout-presents a thorough introduction to the mathematics of Buckminster Fuller's invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.
An overview of an integrated building simulation tool : designer's simulation toolkit (DeST)
Energy Technology Data Exchange (ETDEWEB)
Yan, D.; Jiang, Y. [Tsinghua Univ., Beijing (China). Dept. of Building Science, School of Architecture
2005-07-01
DeST is a simulation engine for handling building thermal calculations. It is capable of simulating a building's energy performance by stages. Among its many features, DeST uses base temperatures to couple building and energy systems to determine the relationship between thermal behaviour of buildings and dynamic performances of heating, ventilation and air conditioning (HVAC) systems. It offers design and simulation by stages and emphasizes the prediction of optimized performance of a system. It also compares user selected design conditions of a space and provides parameters for optimized control. DeSP uses a graphical interface and is adaptable to a compatible platform adopted to TRNSYS. DeST comprises several different modules for handling different functions and areas. These include the meteorological data producer for HVAC analysis (Medpha); VentPlus; computer aided building description (CABD); Bshadow; lighting; and, building analysis and simulation (BAS). When using the platform, designers have to choose the appropriate air handling unit for combined plant simulation. The DeST has been used for China's State Grand Theatre, the State Swimming Centre and also for renovation projects involving HVAC systems. 20 refs., 5 figs.
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
Roman game domination subdivision number of a graph
Directory of Open Access Journals (Sweden)
Jafar Amjadi
2013-12-01
Full Text Available A {em Roman dominating function} on a graph $G = (V ,E$ is a function $f : Vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v = 0$ is adjacent to at least one vertex $u$ for which $f (u = 2$. The {em weight} of a Roman dominating function is the value $w(f=sum_{vin V}f(v$. The Roman domination number of a graph $G$, denoted by $gamma_R(G$, equals the minimum weight of a Roman dominating function on G. The Roman game domination subdivision number of a graph $G$ is defined by the following game. Two players $mathcal D$ and $mathcal A$, $mathcal D$ playing first, alternately mark or subdivide an edge of $G$ which is not yet marked nor subdivided. The game ends when all the edges of $G$ are marked or subdivided and results in a new graph $G'$. The purpose of $mathcal D$ is to minimize the Roman dominating number $gamma_R(G'$ of $G'$ while $mathcal A$ tries to maximize it. If both $mathcal A$ and $mathcal D$ play according to their optimal strategies, $gamma_R(G'$ is well defined. We call this number the {em Roman game domination subdivision number} of $G$ and denote it by $gamma_{Rgs}(G$. In this paper we initiate the study of the Roman game domination subdivision number of a graph and present sharp bounds on the Roman game domination subdivision number of a tree.
Convexity preservation of the four-point interpolatory subdivision scheme
Dyn, Nira; Kuijt, F.; Levin, David; van Damme, Rudolf M.J.
1998-01-01
In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly-convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These
24 CFR 1710.215 - Subdivision characteristics and climate.
2010-04-01
... HOUSING AND URBAN DEVELOPMENT (INTERSTATE LAND SALES REGISTRATION PROGRAM) LAND REGISTRATION Reporting... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Subdivision characteristics and climate. 1710.215 Section 1710.215 Housing and Urban Development Regulations Relating to Housing and Urban...
A Critical Analysis of Football Bowl Subdivision Coaching Contract Components
Nichols, Justin Keith
2012-01-01
This exploratory study is designed to inventory and analyze contract components used by Football Bowl Subdivision (FBS) institutions in the National Collegiate Athletic Association (NCAA) to further contribute to the body research. The FBS is comprised of 120 institutions and 94 of those institutions submitted contracts to "USA Today"…
29 CFR 1975.5 - States and political subdivisions thereof.
2010-07-01
... subdivisions of a State: (5) The term “employer” means a person engaged in a business affecting commerce who..., not subject to the Act as an employer. (c) Factors for meeting the tests. Various factors will be... of these factors are: Are the individuals who administer the entity appointed by a public official or...
24 CFR 1710.115 - Subdivision characteristics and climate.
2010-04-01
..., ditches, outlet channels, waterway stabilizers and sediment control basins.) (f) Nuisances. Are there any... purchaser is responsible, what are the estimated costs? (d) Flood plain. Is the subdivision located within a flood plain or an area designated by any Federal, State or local agency as being flood prone? What lots...
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 8. Geometry VI - Space-the Final Frontier. Kapil H Paranjape. Series Article Volume 1 Issue 8 August 1996 pp 28-33. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/08/0028-0033 ...
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
From a different perspective artists had all along pointed out that parallel lines do meet at the horizon (Figure 1). In fact all pairs of coplanar lines meet and parallel lines .... A more advanced treatment can be found in this book. D Hilbert and S Cohn-Vossen. Geometry and the Imagination. Chelsea, NY,. USA. 1952. A difficult ...
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
Directory of Open Access Journals (Sweden)
Leonardo Paris
2012-06-01
Full Text Available Lo studio degli ingranaggi si basa sulle geometrie coniugate in cui due curve o due superfici si mantengono costantemente in contatto pur se in movimento reciproco. La teoria geometrica degli ingranaggi fino alla fine del XIX secolo era uno dei molteplici rami nelle applicazioni della Geometria Descrittiva. Lo studio si basa sulla conoscenza delle principali proprietà delle curve piane e gobbe e delle loro derivate. La specificità del tema è che queste geometrie nel momento in cui si devono relazionare con le loro coniugate, devono rispettare dei vincoli che altrimenti non avrebbero. Si vuole evidenziare attraverso casi concreti il ruolo della geometria descrittiva nel passaggio dal teorico al pratico riproponendo in chiave informatica, temi e procedure di indagine spesso passati in secondo piano se non addirittura dimenticati.
Outline of The probabilistic Concept of Ship Subdivision
DEFF Research Database (Denmark)
Pawlowski, Maciej
1996-01-01
concept. This may facilitate our present efforts in developing a sound assessment, consistent with the results of damage stability model tests. A new method is provided regarding the capsizal probability, based on the theory underlying numerical simulations of damaged ship behaviour in natural sea......An outline of the whole probabilistic concept of ship subdivision is given, comprising the latest advances in determination of pi and s1 factors - the two probabilistic factors that form the basis of the new regulations.The method for calculating the pi factor for dry cargo ships is thoroughly...... presented and compared with the original method, developed by IMO inthe late 60's for passenger ships. After that, a review is presented of the past efforts to develop an estimate for the factor si - the most difficultand controversial part of the new subdivision regulations based on the probabilistic...
Optimized medium culture for Acidobacteia subdivision 1 strains
Campanharo, J.C.; Kielak, A.M.; Castellane, T.C.; Kuramae, E.E.; Lemos, E.G.
2016-01-01
The members of subdivision 1 Acidobacterium were grown at different pH values in a new medium formulation named PSYL 5 includes sucrose, as a carbon source and other compounds (such as KH2PO4 and MgSO4.7H2O). Growth rate was nearly constant at pH 5 and declined at pH 3–4 and 6–7. However, it was
Ciarlet, Philippe G
2007-01-01
This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and
A subdivision algorithm for phase equilibrium calculations at high pressures
Directory of Open Access Journals (Sweden)
M. L. Corazza
2007-12-01
Full Text Available Phase equilibrium calculations at high pressures have been a continuous challenge for scientists and engineers. Traditionally, this task has been performed by solving a system of nonlinear algebraic equations originating from isofugacity equations. The reliability and accuracy of the solutions are strongly dependent on the initial guess, especially due to the fact that the phase equilibrium problems frequently have multiple roots. This work is focused on the application of a subdivision algorithm for thermodynamic calculations at high pressures. The subdivision algorithm consists in the application of successive subdivisions at a given initial interval (rectangle of variables and a systematic test to verify the existence of roots in each subinterval. If the interval checked passes in the test, then it is retained; otherwise it is discharged. The algorithm was applied for vapor-liquid, solid-fluid and solid-vapor-liquid equilibrium as well as for phase stability calculations for binary and multicomponent systems. The results show that the proposed algorithm was capable of finding all roots of all high-pressure thermodynamic problems investigated, independent of the initial guess used.
Nicolaidis, A.; Kiosses, V.
2012-09-01
It has been proposed that quantum mechanics and string theory share a common inner syntax, the relational logic of C. S. Peirce. Along this line of thought we consider the relations represented by spinors. Spinor composition leads to the emergence of Minkowski space-time. Inversely, the Minkowski space-time is istantiated by the Weyl spinors, while the merger of two Weyl spinors gives rise to a Dirac spinor. Our analysis is applied also to the string geometry. The string constraints are represented by real spinors, which create a parametrization of the string worldsheet identical to the Enneper-Weierstass representation of minimal surfaces. Further, a spinorial study of the AdS3 space-time reveals a Hopf fibration AdS3 → AdS2. The conformal symmetry inherent in AdS3 is pointed out. Our work indicates the hidden ties between logic-quantum mechanics-string theory-geometry and vindicates the Wheeler's proposal of pregeometry as a large network of logical propositions.
Classification and treatment of Class II subdivision malocclusions.
Cassidy, Sara E; Jackson, Stona R; Turpin, David L; Ramsay, Douglas S; Spiekerman, Charles; Huang, Greg J
2014-04-01
Patients with Class II subdivision malocclusions are a challenge for clinicians because reestablishing symmetry in 1 arch or both arches is often a treatment goal. In patients with mandibular skeletal asymmetry, surgery is often a treatment option. However, patients may be unwilling to undergo surgery, and other options might have to be considered. The aim of this study was to evaluate the etiologies and outcomes of Class II subdivision patients treated at the University of Washington graduate orthodontic clinic in Seattle from 1995 through 2011. A search of patients treated between 1995 and 2011 resulted in the identification of 110 consecutively treated Class II subdivision subjects with complete records. Ninety-eight subjects could be classified into 1 of 3 groups, based on midline position and dental or skeletal etiology. Initial and final models were used to measure the peer assessment rating scores, midlines, overjet, overbite, and molar positions. Initial and final cephalograms were traced and measured. Charts were reviewed for information regarding treatment. Twenty-five percent of the 98 subjects had their maxillary and mandibular midlines coincident with the facial midline; their asymmetries were due to a maxillary posterior dental asymmetry. Another 15% had maxillary midlines deviated from their facial midlines, caused by maxillary anterior and posterior dental asymmetry. About 50% of the subjects had mandibular midlines that were not coincident with their facial midlines, and most of them exhibited some degree of mandibular skeletal asymmetry. Over the past 15 years, treatment strategies used at the University of Washington indicated trends toward less surgery, fewer extractions, less use of headgear, and more reliance on fixed functional appliances. Ideal correction of midlines was not always achieved, especially in patients with mandibular skeletal asymmetry, with undercorrection occurring more commonly than overcorrection. Final peer assessment
Terrain Quantization Model Based on Global Subdivision Grid
Directory of Open Access Journals (Sweden)
MENG Li
2016-12-01
Full Text Available To solve the current problems in terrain quantization, such as the limitation of grid levels, the difficulties in data organization and management, and other issues, a quadrilateral terrain quantization model based on global subdivision grid is proposed. The model adopts GeoSOT as the spatial reference, and realize the correlation and retrieval of quantization data among different layers based on GeoSOT location identification code, which provides methods of the the quantization procession, the organization and storage, the data aggregation of the vector data and regular grid data.
National Research Council Canada - National Science Library
Meloti, Aparecida Fernanda; Gonçalves, Renata de Cássia; Silva, Ertty; Martins, Lídia Parsekian; dos Santos-Pinto, Ary
2014-01-01
.... The objective of the present study was to use lateral cephalometric radiographs to identify existing skeletal and dentoalveolar morphological alterations in Class II subdivision and to compare...
Upright, Paula A.
2009-01-01
The purpose of this study was to describe the reclassification process of Western Kentucky University's football program from the Football Championship Subdivision (FCS) to the Football Bowl Subdivision (FBS), the highest and most visible level of NCAA competition. Three research questions guided the study: (a) Why did Western Kentucky University…
Stability Verification for Energy-Aware Hydraulic Pressure Control via Simplicial Subdivision
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2015-01-01
This paper presents a linear programming-based method for finding Lyapunov functions of dynamical systems with polynomial vector fields. We propose to utilize a certificate of positivity in the Bernstein basis based on subdivisioning to find a Lyapunov function. The subdivision-based method is pr...
40 CFR 35.6060 - Political subdivision-lead pre-remedial Cooperative Agreements.
2010-07-01
... 40 Protection of Environment 1 2010-07-01 2010-07-01 false Political subdivision-lead pre-remedial... Contracts for Superfund Response Actions Pre-Remedial Response Cooperative Agreements § 35.6060 Political subdivision-lead pre-remedial Cooperative Agreements. (a) If the Award Official determines that a political...
40 CFR 35.6115 - Political subdivision-lead remedial Cooperative Agreements.
2010-07-01
... 40 Protection of Environment 1 2010-07-01 2010-07-01 false Political subdivision-lead remedial... Contracts for Superfund Response Actions Remedial Response Cooperative Agreements § 35.6115 Political subdivision-lead remedial Cooperative Agreements. (a) General. If the State concurs, EPA may allow a political...
14 CFR 1261.405 - Subdivision of claims not authorized; other administrative proceedings.
2010-01-01
... administrative proceedings. 1261.405 Section 1261.405 Aeronautics and Space NATIONAL AERONAUTICS AND SPACE... Subdivision of claims not authorized; other administrative proceedings. (a) Subdivision of claims. Claims may...). The debtor's liability arising from a particular transaction or contract shall be considered a single...
Interactive Display of Surfaces Using Subdivision Surfaces and Wavelets
Energy Technology Data Exchange (ETDEWEB)
Duchaineau, M A; Bertram, M; Porumbescu, S; Hamann, B; Joy, K I
2001-10-03
Complex surfaces and solids are produced by large-scale modeling and simulation activities in a variety of disciplines. Productive interaction with these simulations requires that these surfaces or solids be viewable at interactive rates--yet many of these surfaced solids can contain hundreds of millions of polygondpolyhedra. Interactive display of these objects requires compression techniques to minimize storage, and fast view-dependent triangulation techniques to drive the graphics hardware. In this paper, we review recent advances in subdivision-surface wavelet compression and optimization that can be used to provide a framework for both compression and triangulation. These techniques can be used to produce suitable approximations of complex surfaces of arbitrary topology, and can be used to determine suitable triangulations for display. The techniques can be used in a variety of applications in computer graphics, computer animation and visualization.
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
Directory of Open Access Journals (Sweden)
Magda Dettlaff
2016-01-01
Full Text Available Given a graph \\(G=(V,E\\, the subdivision of an edge \\(e=uv\\in E(G\\ means the substitution of the edge \\(e\\ by a vertex \\(x\\ and the new edges \\(ux\\ and \\(xv\\. The domination subdivision number of a graph \\(G\\ is the minimum number of edges of \\(G\\ which must be subdivided (where each edge can be subdivided at most once in order to increase the domination number. Also, the domination multisubdivision number of \\(G\\ is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision numbers are defined similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision numbers of the generalized corona graphs.
DEFF Research Database (Denmark)
Otten, Roald; Tol, Johannes L; Holmich, Per
2015-01-01
deficits and guide specific rehabilitation programs. However, the optimal positions for assessing the strength and activation of these subdivisions are unknown. OBJECTIVE: The first aim was to establish which strength-testing positions produce the highest surface electromyography (sEMG) activation levels...... of the individual GM subdivisions. The second aim was to evaluate differences in sEMG activation levels between the tested and contralateral (stabilizing) leg. METHOD: Twenty healthy physically active male subjects participated in this study. Muscle activity using sEMG was recorded for the GM subdivisions in 8...... different strength-testing positions and analyzed using repeated-measures analysis of variance. RESULTS: Significant differences between testing positions for all 3 GM subdivisions were found. There were significant differences between the tested and the contralateral anterior and middle GM subdivisions (P...
Directory of Open Access Journals (Sweden)
Adriano Yacubian-Fernandes
2005-12-01
desenvolvimento cognitivo destes pacientes.
2010-12-07
... Employment and Training Administration Zach System Corporation a Subdivision of Zambon Company, SPA Including... Corporation, a subdivision of Zach System SPA, La Porte, Texas, including on-site leased workers from Turner... subdivision of Zambon Company, SPA, not Zach System SPA. Based on these findings, the Department is amending...
Notes on noncommutative geometry
Nikolaev, Igor
2015-01-01
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises is attached. Our notes are intended for the graduate students and faculty with interests in noncommutative geometry; they can be read by non-experts in the field.
Simulating Sand Behavior through Terrain Subdivision and Particle Refinement
Clothier, M.
2013-12-01
Advances in computer graphics, GPUs, and parallel processing hardware have provided researchers with new methods to visualize scientific data. In fact, these advances have spurred new research opportunities between computer graphics and other disciplines, such as Earth sciences. Through collaboration, Earth and planetary scientists have benefited by using these advances in hardware technology to process large amounts of data for visualization and analysis. At Oregon State University, we are collaborating with the Oregon Space Grant and IGERT Ecosystem Informatics programs to investigate techniques for simulating the behavior of sand. In addition, we have also been collaborating with the Jet Propulsion Laboratory's DARTS Lab to exchange ideas on our research. The DARTS Lab specializes in the simulation of planetary vehicles, such as the Mars rovers. One aspect of their work is testing these vehicles in a virtual "sand box" to test their performance in different environments. Our research builds upon this idea to create a sand simulation framework to allow for more complex and diverse environments. As a basis for our framework, we have focused on planetary environments, such as the harsh, sandy regions on Mars. To evaluate our framework, we have used simulated planetary vehicles, such as a rover, to gain insight into the performance and interaction between the surface sand and the vehicle. Unfortunately, simulating the vast number of individual sand particles and their interaction with each other has been a computationally complex problem in the past. However, through the use of high-performance computing, we have developed a technique to subdivide physically active terrain regions across a large landscape. To achieve this, we only subdivide terrain regions where sand particles are actively participating with another object or force, such as a rover wheel. This is similar to a Level of Detail (LOD) technique, except that the density of subdivisions are determined by
Macroscopic Subdivision of Silica Aerogel Collectors for Sample Return Missions
Energy Technology Data Exchange (ETDEWEB)
Ishii, H A; Bradley, J P
2005-09-14
Silica aerogel collector tiles have been employed for the collection of particles in low Earth orbit and, more recently, for the capture of cometary particles by NASA's Stardust mission. Reliable, reproducible methods for cutting these and future collector tiles from sample return missions are necessary to maximize the science output from the extremely valuable embedded particles. We present a means of macroscopic subdivision of collector tiles by generating large-scale cuts over several centimeters in silica aerogel with almost no material loss. The cut surfaces are smooth and optically clear allowing visual location of particles for analysis and extraction. This capability is complementary to the smaller-scale cutting capabilities previously described [Westphal (2004), Ishii (2005a, 2005b)] for removing individual impacts and particulate debris in tiny aerogel extractions. Macroscopic cuts enable division and storage or distribution of portions of aerogel tiles for immediate analysis of samples by certain techniques in situ or further extraction of samples suited for other methods of analysis.
The angular gyrus: multiple functions and multiple subdivisions.
Seghier, Mohamed L
2013-02-01
There is considerable interest in the structural and functional properties of the angular gyrus (AG). Located in the posterior part of the inferior parietal lobule, the AG has been shown in numerous meta-analysis reviews to be consistently activated in a variety of tasks. This review discusses the involvement of the AG in semantic processing, word reading and comprehension, number processing, default mode network, memory retrieval, attention and spatial cognition, reasoning, and social cognition. This large functional neuroimaging literature depicts a major role for the AG in processing concepts rather than percepts when interfacing perception-to-recognition-to-action. More specifically, the AG emerges as a cross-modal hub where converging multisensory information is combined and integrated to comprehend and give sense to events, manipulate mental representations, solve familiar problems, and reorient attention to relevant information. In addition, this review discusses recent findings that point to the existence of multiple subdivisions in the AG. This spatial parcellation can serve as a framework for reporting AG activations with greater definition. This review also acknowledges that the role of the AG cannot comprehensibly be identified in isolation but needs to be understood in parallel with the influence from other regions. Several interesting questions that warrant further investigations are finally emphasized.
About the Subdivision of Indoor Spaces in Indoorgml
Diakité, A. A.; Zlatanova, S.; Li, K.-J.
2017-10-01
Boosted by the dynamic urbanization of cities, indoor environments are getting more and more complex in order to be able to host people properly. While most of our time is spent inside buildings, the need of GIS tools to assist our daily activities that can become tedious, such as indoor navigation or facility management, became more and more urgent. In that perspective, the IndoorGML standard is aiming to address the gaps left by other standards regarding the spatial modelling for indoor navigation. It includes several concepts such as the organization of the spaces into cells along with their network representation and the possibility to represent multiple connected layers. However, being at its first stage, several concepts of the standard could be improved. One of these is the cell subspacing that is not enough discussed in the current version of the standard. In this paper, we explore all the aspects involved in the subdivision process, from the identification of the navigable and non-navigable space cells to the generation of a navigation graph. We propose several criteria on which the indoor sub-spacing can rely to be automatically performed and and illustrate them on a 3D indoor model.
ABOUT THE SUBDIVISION OF INDOOR SPACES IN INDOORGML
Directory of Open Access Journals (Sweden)
A. A. Diakité
2017-10-01
Full Text Available Boosted by the dynamic urbanization of cities, indoor environments are getting more and more complex in order to be able to host people properly. While most of our time is spent inside buildings, the need of GIS tools to assist our daily activities that can become tedious, such as indoor navigation or facility management, became more and more urgent. In that perspective, the IndoorGML standard is aiming to address the gaps left by other standards regarding the spatial modelling for indoor navigation. It includes several concepts such as the organization of the spaces into cells along with their network representation and the possibility to represent multiple connected layers. However, being at its first stage, several concepts of the standard could be improved. One of these is the cell subspacing that is not enough discussed in the current version of the standard. In this paper, we explore all the aspects involved in the subdivision process, from the identification of the navigable and non-navigable space cells to the generation of a navigation graph. We propose several criteria on which the indoor sub-spacing can rely to be automatically performed and and illustrate them on a 3D indoor model.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Census County Subdivisions for the United States Virgin Islands (CENSUS.COUNTY_SUBDIV_USVI)
U.S. Environmental Protection Agency — County subdivisions are the primary divisions of counties and statistically equivalent entities for the reporting of decennial census data. They include census...
Research of subdivision driving technology for brushless DC motors in optical fiber positioning
Kan, Yi; Gu, Yonggang; Zhu, Ye; Zhai, Chao
2016-07-01
In fiber spectroscopic telescopes, optical fiber positioning units are used to position thousands of fibers on the focal plane quickly and precisely. Stepper motors are used in existing units, however, it has some inherent deficiencies, such as serious heating and low efficiency. In this work, the universally adopted subdivision driving technology for stepper motors is transplanted to brushless DC motors. It keeps the advantages of stepper motors such as high positioning accuracy and resolution, while overcomes the disadvantages mentioned above. Thus, this research mainly focuses on develop a novel subdivision driving technology for brushless DC motor. By the proving of experiments of online debug and subdivision speed and position, the proposed brushless DC motor subdivision technology can achieve the expected functions.
Meyer, Walter J
2006-01-01
Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Nomi, Jason S.; Farrant, Kristafor; Damaraju, Eswar; Rachakonda, Srinivas; Calhoun, Vince D.; Uddin, Lucina Q.
2016-01-01
The human insular cortex consists of functionally diverse subdivisions that engage during tasks ranging from interoception to cognitive control. The multiplicity of functions subserved by insular subdivisions calls for a nuanced investigation of their functional connectivity profiles. Four insula subdivisions (dorsal anterior, dAI; ventral, VI; posterior, PI; middle, MI) derived using a data-driven approach were subjected to static- and dynamic-functional network connectivity (s-FNC and d-FNC) analyses. Static-FNC analyses replicated previous work demonstrating a cognition-emotion-interoception division of the insula, where the dAI is functionally connected to frontal areas, the VI to limbic areas, and the PI and MI to sensorimotor areas. Dynamic-FNC analyses consisted of k-means clustering of sliding windows to identify variable insula connectivity states. The d-FNC analysis revealed that the most frequently occurring dynamic state mirrored the cognition-emotion-interoception division observed from the s-FNC analysis, with less frequently occurring states showing overlapping and unique subdivision connectivity profiles. In two of the states, all subdivisions exhibited largely overlapping profiles, consisting of subcortical, sensory, motor, and frontal connections. Two other states showed the dAI exhibited a unique connectivity profile compared with other insula subdivisions. Additionally, the dAI exhibited the most variable functional connections across the s-FNC and d-FNC analyses, and was the only subdivision to exhibit dynamic functional connections with regions of the default mode network. These results highlight how a d-FNC approach can capture functional dynamics masked by s-FNC approaches, and reveal dynamic functional connections enabling the functional flexibility of the insula across time. PMID:26880689
Lin, Chao-Yuan; Fu, Kuei-Lin; Lin, Cheng-Yu
2016-11-01
Recent extreme rainfall events led to many landslides due to climate changes in Taiwan. How to effectively promote post-disaster treatment and/or management works in a watershed/drainage basin is a crucial issue. Regarding the processes of watershed treatment and/or management works, disaster hotspot scanning and treatment priority setup should be carried out in advance. A scanning method using landslide ratio to determine the appropriate outlet of an interested watershed, and an optimal subdivision system with better homogeneity and accuracy in landslide ratio estimation were developed to help efficient executions of treatment and/or management works. Topography is a key factor affecting watershed landslide ratio. Considering the complexity and uncertainty of the natural phenomenon, multivariate analysis was applied to understand the relationship between topographic factors and landslide ratio in the interested watershed. The concept of species-area curve, which is usually adopted at on-site vegetation investigation to determinate the suitable quadrate size, was used to derive the optimal threshold in subdivisions. Results show that three main component axes including factors of scale, network and shape extracted from Digital Terrain Model coupled with areas of landslide can effectively explain the characteristics of landslide ratio in the interested watershed, and a relation curve obtained from the accuracy of landslide ratio classification and number of subdivisions could be established to derive optimal subdivision of the watershed. The subdivision method promoted in this study could be further used for priority rank and benefit assessment of landslide treatment in a watershed.
Bárány, Imre; Vilcu, Costin
2016-01-01
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Smith, James T
2000-01-01
A practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An
O'Leary, Michael
2010-01-01
Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Fundamental concepts of geometry
Meserve, Bruce E
1983-01-01
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
Geometry Professionalized for Teachers.
Christofferson, Halbert Carl
Written in 1933, this book grew out of the author's concern that college matehmatics sequences of the day, although appropriate in algebra preparation, did not adequately prepare teachers of geometry. This book describes a course intended to remedy this by providing for both a comprehensive study of geometry as an axiomatically defined structure…
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Supersymmetric Sigma Model Geometry
Directory of Open Access Journals (Sweden)
Ulf Lindström
2012-08-01
Full Text Available This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyperkähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.
Energy Technology Data Exchange (ETDEWEB)
Grotz, Andreas
2011-10-07
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Nina, Nailson Celson da Silva
2011-01-01
Foram instalados tr?s experimentos com o objetivo avaliar o controle de plantas daninhas com herbicidas e a seletividade destes sobre o crescimento e a produtividade de feij?o-caupi (Vigna unguiculata (L.) Walp.). O primeiro experimento foi instalado em uma ?rea de v?rzea onde foi avaliado o controle de plantas daninhas com oitos herbicidas: bentazon (720 g ha-1), clethodim (108 g ha-1), fluazifop-p-butyl (250 g ha-1), fomesafen (250 g ha-1), linuron (1490 g ha-1), oxyfluorf...
2010-07-01
... population bears to the population of all coastal political subdivisions in the producing State; (b) Twenty... allocated to coastal political subdivisions within the Gulf producing States? 219.416 Section 219.416... DISTRIBUTION AND DISBURSEMENT OF ROYALTIES, RENTALS, AND BONUSES Oil and Gas, Offshore § 219.416 How will the...
2012-02-14
... Employment and Training Administration Quad/Graphics, a Subdivision of Quad Graphics, Inc., Including On-Site... filed on March 15, 2011, on behalf of workers of Quad/Graphics, a Subdivision of Quad Graphics, Inc... (TA-W-73,441G) applicable to workers and former workers of Quad Graphics, Inc., a wholly-owned...
Livas, Christos; Pandis, Nikolaos; Booij, Johan Willem; Halazonetis, Demetrios J.; Katsaros, Christos; Ren, Yijin
Objective: To assess the maxillary second molar (M2) and third molar (M3) inclination following orthodontic treatment of Class II subdivision malocclusion with unilateral maxillary first molar (M1) extraction. Materials and Methods: Panoramic radiographs of 21 Class II subdivision adolescents (eight
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
Fawzi, Nicolas L; Libich, David S; Ying, Jinfa; Tugarinov, Vitali; Clore, G Marius
2014-09-22
Many details pertaining to the formation and interactions of protein aggregates associated with neurodegenerative diseases are invisible to conventional biophysical techniques. We recently introduced (15)N dark-state exchange saturation transfer (DEST) and (15)N lifetime line-broadening to study solution backbone dynamics and position-specific binding probabilities for amyloid β (Aβ) monomers in exchange with large (2-80 MDa) protofibrillar Aβ aggregates. Here we use (13)C(methyl)DEST and lifetime line-broadening to probe the interactions and dynamics of methyl-bearing side chains in the Aβ-protofibril-bound state. We show that all methyl groups of Aβ40 populate direct-contact bound states with a very fast effective transverse relaxation rate, indicative of side-chain-mediated direct binding to the protofibril surface. The data are consistent with position-specific enhancements of (13)C(methyl)-R₂(tethered) values in tethered states, providing further insights into the structural ensemble of the protofibril-bound state. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Jones, Willis A.
2014-01-01
In recent years, a number of colleges and universities have made the decision to pursue membership in the NCAA's Football Bowl Subdivision (FBS) with the idea that participating in higher profile intercollegiate football can help attract students to their institution. This belief, however, has not been empirically examined. Using…
Effects of subdivision and access restrictions on private land recreation opportunities
H. Ken Cordell; Donald B.K. English; Sharon A. Randall
1993-01-01
Continuing conversion of woodlands, greater restrictions on recreational access, and subdivision are trends seeming to have important implicaitons for future public recreation supply. The nature of these implicaitons has not been adequately explored in previous research, a void that has led to questions about the actual effects these factors have on future recreational...
46 CFR 46.10-40 - Nonsubmergence subdivision load line (Great Lakes).
2010-10-01
... 46 Shipping 2 2010-10-01 2010-10-01 false Nonsubmergence subdivision load line (Great Lakes). 46.10-40 Section 46.10-40 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) LOAD LINES... (Great Lakes). (a) Passenger vessels on the Great Lakes of 150 gross tons or over shall not submerge the...
24 CFR 1715.50 - Advertising disclaimers; subdivisions registered and effective with HUD.
2010-04-01
...-FEDERAL HOUSING COMMISSIONER, DEPARTMENT OF HOUSING AND URBAN DEVELOPMENT (INTERSTATE LAND SALES... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Advertising disclaimers; subdivisions registered and effective with HUD. 1715.50 Section 1715.50 Housing and Urban Development...
24 CFR 1710.15 - Regulatory exemption-multiple site subdivision-determination required.
2010-04-01
... HOUSING COMMISSIONER, DEPARTMENT OF HOUSING AND URBAN DEVELOPMENT (INTERSTATE LAND SALES REGISTRATION... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Regulatory exemption-multiple site subdivision-determination required. 1710.15 Section 1710.15 Housing and Urban Development Regulations Relating...
da Rocha, Ulisses Nunes; van Elsas, Jan Dirk; van Overbeek, Leonard Simon
2011-01-01
Strains CHC12 and CHC8, belonging to, respectively, Luteolibacter and Candidatus genus Rhizospheria (Verrucomicrobia subdivision 1), were recently isolated from the leek rhizosphere. The key question addressed in this study was: does attraction to and colonization of the rhizosphere occur in the
Energy Technology Data Exchange (ETDEWEB)
Gubenko, I.V.
1982-01-01
Experimental development of plans with participation of enterprises and their subdivisions is presented. The method of determining the intensity of the plans of the drilling enterprises is revealed. Data are presented on the use of a computer to develop a technical-industrial financial plan of the enterprise and association.
Manûtu ša Bābili = the Babylonian subdivision of the mina
van der Spek, R.J.
A new interpretation of the term Manûtu ša Bābili is presented here. It is not the exchange rate between shekels and drachmas, as was generally assumed, but it is the Babylonian subdivision ("counting") of the mina as opposed to the Greek mina. A Babylonian mina counts 30 staters, a Greek mina 25
Simple Derivation of the Lifetime and the Distribution of Faces for a Binary Subdivision Model
Hayashi, Yukio
2015-01-01
The iterative random subdivision of rectangles is used as a generation model of networks in physics, computer science, and urban planning. However, these researches were independent. We consider some relations in them, and derive fundamental properties for the average lifetime depending on birth-time and the balanced distribution of rectangle faces.
Geometry without topology as a new conception of geometry
Directory of Open Access Journals (Sweden)
Yuri A. Rylov
2002-01-01
geometry. In T-geometry, any space region is isometrically embeddable in the space, whereas in Riemannian geometry only convex region is isometrically embeddable. T-geometric conception appears to be more consistent logically, than the Riemannian one.
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Bénichou, O; Chevalier, C; Klafter, J; Meyer, B; Voituriez, R
2010-06-01
It has long been appreciated that the transport properties of molecules can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target-the first-passage time (FPT). Determining the FPT distribution in realistic confined geometries has until now, however, seemed intractable. Here, we calculate this FPT distribution analytically and show that transport processes as varied as regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, fall into the same universality classes. Beyond the theoretical aspect, this result changes our views on standard reaction kinetics and we introduce the concept of 'geometry-controlled kinetics'. More precisely, we argue that geometry-and in particular the initial distance between reactants in 'compact' systems-can become a key parameter. These findings could help explain the crucial role that the spatial organization of genes has in transcription kinetics, and more generally the impact of geometry on diffusion-limited reactions.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Elementary differential geometry
Pressley, Andrew
2001-01-01
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Energy Technology Data Exchange (ETDEWEB)
Martinez Barrios, M.; Garcia Gonzalez, M.; Perez Martin, F. J.
2013-07-01
The main goal of the UNESA MAAP5-SFP project is to analyze the capabilities of MAAP5 code and, particularly, the Spent Fuel Pool (SFP) module in order to tackle its modeling and facilitate the development of specific SFP models of Spanish NPPs. Within the project, Empresarios Agrupados (EEAA) is the responsible for the development of the Guide for the subdivision of the Spent Fuel Pool (SFP). This Guide includes a theoretical description of the model that is used by the code and a sequence of practical cases with the aim to evaluate the influence of specific parameters.
Sources of hyperbolic geometry
Stillwell, John
1996-01-01
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...
Energy Technology Data Exchange (ETDEWEB)
Duchaineau, M. [Los Alamos National Lab., NM (United States)]|[Lawrence Livermore National Lab., CA (United States); Wolinsky, M.; Sigeti, D.E. [Los Alamos National Lab., NM (United States)] [and others
1997-04-01
Real-time terrain rendering for interactive visualization remains a demanding task. We present a novel algorithm with several advantages over previous methods: our method is unusually stingy with polygons yet achieves real-time performance and is scalable to arbitrary regions and resolutions. The method provides a continuous terrain mesh of specified triangle count having provably minimum error in restricted but reasonably general classes of permissible meshes and error metrics. Our method provides an elegant solution to guaranteeing certain elusive types of consistency in scenes produced by multiple scene generators which share a common finest-resolution database but which otherwise operate entirely independently. This consistency is achieved by exploiting the freedom of choice of error metric allowed by the algorithm to provide, for example, multiple exact lines-of-sight in real-time. Our methods rely on an off-line pre-processing phase to construct a multi-scale data structure consisting of triangular terrain approximations enhanced ({open_quotes}thickened{close_quotes}) with world-space error information. In real time, this error data is efficiently transformed into screen-space where it is used to guide a greedy top-down triangle subdivision algorithm which produces the desired minimal error continuous terrain mesh. Our algorithm has been implemented and it operates at real-time rates.
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Eisenhart, L P
1927-01-01
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o
Graumann, Günter; Blum, Werner
1989-01-01
My conception of "practice-oriented-mathematical-education", which must be seen as one point of view side-by-side with others, has the aim to qualify pupils to master life and is based on a method of working on problems which are true to life. Therefore I plead for geometry teaching, where the formation of sound geometric concepts and the relevance of applications of geometry in everyday life is important. After discussing this conception a schedule of activities of everyday life where geomet...
Bishop, Richard L
2001-01-01
First published in 1964, this book served as a text on differential geometry to several generations of graduate students all over the world. The first half of the book (Chapters 1-6) presents basics of the theory of manifolds, vector bundles, differential forms, and Lie groups, with a special emphasis on the theory of linear and affine connections. The second half of the book (Chapters 7-11) is devoted to Riemannian geometry. Following the definition and main properties of Riemannian manifolds, the authors discuss the theory of geodesics, complete Riemannian manifolds, and curvature. Next, the
Harff, Jan; Bohling, G.C.; Endler, R.; Davis, J.C.; Olea, R.A.
1999-01-01
The Holocene sediment sequence of a core taken within the centre of the Eastern Gotland Basin was subdivided into 12 lithostratigraphic units based on MSCL-data (sound velocity, wet bulk density, magnetic susceptibility) using a multivariate classification method. The lower 6 units embrace the sediments until the Litorina transgression, and the upper 6 units subdivide the brackish-marine Litorina- and post-Litorina sediments. The upper lithostratigraphic units reflect a change of anoxic (laminated) and oxic (non-laminated) sediments. By application of a numerical stratigraphic correlation method the zonation was extended laterally onto contiguous sediment cores within the central basin. Consequently the change of anoxic and oxic sediments can be used for a general lithostratigraphic subdivision of sediments of the Gotland Basin. A quantitative criterion based on the sediment-physical lithofacies is added to existing subdivisions of the Holocene in the Baltic Sea.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 7. Foundations of Basic Geometry. Jasbir S Chahal. General Article Volume 11 Issue 7 July 2006 pp 30-41. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/011/07/0030-0041. Keywords. Area ...
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Towards relativistic quantum geometry
Directory of Open Access Journals (Sweden)
Luis Santiago Ridao
2015-12-01
Full Text Available We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Indian Academy of Sciences (India)
IAS Admin
face area and perimeter of various shapes like sphere, cone, cylinder and circle. But an equally important geo- metric object `torus' { a shape like a scooter tube or a doughnut { is not discussed in school geometry. This is perhaps due to the non availability of this shape at the time when Archimedes (287 BC{212 BC) was ...
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
Atiyah, M.; Dijkgraaf, R.; Hitchin, N.
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology.
Indian Academy of Sciences (India)
revolutionised by the introduction of new con- cepts and techniques by Grothendieck and others; this progress has been instrumental in solving outstanding and famous problems not only in algebraic geometry but also in related fields like number theory. Mathematicians from India have made influ- ential and extensive ...
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Proyeksi Geometri Fuzzy pada Ruang
Directory of Open Access Journals (Sweden)
Muhammad Izzat Ubaidillah
2012-11-01
Full Text Available Fuzzy geometry is an outgrowth of crisp geometry, which in crisp geometry elements are exist and not exist, but also while on fuzzy geometry elements are developed by thickness which is owned by each of these elements. Crisp projective geometries is the formation of a shadow of geometries element projected on the projectors element, with perpendicular properties which are represented by their respective elemental, the discussion focused on the results of the projection coordinates. While the fuzzy projective geometries have richer discussion, which includes about coordinates of projection results, the mutual relation of each element and the thickness of each element. This research was conducted to describe and analyzing procedure fuzzy projective geometries on the plane and explain the differences between crisp projective geometries and fuzzy projective geometries on plane.
Bell, Peter T; Gilat, Moran; O'Callaghan, Claire; Copland, David A; Frank, Michael J; Lewis, Simon J G; Shine, James M
2015-04-01
The pathological hallmark of Parkinson's disease is the degeneration of dopaminergic nigrostriatal neurons, leading to depletion of striatal dopamine. Recent neuroanatomical work has identified pathways for communication across striatal subdivisions, suggesting that the striatum provides a platform for integration of information across parallel corticostriatal circuits. The aim of this study was to investigate whether dopaminergic dysfunction in Parkinson's disease was associated with impairments in functional connectivity across striatal subdivisions, which could potentially reflect reduced integration across corticostriatal circuits. Utilizing resting-state functional magnetic resonance imaging (fMRI), we analyzed functional connectivity in 39 patients with Parkinson's disease, both "on" and "off" their regular dopaminergic medications, along with 40 age-matched healthy controls. Our results demonstrate widespread impairments in connectivity across subdivisions of the striatum in patients with Parkinson's disease in the "off" state. The administration of dopaminergic medication significantly improved connectivity across striatal subdivisions in Parkinson's disease, implicating dopaminergic deficits in the pathogenesis of impaired striatal interconnectivity. In addition, impaired striatal interconnectivity in the Parkinson's disease "off" state was associated with pathological decoupling of the striatum from the thalamic and sensorimotor (SM) networks. Specifically, we found that although the strength of striatal interconnectivity was positively correlated with both (i) the strength of internal thalamic connectivity, and (ii) the strength of internal SM connectivity, in both healthy controls and the Parkinson's disease "on" state, these relationships were absent in Parkinson's disease when in the "off" state. Taken together our findings emphasize the central role of dopamine in integrated striatal function and the pathological consequences of striatal dopamine
Zinc-finger genes Fez and Fez-like function in the establishment of diencephalon subdivisions.
Hirata, Tsutomu; Nakazawa, Masato; Muraoka, Osamu; Nakayama, Rika; Suda, Yoko; Hibi, Masahiko
2006-10-01
Fez and Fez-like (Fezl) are zinc-finger genes that encode transcriptional repressors expressed in overlapping domains of the forebrain. By generating Fez;Fezl-deficient mice we found that a redundant function of Fez and Fezl is required for the formation of diencephalon subdivisions. The caudal forebrain can be divided into three transverse subdivisions: prethalamus (also called ventral thalamus), thalamus (dorsal thalamus) and pretectum. Fez;Fezl-deficient mice showed a complete loss of prethalamus and a strong reduction of the thalamus at late gestation periods. Genetic marker analyses revealed that during early diencephalon patterning in Fez;Fezl-deficient mice, the rostral diencephalon (prospective prethalamus) did not form and the caudal diencephalon (prospective thalamus and pretectum) expanded rostrally. Fez;Fezl-deficient mice also displayed defects in the formation of the zona limitans intrathalamica (ZLI), which is located on the boundary between the prethalamus and thalamus. Fez and Fezl are expressed in the region rostral to the rostral limit of Irx1 expression, which marks the prospective position of the ZLI. Transgene-mediated misexpression of Fezl or Fez caudal to the ZLI repressed the caudal diencephalon fate and affected the formation of the Shh-expressing ZLI. These data indicate that Fez and Fezl repress the caudal diencephalon fate in the rostral diencephalon, and ZLI formation probably depends on Fez/Fezl-mediated formation of diencephalon subdivisions.
Integration and management of massive remote-sensing data based on GeoSOT subdivision model
Li, Shuang; Cheng, Chengqi; Chen, Bo; Meng, Li
2016-07-01
Owing to the rapid development of earth observation technology, the volume of spatial information is growing rapidly; therefore, improving query retrieval speed from large, rich data sources for remote-sensing data management systems is quite urgent. A global subdivision model, geographic coordinate subdivision grid with one-dimension integer coding on 2n-tree, which we propose as a solution, has been used in data management organizations. However, because a spatial object may cover several grids, ample data redundancy will occur when data are stored in relational databases. To solve this redundancy problem, we first combined the subdivision model with the spatial array database containing the inverted index. We proposed an improved approach for integrating and managing massive remote-sensing data. By adding a spatial code column in an array format in a database, spatial information in remote-sensing metadata can be stored and logically subdivided. We implemented our method in a Kingbase Enterprise Server database system and compared the results with the Oracle platform by simulating worldwide image data. Experimental results showed that our approach performed better than Oracle in terms of data integration and time and space efficiency. Our approach also offers an efficient storage management system for existing storage centers and management systems.
A Subdivision Method to Unify the Existing Latitude and Longitude Grids
Directory of Open Access Journals (Sweden)
Chengqi Cheng
2016-09-01
Full Text Available As research on large regions of earth progresses, many geographical subdivision grids have been established for various spatial applications by different industries and disciplines. However, there is no clear relationship between the different grids and no consistent spatial reference grid that allows for information exchange and comprehensive application. Sharing and exchange of data across departments and applications are still at a bottleneck. It would represent a significant step forward to build a new grid model that is inclusive of or compatible with most of the existing geodesic grids and that could support consolidation and exchange within existing data services. This study designs a new geographical coordinate global subdividing grid with one dimension integer coding on a 2n tree (GeoSOT that has 2n coordinate subdivision characteristics (global longitude and latitude subdivision and can form integer hierarchies at degree, minute, and second levels. This grid has the multi-dimensional quadtree hierarchical characteristics of a digital earth grid, but also provides good consistency with applied grids, such as those used in mapping, meteorology, oceanography and national geographical, and three-dimensional digital earth grids. No other existing grid codes possess these characteristics.
Large Scale Isosurface Bicubic Subdivision-Surface Wavelets for Representation and Visualization
Energy Technology Data Exchange (ETDEWEB)
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-01-05
We introduce a new subdivision-surface wavelet transform for arbitrary two-manifolds with boundary that is the first to use simple lifting-style filtering operations with bicubic precision. We also describe a conversion process for re-mapping large-scale isosurfaces to have subdivision connectivity and fair parameterizations so that the new wavelet transform can be used for compression and visualization. The main idea enabling our wavelet transform is the circular symmetrization of the filters in irregular neighborhoods, which replaces the traditional separation of filters into two 1-D passes. Our wavelet transform uses polygonal base meshes to represent surface topology, from which a Catmull-Clark-style subdivision hierarchy is generated. The details between these levels of resolution are quickly computed and compactly stored as wavelet coefficients. The isosurface conversion process begins with a contour triangulation computed using conventional techniques, which we subsequently simplify with a variant edge-collapse procedure, followed by an edge-removal process. This provides a coarse initial base mesh, which is subsequently refined, relaxed and attracted in phases to converge to the contour. The conversion is designed to produce smooth, untangled and minimally-skewed parameterizations, which improves the subsequent compression after applying the transform. We have demonstrated our conversion and transform for an isosurface obtained from a high-resolution turbulent-mixing hydrodynamics simulation, showing the potential for compression and level-of-detail visualization.
Optimal Synthesis of Compliant Mechanisms using Subdivision and Commercial FEA (DETC2004-57497)
Hull, Patrick V.; Canfield, Stephen
2004-01-01
The field of distributed-compliance mechanisms has seen significant work in developing suitable topology optimization tools for their design. These optimal design tools have grown out of the techniques of structural optimization. This paper will build on the previous work in topology optimization and compliant mechanism design by proposing an alternative design space parameterization through control points and adding another step to the process, that of subdivision. The control points allow a specific design to be represented as a solid model during the optimization process. The process of subdivision creates an additional number of control points that help smooth the surface (for example a C(sup 2) continuous surface depending on the method of subdivision chosen) creating a manufacturable design free of some traditional numerical instabilities. Note that these additional control points do not add to the number of design parameters. This alternative parameterization and description as a solid model effectively and completely separates the design variables from the analysis variables during the optimization procedure. The motivation behind this work is to create an automated design tool from task definition to functional prototype created on a CNC or rapid-prototype machine. This paper will describe the proposed compliant mechanism design process and will demonstrate the procedure on several examples common in the literature.
Göçmen, Z Aslıgül
2014-11-01
Insight into land developers' perspectives on alternative residential developments and the barriers they experience in trying to develop them can be crucial in efforts to change environmentally damaging low-density, large-lot, and automobile-dependent residential patterns. Using a semi-structured interview instrument followed by short surveys, I examined the views of 16 developers in Waukesha County, WI, USA, a county that has experienced significant development pressures and widespread implementation of conservation subdivision design. The land developer investigation focused on conservation subdivision design familiarity and implementation, and identified a number of barriers that developers experienced in implementing the design. While the majority of the developers appeared familiar with the design and had experience developing conservation subdivisions, their motivations for developing them varied, as did their on-site conservation practices. The barriers included the lack of land use regulations supporting the design, economic factors, community opposition, and a lack of knowledge about sustainable residential development practices. Strategies to promote more environmentally sustainable residential land development patterns include providing a more supportive institutional environment, enacting different regulations and guidelines for natural resources protection, and offering education on ecologically sound development and planning practices.
NSGIC Local Govt | GIS Inventory — Cities, Towns and Villages dataset current as of 2008. Sedgwick County subdivision or platted areas. Derived from countywide parcel-lot-block cover. Each polygon...
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Paralisia cerebral: conhecimento das mães sobre o diagnóstico e o impacto deste na dinâmica familiar
Directory of Open Access Journals (Sweden)
Eucia Beatriz Lopes Petean
2000-12-01
Full Text Available A Paralisia Cerebral (P.C. é um problema neurológico, que envolve danos da função neuromuscular, com ou sem déficit intelectual. Os danos são de caráter não progressivo e se devem à lesões cerebrais ocorridas no período pré-natal, peri e pós-natal. As conseqüências são alterações motoras e/ou psíquicas, paralisias, epilepsia, hipotonia, entre outros. Os problemas acarretados à criança devido à P.C. podem ocasionar transtornos diversos aos pais. O objetivo deste trabalho consiste em aprender qual o conhecimento que as mães possuem sobre P.C. e o impacto desta sobre a dinâmica familiar. Foram realizadas 20 entrevistas com mães de crianças com diagnóstico de P.C., de recém nascidos 4 anos, atendidos no Ambulátorio NPHC da FMRP-USP, no Setor de Estimulação Precose da APAE-RP, no Centro de Educação EP. Foi utilizado um roteiro semo-estruturado, previamente testado. Os dados obtidos passaram, pela Análise Temática de Conteúdo. As limitações percebidas são princopalmente atrasos geral e atraso motor. O impacto de deficiência na família, positivo ou negativo altera a dinâmica familiar, e a mãe é a principal afetada.
Caravelli, Francesco
2011-01-01
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a particle hopping on the graph. We discuss the role of connectivity in emergent Lorentzian perturbations in a curved background and the Bose--Hubbard (BH) model defined on graphs with particular symmetries.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Emergent geometry, emergent forces
Selesnick, S. A.
2017-10-01
We give a brief account of some aspects of Finkelstein’s quantum relativity, namely an extension of it that derives elements of macroscopic geometry and the Lagrangians of the standard model including gravity from a presumed quantum version of spacetime. These emerge as collective effects in this quantal substrate. Our treatment, which is largely self-contained, differs mathematically from that originally given by Finkelstein. Dedicated to the memory of David Ritz Finkelstein
Integral geometry and valuations
Solanes, Gil
2014-01-01
Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...
Emergent complex network geometry.
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-05-18
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.
Editors, LearningExpress
2010-01-01
Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day is an invaluable resource for both students and adults.
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Gruber, Peter M
1987-01-01
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
Haran, Shai
2015-01-01
We shall describe a simple generalization of commutative rings. The category GR of such "rings", contains the ordinary commutative rings (fully faithfully), but also the "integers" and "residue field" at a real or complex place of a field ; the "field with one element" (the initial object of GR ); the "arithmetical surface" ( the sum in the category GR of the integers with them self: Z(x)Z ) . We shall show that this geometry "see" the real and complex places of a number field (there is an Os...
Inference of population subdivision from the VNTR distributions of New Zealanders.
Clark, A G; Hamilton, J F; Chambers, G K
1995-01-01
A population sample from people of diverse ethnic origins living in New Zealand serves as a database to test methods for inference of population subdivision. The initial null hypothesis, that the population sample is homogeneous across ethnic groups, is easily rejected by likelihood ratio tests. Beyond this, methods for quantifying subdivision can be based on the probability of drawing alleles identical by descent (FST), probabilities of matching multiple locus genotypes, and occurrence of unique alleles. Population genetic theory makes quantitative predictions about the relation between FST, population sizes, and rates of migration and mutation. Some VNTR loci have mutation rates of 10(-2) per generation, but, contrary to theory, we find no consistent association between the degree of population subdivision and mutation rate. Quantification of population substructure also allows us to relate the magnitudes of genetic distances between ethnic groups in New Zealand to the colonization history of the country. The data suggests that the closest relatives to the Maori are Polynesians, and that no severe genetic bottleneck occurred when the Maori colonized New Zealand. One of the central points of contention regarding the application of VNTR loci in forensics is the appropriate means for estimating match probabilities. Simulations were performed to test the merits of the product rule in the face of subpopulation heterogeneity. Population heterogeneity results in large differences in estimates of multilocus genotype frequencies depending on which subpopulation is used for reference allele frequencies, but, of greater importance for forensic purposes, no five locus genotype had an expected frequency greater than 10(-6). Although this implies that a match with an innocent individual is unlikely, in a large urban area such chance matches are going to occur.
Directory of Open Access Journals (Sweden)
Siddharth Mehta
2014-01-01
Full Text Available Orthodontic treatment for patients with unilateral or bilateral congenitally missing lateral incisor poses a challenge mainly with regard to treatment planning. The use of a diagnostic setup is one of the most important aids in the decision-making process. Two alternatives, orthodontic space closure or space opening for prosthetic replacement exist. The present case report shows use of the microimplant for unilateral upper molar distalization and space closure in a Class-II division 1 subdivision malocclusion case with bilateral congenitally missing upper lateral incisors.
Vitral, Robert Willer Farinazzo; Telles, Carlos De Souza
2002-04-01
Thirty persons ranging from 12 years 8 months to 42 years of age with Class II Division 1 subdivision malocclusions underwent computed tomography of the temporomandibular joints. The images obtained from axial slices were evaluated for possible asymmetries in size and position that may exist between the condylar processes associated with this malocclusion. Paired Student t tests were applied, and Pearson product moment correlations were determined after measurements on both Class I and Class II sides were obtained. The results of this study showed no statistically significant asymmetries between the condylar processes evaluated in this sample.
DEFF Research Database (Denmark)
Clausen, Jens; Zilinskas, A,
2002-01-01
are based on the sampling of function values. We propose a branch and bound algorithm based on regular simplexes. Initially, the domain in question is covered with regular simplexes, and our subdivision scheme maintains this property. The bound calculation becomes both simple and efficient, and we describe...... two schemes for sampling points of the function: midpoint sampling and vertex sampling. The convergence of the algorithm is proved, and numerical results are presented for the two dimensional case, for which also a special initial covering is presented. (C) 2002 Elsevier Science Ltd. All rights...
Subdivision design and stewardship affect bird and mammal use of conservation developments.
Farr, Cooper M; Pejchar, Liba; Reed, Sarah E
2017-06-01
Developing effective tools for conservation on private lands is increasingly important for global biodiversity conservation; private lands are located in more productive and biologically diverse areas, and they face accelerated rates of land conversion. One strategy is conservation development (CD) subdivisions, which cluster houses in a small portion of a property and preserve the remaining land as protected open space. Despite widespread use, the characteristics that make CD more or less effective at achieving biodiversity conservation are not well understood. We investigated CD's ability to successfully protect animal populations by examining bird and mammal occurrences in 14 CD subdivisions and four undeveloped areas (range: 14-432 ha) in northern Colorado, USA. Using point count and camera trap data in an occupancy modeling framework, we evaluated the relative importance of nine subdivision design factors (e.g., housing density, proportion of CD protected) and 14 stewardship factors (e.g., presence of livestock, percent native vegetation cover) in influencing the overall community composition and the probability of use by 16 birds and six mammals. We found that habitat use by 75% of birds and 83% of mammals was associated with design characteristics that maximized the natural or undisturbed land area both within and near the development (e.g., proportion of CD protected, total area of protected open space, proportion of natural land cover in the surrounding landscape). These factors were also associated with an increasing dominance of human-sensitive bird species, larger-bodied mammals, and mammals with larger home ranges. Habitat use by birds was also influenced by local land use composition and quality, and use by several bird and mammal species decreased with increased localized disturbances. We found few differences in habitat use between sampling sites in undeveloped areas and in CD subdivisions. These similarities indicate that, if CDs are large enough
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners.......The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...
Clustering of Expression Data in Chronic Lymphocytic Leukemia Reveals New Molecular Subdivisions.
Directory of Open Access Journals (Sweden)
Sally Yepes
Full Text Available Although the identification of inherent structure in chronic lymphocytic leukemia (CLL gene expression data using class discovery approaches has not been extensively explored, the natural clustering of patient samples can reveal molecular subdivisions that have biological and clinical implications. To explore this, we preprocessed raw gene expression data from two published studies, combined the data to increase the statistical power, and performed unsupervised clustering analysis. The clustering analysis was replicated in 4 independent cohorts. To assess the biological significance of the resultant clusters, we evaluated their prognostic value and identified cluster-specific markers. The clustering analysis revealed two robust and stable subgroups of CLL patients in the pooled dataset. The subgroups were confirmed by different methodological approaches (non-negative matrix factorization NMF clustering and hierarchical clustering and validated in different cohorts. The subdivisions were related with differential clinical outcomes and markers associated with the microenvironment and the MAPK and BCR signaling pathways. It was also found that the cluster markers were independent of the immunoglobulin heavy chain variable (IGVH genes mutational status. These findings suggest that the microenvironment can influence the clinical behavior of CLL, contributing to prognostic differences. The workflow followed here provides a new perspective on differences in prognosis and highlights new markers that should be explored in this context.
da Rocha, Ulisses Nunes; van Elsas, Jan Dirk; van Overbeek, Leonard Simon
2011-11-01
Strains CHC12 and CHC8, belonging to, respectively, Luteolibacter and Candidatus genus Rhizospheria (Verrucomicrobia subdivision 1), were recently isolated from the leek rhizosphere. The key question addressed in this study was: does attraction to and colonization of the rhizosphere occur in the same way for both strains? Therefore, the fate of the two strains was studied near in vitro-grown leek roots and in soil zones proximate to and at a further distance from roots in a model plant-soil microcosm set-up. Quantitative PCR detection with specific primers was used, as the cultivation of these bacteria from soil is extremely fastidious. The data indicated that natural populations of Luteolibacter (akin to strain CHC12) had lower numbers in the rhizosphere than in the corresponding bulk soil. On the other hand, the populations of Candidatus genus Rhizospheria, i.e. strain CHC8, showed higher numbers in the rhizosphere than in the bulk soil. Increased strain CHC8 cell-equivalent numbers in the rhizosphere were not only the result of in situ cell multiplication, but also of the migration of cells towards the roots. Luteolibacter and Candidatus genus Rhizospheria cells displayed differences in attraction to the rhizosphere and colonization thereof, irrespective of the fact that both belonged to Verrucomicrobia subdivision 1. © 2011 Federation of European Microbiological Societies. Published by Blackwell Publishing Ltd. All rights reserved.
A 3D Voronoi and subdivision model for calibration of rock properties
Zhu, De-Fu; Tu, Shi-Hao; Ma, Hang-sheng; Zhang, Xin-wang
2017-12-01
Rock cleavages consist of the cracks between blocks and the internal faults in blocks. The built-in modeling module in the Three-dimension Distinct Element Code cannot accurately describe the internal structure and the cleavage development characteristics of rock. This study combined 3D Voronoi block elements and scanning electron microscope images, to construct a numerical model equivalent to the rock meso structures. Three strategies are proposed to refine the initial model by block subdivision to achieve a function that allows cleavages in the model to cross through the blocks. A physical uniaxial compression test was performed in the laboratory to calibrate the mechanical parameters of the siltstone and the calibrated parameters then were validated by a Brazilian disc test. Sensitivity analysis was conducted to investigate the relationship between the meso-parameters and the model’s macro-response, and a calibration procedure was established for accurate replication of rock mechanical behavior. The statistics and analyses of failure characteristics for joints in the model showed that when the compressive and tensile strength values peaked, the percentages of tensile failures were approximately 37% and 10%, respectively. Comparing the cleavages after sample failure in lab tests with the cleavage development paths predicted by the models, the compressive and tensile characteristics were analyzed and the results confirmed the reliability of applying the 3D Voronoi block and subdivision modeling method in the numerical simulation study of the mechanical properties of the rock.
Bowman, Troy; Tyndall, John C; Thompson, Janette; Kliebenstein, James; Colletti, Joe P
2012-08-15
Residents, developers and civic officials are often faced with difficult decisions about appropriate land uses in and around metropolitan boundaries. Urban expansion brings with it the potential for negative environmental impacts, but there are alternatives, such as conservation subdivision design (CSD) or low-impact development (LID), which offer the possibility of mitigating some of these effects at the development site. Many urban planning jurisdictions across the Midwest do not currently have any examples of these designs and lack information to identify public support or barriers to use of these methods. This is a case study examining consumer value for conservation and low-impact design features in one housing market by using four different valuation techniques to estimate residents' willingness to pay for CSD and LID features in residential subdivisions. A contingent valuation survey of 1804 residents in Ames, IA assessed familiarity with and perceptions of subdivision development and used an ordered value approach to estimate willingness to pay for CSD and LID features. A majority of residents were not familiar with CSD or LID practices. Residents indicated a willingness to pay for most CSD and LID features with the exception of clustered housing. Gender, age, income, familiarity with LID practices, perceptions of attractiveness of features and the perceived effect of CSD and LID features on ease of future home sales were important factors influencing residents' willingness to pay. A hypothetical referendum measured willingness to pay for tax-funded conservation land purchases and estimated that a property tax of around $50 would be the maximum increase that would pass. Twenty-seven survey respondents participated in a subsequent series of experimental real estate negotiations that used an experimental auction mechanism to estimate willingness to pay for CSD and LID features. Participants indicated that clustered housing (with interspersed preserved forest
Directory of Open Access Journals (Sweden)
Julia Ganz
2015-11-01
Full Text Available Background: The telencephalon shows a remarkable structural diversity among vertebrates. In particular, the everted telencephalon of ray-finned fishes has a markedly different morphology compared to the evaginated telencephalon of all other vertebrates. This difference in development has hampered the comparison between different areas of the pallium of ray-finned fishes and the pallial nuclei of all other vertebrates. Various models of homology between pallial subdivisions in ray-finned fishes and the pallial nuclei in tetrapods have been proposed based on connectional, neurochemical, gene expression and functional data. However, no consensus has been reached so far. In recent years, the analysis of conserved developmental marker genes has assisted the identification of homologies for different parts of the telencephalon among several tetrapod species. Results: We have investigated the gene expression pattern of conserved marker genes in the adult zebrafish (Danio rerio pallium to identify pallial subdivisions and their homology to pallial nuclei in tetrapods. Combinatorial expression analysis of ascl1a, eomesa, emx1, emx2, emx3, and Prox1 identifies four main divisions in the adult zebrafish pallium. Within these subdivisions, we propose that Dm is homologous to the pallial amygdala in tetrapods and that the dorsal subdivision of Dl is homologous to part of the hippocampal formation in mouse. We have complemented this analysis be examining the gene expression of emx1, emx2 and emx3 in the zebrafish larval brain. Conclusions: Based on our gene expression data, we propose a new model of subdivisions in the adult zebrafish pallium and their putative homologies to pallial nuclei in tetrapods. Pallial nuclei control sensory, motor, and cognitive functions, like memory, learning and emotion. The identification of pallial subdivisions in the adult zebrafish and their homologies to pallial nuclei in tetrapods will contribute to the use of the zebrafish
An introduction to incidence geometry
De Bruyn, Bart
2016-01-01
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Self-designing parametric geometries
Sobester, Andras
2015-01-01
The thesis of this paper is that script-based geometry modelling offers the possibility of building `self-designing' intelligence into parametric airframe geometries. We show how sophisticated heuristics (such as optimizers and complex decision structures) can be readily integrated into the parametric geometry model itself using a script-driven modelling architecture. The result is an opportunity for optimization with the scope of conceptual design and the fidelity of preliminary design. Addi...
Geometry aware Stationary Subspace Analysis
2016-11-22
JMLR: Workshop and Conference Proceedings 63:430–444, 2016 ACML 2016 Geometry -aware Stationary Subspace Analysis Inbal Horev inbal@ms.k.u-tokyo.ac.jp... geometry of the SPD matrix manifold and the invariance properties of its metrics. Most notably we show that these invariances alleviate the need to...Horev, F. Yger & M. Sugiyama. Geometry -aware SSA many theoretical and practical aspects have been addressed (see Sugiyama and Kawanabe (2012) for an in
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Guijosa, A
1999-01-01
This thesis explores some aspects of the recently uncovered connection between gauge theories and gravity, known as the AdS/CFT, or bulk-boundary, correspondence. This is a remarkable statement of equivalence between string or M-theory on certain backgrounds and field theories living on the boundaries of the corresponding spacetimes. Under the duality between four-dimensional N = 4 SU(N) superYang-Mills (SYM) and Type IIB string theory on AdS5 × S5, a baryon is mapped onto N fundamental strings terminating on a wrapped D5-brane. We examine the structure and energetics of this system from the vantage point of the fivebrane worldvolume action, making use of the Born-Infeld string approach. We construct supersymmetric fivebrane embeddings which correspond to gauge theory configurations with n external quarks, 0 ≤ n ≤ N. The extension of these solutions to the full asymptotically flat geometry of N D3-branes provides a detailed description of the creation of strings as the fivebrane is...
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Speziale, Simone
2013-01-01
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Positive geometries and canonical forms
Arkani-Hamed, Nima; Bai, Yuntao; Lam, Thomas
2017-11-01
Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects — the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra — which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. The structures seen in the physical setting of the Amplituhedron are both rigid and rich enough to motivate an investigation of the notions of "positive geometries" and their associated "canonical forms" as objects of study in their own right, in a more general mathematical setting. In this paper we take the first steps in this direction. We begin by giving a precise definition of positive geometries and canonical forms, and introduce two general methods for finding forms for more complicated positive geometries from simpler ones — via "triangulation" on the one hand, and "push-forward" maps between geometries on the other. We present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties, both for the simplest "simplex-like" geometries and the richer "polytope-like" ones. We also illustrate a number of strategies for computing canonical forms for large classes of positive geometries, ranging from a direct determination exploiting knowledge of zeros and poles, to the use of the general triangulation and push-forward methods, to the representation of the form as volume integrals over dual geometries and contour integrals over auxiliary spaces. These methods yield interesting representations for the canonical forms of wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex
Directory of Open Access Journals (Sweden)
Harishchandra S. Ramane
2017-04-01
Full Text Available The general sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graphs of subdivision graphs of tadpole graphs, wheels and ladders have been reported in the literature. In this paper, we obtain general expressions for these topological indices for the line graph of the subdivision graphs, thus generalizing the existing results.
Directory of Open Access Journals (Sweden)
Ciyun Lin
2015-01-01
Full Text Available This paper aims at the traffic flow agglomeration effect characteristics and rapid evacuation requirement in sudden disaster; operation time of intraregional boundaries traffic signal coordination was presented firstly. Then intraregional boundaries intersection group dynamic subdivision and consolidation method based on relative similarity degree and similarity coefficient of adjacent intersections was put forward. As to make the traffic control strategy adapt to traffic condition of different intraregional boundaries intersection groups, this paper proposes an intraregional boundaries traffic signal coordination and optimization technology based on organic computing theory. Finally, this paper uses Delphi 7.0, MapX, and Oracle developing a software package, combined with Paramics V6 Simulator to validate the methods of this paper. The result shows that it can obviously improve disaster affected regional traffic signal control efficiency which reduces average traffic delay by 30–35%, decreases vehicle queue by more than 20% and reduces evacuation time more than 13.06%.
Directory of Open Access Journals (Sweden)
Medikondu Kishore
2010-01-01
Full Text Available A systematic study has been carried out to explore the physicochemical characteristics of drinking water sources of Tipparthy revenue sub-division, Nalgonda (District, Andhra Pradesh, India. Totally 49 water samples were collected from the different locations (22 villages of the study area including bore well, open well and hand pump water and analyzed for pH, EC, TDS, turbidity, total hardness, fluoride, chloride, nitrate, nitrite, sulphate, phosphates, calcium, magnesium, sodium, potassium, Iron and dissolved oxygen. On an average, in almost all the samples, one or the other chemical constituent was beyond the permissible limits it was also concluded that water sources in the study area not fit for potability. Sodium absorption ratio (SAR and water quality (WQI studies indicate water available from all sources not fit for irrigation also. The study indicates the need for periodic monitoring of ground water in the study area.
Meinhold, Guido
2017-04-01
This work is in honour of Franz Kossmat (1871-1938) and his esteemed paper the Gliederung des varistischen Gebirgsbaues published 1927 in Abhandlungen des Sächsischen Geologischen Landesamts, Volume 1, pages 1 to 39. It constitutes the foundation of the general subdivision of the Central European Variscides into several geotectonic zones and the idea of large-scale nappe transport of individual units. In the English translation presented here an attempt is made to provide a readable text, which should still reflect Kossmat's style but would also be readable for a non-German speaking community either working in the Variscan Mountains or having specific interests in historical aspects of geosciences. Supplementary notes provide information about Kossmat's life and the content of the text. Kossmat's work is a superb example of how important geological fieldwork and mapping are for progress in geoscientific research.
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame-dependent and fr...
Geometry of the quantum universe
Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Loll, R.
2010-01-01
A quantum universe with the global shape of a (Euclidean) de Sitter spacetime appears as dynamically generated background geometry in the causal dynamical triangulation (CDT) regularisation of quantum gravity. We investigate the micro- and macro-geometry of this universe, using geodesic shell
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Caspers, Julian; Mathys, Christian; Hoffstaedter, Felix; Südmeyer, Martin; Cieslik, Edna C.; Rubbert, Christian; Hartmann, Christian J.; Eickhoff, Claudia R.; Reetz, Kathrin; Grefkes, Christian; Michely, Jochen; Turowski, Bernd; Schnitzler, Alfons; Eickhoff, Simon B.
2017-01-01
Patients suffering from Parkinson's disease (PD) often show impairments in executive function (EF) like decision-making and action control. The right dorsolateral prefrontal cortex (dlPFC) has been strongly implicated in EF in healthy subjects and has repeatedly been reported to show alterations related to EF impairment in PD. Recently, two key regions for cognitive action control have been identified within the right dlPFC by co-activation based parcellation. While the posterior region is engaged in rather basal EF like stimulus integration and working memory, the anterior region has a more abstract, supervisory function. To investigate whether these functionally distinct subdivisions of right dlPFC are differentially affected in PD, we analyzed resting-state functional connectivity (FC) in 39 PD patients and 44 age- and gender-matched healthy controls. Patients were examined both after at least 12 h withdrawal of dopaminergic drugs (OFF) and under their regular dopaminergic medication (ON). We found that only the posterior right dlPFC subdivision shows FC alterations in PD, while the anterior part remains unaffected. PD-related decreased FC with posterior right dlPFC was found in the bilateral medial posterior parietal cortex (mPPC) and left dorsal premotor region (PMd) in the OFF state. In the medical ON, FC with left PMd normalized, while decoupling with bilateral mPPC remained. Furthermore, we observed increased FC between posterior right dlPFC and the bilateral dorsomedial prefrontal cortex (dmPFC) in PD in the ON state. Our findings point to differential disturbances of right dlPFC connectivity in PD, which relate to its hierarchical organization of EF processing by stronger affecting the functionally basal posterior aspect than the hierarchically higher anterior part. PMID:28611616
Directory of Open Access Journals (Sweden)
Julian Caspers
2017-05-01
Full Text Available Patients suffering from Parkinson's disease (PD often show impairments in executive function (EF like decision-making and action control. The right dorsolateral prefrontal cortex (dlPFC has been strongly implicated in EF in healthy subjects and has repeatedly been reported to show alterations related to EF impairment in PD. Recently, two key regions for cognitive action control have been identified within the right dlPFC by co-activation based parcellation. While the posterior region is engaged in rather basal EF like stimulus integration and working memory, the anterior region has a more abstract, supervisory function. To investigate whether these functionally distinct subdivisions of right dlPFC are differentially affected in PD, we analyzed resting-state functional connectivity (FC in 39 PD patients and 44 age- and gender-matched healthy controls. Patients were examined both after at least 12 h withdrawal of dopaminergic drugs (OFF and under their regular dopaminergic medication (ON. We found that only the posterior right dlPFC subdivision shows FC alterations in PD, while the anterior part remains unaffected. PD-related decreased FC with posterior right dlPFC was found in the bilateral medial posterior parietal cortex (mPPC and left dorsal premotor region (PMd in the OFF state. In the medical ON, FC with left PMd normalized, while decoupling with bilateral mPPC remained. Furthermore, we observed increased FC between posterior right dlPFC and the bilateral dorsomedial prefrontal cortex (dmPFC in PD in the ON state. Our findings point to differential disturbances of right dlPFC connectivity in PD, which relate to its hierarchical organization of EF processing by stronger affecting the functionally basal posterior aspect than the hierarchically higher anterior part.
The Jurassic of Denmark and Greenland: The Upper Jurassic of Europe: its subdivision and correlation
Directory of Open Access Journals (Sweden)
Zeiss, Arnold
2003-10-01
Full Text Available In the last 40 years, the stratigraphy of the Upper Jurassic of Europe has received much attention and considerable revision; much of the impetus behind this endeavour has stemmed from the work of the International Subcommission on Jurassic Stratigraphy. The Upper Jurassic Series consists of three stages, the Oxfordian, Kimmeridgian and Tithonian which are further subdivided into substages, zones and subzones, primarily on the basis of ammonites. Regional variations between the Mediterranean, Submediterranean and Subboreal provinces are discussed and correlation possibilities indicated. The durations of the Oxfordian, Kimmeridgian and Tithonian Stages are reported to have been 5.3, 3.4 and 6.5 Ma, respectively. This review of the present status of Upper Jurassic stratigraphy aids identification of a number of problems of subdivision and definition of Upper Jurassic stages; in particular these include correlation of the base of the Kimmeridgian and the top of the Tithonian between Submediterranean and Subboreal Europe. Although still primarily based on ammonite stratigraphy, subdivision of the Upper Jurassic is increasingly being refined by the incorporation of other fossil groups; these include both megafossils, such as aptychi, belemnites, bivalves, gastropods, brachiopods, echinoderms, corals, sponges and vertebrates, and microfossils such as foraminifera, radiolaria, ciliata, ostracodes, dinoflagellates, calcareous nannofossils, charophyaceae, dasycladaceae, spores and pollen. Important future developments will depend on the detailed integration of these disparate biostratigraphic data and their precise combination with the abundant new data from sequence stratigraphy, utilising the high degree of stratigraphic resolution offered by certain groups of fossils. This article also contains some notes on the recent results of magnetostratigraphy and sequence chronostratigraphy.
Santos-Durán, Gabriel N.; Ferreiro-Galve, Susana; Menuet, Arnaud; Quintana-Urzainqui, Idoia; Mazan, Sylvie; Rodríguez-Moldes, Isabel; Candal, Eva
2016-01-01
The hypothalamus is an important physiologic center of the vertebrate brain involved in the elaboration of individual and species survival responses. To better understand the ancestral organization of the alar hypothalamus we revisit previous data on ScOtp, ScDlx2/5, ScTbr1, ScNkx2.1 expression and Pax6 immunoreactivity jointly with new data on ScNeurog2, ScLhx9, ScLhx5, and ScNkx2.8 expression, in addition to immunoreactivity to serotonin (5-HT) and doublecortin (DCX) in the catshark Scyliorhinus canicula, a key species for this purpose since cartilaginous fishes are basal representatives of gnathostomes (jawed vertebrates). Our study revealed a complex genoarchitecture for the chondrichthyan alar hypothalamus. We identified terminal (rostral) and peduncular (caudal) subdivisions in the prosomeric paraventricular and subparaventricular areas (TPa/PPa and TSPa/PSPa, respectively) evidenced by the expression pattern of developmental genes like ScLhx5 (TPa) and immunoreactivity against Pax6 (PSPa) and 5-HT (PPa and PSPa). Dorso-ventral subdivisions were only evidenced in the SPa (SPaD, SPaV; respectively) by means of Pax6 and ScNkx2.8 (respectively). Interestingly, ScNkx2.8 expression overlaps over the alar-basal boundary, as Nkx2.2 does in other vertebrates. Our results reveal evidences for the existence of different groups of tangentially migrated cells expressing ScOtp, Pax6, and ScDlx2. The genoarchitectonic comparative analysis suggests alternative interpretations of the rostral-most alar plate in prosomeric terms and reveals a conserved molecular background for the vertebrate alar hypothalamus likely acquired before/during the agnathan-gnathostome transition, on which Otp, Pax6, Lhx5, and Neurog2 are expressed in the Pa while Dlx and Nkx2.2/Nkx2.8 are expressed in the SPa. PMID:27932958
Shafarevich, Igor Rostislavovich
1994-01-01
Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...
46 CFR 171.080 - Damage stability standards for vessels with Type I or Type II subdivision.
2010-10-01
... damage stability required for that vessel by the International Convention for the Safety of Life at Sea... 46 Shipping 7 2010-10-01 2010-10-01 false Damage stability standards for vessels with Type I or... (CONTINUED) SUBDIVISION AND STABILITY SPECIAL RULES PERTAINING TO VESSELS CARRYING PASSENGERS Large Vessels...
24 CFR 1710.20 - Requirements for registering a subdivision-Statement of Record-filing and form.
2010-04-01
...-FEDERAL HOUSING COMMISSIONER, DEPARTMENT OF HOUSING AND URBAN DEVELOPMENT (INTERSTATE LAND SALES... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Requirements for registering a subdivision-Statement of Record-filing and form. 1710.20 Section 1710.20 Housing and Urban Development...
Luttikhuizen, PC; Drent, J; Baker, AJ
Mitochondrial DNA sequence data for 295 individuals of the marine bivalve Macoma balthica (L.) were collected from 10 sites across the European distribution, and from Alaska. The data were used to infer population subdivision history and estimate current levels of gene flow. Inferred historical
Molen, A.S. van der; Wong, Th.E.
2007-01-01
In the Netherlands North Sea area, the Chalk Group has thus far been subdivided into the Cenomanian Texel Formation, the Turonian to Maastrichtian Ommelanden Formation and the Danian Ekofisk Formation. This paper describes the attempt to arrive at a more detailed lithostratigraphic subdivision for
Ether- and Ester-Bound iso-Diabolic Acid and Other Lipids in Members of Acidobacteria Subdivision 4
Rijpstra, W. Irene C.; Hopmans, Ellen C.; Foesel, Bärbel U.; Wüst, Pia K.; Overmann, Jörg; Tank, Marcus; Bryant, Donald A.; Dunfield, Peter F.; Houghton, Karen; Stott, Matthew B.
2014-01-01
Recently, iso-diabolic acid (13,16-dimethyl octacosanedioic acid) has been identified as a major membrane-spanning lipid of subdivisions 1 and 3 of the Acidobacteria, a highly diverse phylum within the Bacteria. This finding pointed to the Acidobacteria as a potential source for the bacterial glycerol dialkyl glycerol tetraethers that occur ubiquitously in peat, soil, lakes, and hot springs. Here, we examined the lipid composition of seven phylogenetically divergent strains of subdivision 4 of the Acidobacteria, a bacterial group that is commonly encountered in soil. Acid hydrolysis of total cell material released iso-diabolic acid derivatives in substantial quantities (11 to 48% of all fatty acids). In contrast to subdivisions 1 and 3 of the Acidobacteria, 6 out of the 7 species of subdivision 4 (excepting “Candidatus Chloracidobacterium thermophilum”) contained iso-diabolic acid ether bound to a glycerol in larger fractional abundance than iso-diabolic acid itself. This is in agreement with the analysis of intact polar lipids (IPLs) by high-performance liquid chromatography-mass spectrometry (HPLC-MS), which showed the dominance of mixed ether-ester glycerides. iso-Diabolic acid-containing IPLs were not identified, because these IPLs are not released with a Bligh-Dyer extraction, as observed before when studying lipid compositions of subdivisions 1 and 3 of the Acidobacteria. The presence of ether bonds in the membrane lipids does not seem to be an adaptation to temperature, because the five mesophilic isolates contained a larger amount of ether lipids than the thermophile “Ca. Chloracidobacterium thermophilum.” Furthermore, experiments with Pyrinomonas methylaliphatogenes did not reveal a major influence of growth temperature over the 50 to 69°C range. PMID:24928878
Energy Technology Data Exchange (ETDEWEB)
Hogan, Craig
2013-03-24
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It does not describe elementary particles, but may be a better, fully consistent quantum description for position states in laboratory-scale systems. Gravitational theory suggests that the geometrical quantum system has an information density of about one qubit per Planck length squared. If so, the model here predicts that the quantum uncertainty of geometry creates a new form of noise in the position of massive bodies, detectable by interferometers.
Walsh, Edward T
2014-01-01
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Differential geometry curves, surfaces, manifolds
Kühnel, Wolfgang
2015-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and-as a new feature-a good number of so
Differential geometry and symmetric spaces
Helgason, Sigurdur
2001-01-01
Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
An improved combinatorial geometry model for arbitrary geometry in DSMC
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Higgs mass in noncommutative geometry
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Devastato, A.; Martinetti, P. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Lizzi, F. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Departament de Estructura i Constituents de la Materia, Universitat de Barcelona, Marti y Franques, Barcelona, Catalonia (Spain)
2014-09-11
In the noncommutative geometry approach to the standard model, an extra scalar field σ - initially suggested by particle physicist to stabilize the electroweak vacuum - makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The Common Geometry Module (CGM).
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Tautges, Timothy James
2004-12-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
Ms, Suzie Aparicio; Welch Bacon, Cailee E; Parsons, John T; Bay, R Curtis; Cohen, Randy P; DeZeeuw, Terry; McLeod, Tamara C Valovich
2015-12-01
The "Appropriate Medical Coverage for Intercollegiate Athletics" (AMCIA) document was created to support assessment and calculation of athletic training personnel requirements. However, little is known regarding disparities between current and recommended staffing practices. To identify the staffing and employment characteristics of athletic health care services at Football Bowl Subdivision-level institutions. Cross-sectional study. Web-based survey. Head athletic trainers and athletic training staff members who were knowledgeable about budget and staff. The survey, Assessment of Staffing Levels at National Collegiate Athletic Association Football Bowl Subdivision-Level Institutions, was used to evaluate personal, university, and staff demographics; staffing and employment topics; and AMCIA variables and use. The survey was accessed and partially completed by 104 individuals (response rate = 84.6%). A total of 79 athletic trainers (response rate = 76%) completed the entire survey. One-third of the respondents (34.2%, n = 26) met the recommended number of full-time equivalents (FTEs) for football, two-thirds of the respondents (65.7%, n = 50) failed to meet the recommendation, and 26.2% (n = 27) were missing data needed for FTE calculation. Among those who did not meet the recommended FTEs (n = 50), 38.0% (n = 19) were within 1 FTE of being compliant, 26.0% (n = 13) were within 2 FTEs, and 24.0% (n = 12) were within 3 FTEs. About one-third of respondents (35.9%, n = 37) reported not using the AMCIA, citing lack of funding (29.7%, n = 11), lack of administrative support (21.6%, n = 8), and other reasons (37.8%, n = 14). The majority of institutions that used the AMCIA were able to provide justification for staffing. For most of the institutions that failed to meet their recommendation, adding 1-3 FTE athletic trainers for football would change their compliance status. A uniform definition of the term FTE within collegiate athletics is needed to allow for structured
MS, Suzie Aparicio; Welch Bacon, Cailee E.; Parsons, John T.; Bay, R. Curtis; Cohen, Randy P.; DeZeeuw, Terry; McLeod, Tamara C. Valovich
2015-01-01
Context The “Appropriate Medical Coverage for Intercollegiate Athletics” (AMCIA) document was created to support assessment and calculation of athletic training personnel requirements. However, little is known regarding disparities between current and recommended staffing practices. Objective To identify the staffing and employment characteristics of athletic health care services at Football Bowl Subdivision-level institutions. Design Cross-sectional study. Setting Web-based survey. Patients or Other Participants Head athletic trainers and athletic training staff members who were knowledgeable about budget and staff. Main Outcome Measure(s) The survey, Assessment of Staffing Levels at National Collegiate Athletic Association Football Bowl Subdivision-Level Institutions, was used to evaluate personal, university, and staff demographics; staffing and employment topics; and AMCIA variables and use. Results The survey was accessed and partially completed by 104 individuals (response rate = 84.6%). A total of 79 athletic trainers (response rate = 76%) completed the entire survey. One-third of the respondents (34.2%, n = 26) met the recommended number of full-time equivalents (FTEs) for football, two-thirds of the respondents (65.7%, n = 50) failed to meet the recommendation, and 26.2% (n = 27) were missing data needed for FTE calculation. Among those who did not meet the recommended FTEs (n = 50), 38.0% (n = 19) were within 1 FTE of being compliant, 26.0% (n = 13) were within 2 FTEs, and 24.0% (n = 12) were within 3 FTEs. About one-third of respondents (35.9%, n = 37) reported not using the AMCIA, citing lack of funding (29.7%, n = 11), lack of administrative support (21.6%, n = 8), and other reasons (37.8%, n = 14). Conclusions The majority of institutions that used the AMCIA were able to provide justification for staffing. For most of the institutions that failed to meet their recommendation, adding 1–3 FTE athletic trainers for football would change their
Szeberényi, Jozsef; Bradak-Hayashi, Balázs; Kiss, Klaudia; Kovács, József; Varga, György; Balázs, Réka; Szalai, Zoltán; Viczián, István
2016-04-01
The different varieties of loess (and intercalated paleosol layers) together constitute one of the most widespread terrestrial sediments, which was deposited, altered, and redeposited in the course of the changing climatic conditions of the Pleistocene. To reveal more information about Pleistocene climate cycles and/or environments the detailed lithostratigraphical subdivision and classification of the loess variations and paleosols are necessary. Beside the numerous method such as various field measurements, semi-quantitative tests and laboratory investigations, diffuse reflectance spectroscopy (DRS) is one of the well applied method on loess/paleosol sequences. Generally, DRS has been used to separate the detrital and pedogenic mineral component of the loess sections by the hematite/goethite ratio. DRS also has been applied as a joint method of various environmental magnetic investigations such as magnetic susceptibility- and isothermal remanent magnetization measurements. In our study the so-called "combined reflectance stratigraphy method" were developed. At First, complex mathematical method was applied to compare the results of the spectral reflectance measurements. One of the most preferred multivariate methods is cluster analysis. Its scope is to group and compare the loess variations and paleosol based on the similarity and common properties of their reflectance curves. In the Second, beside the basic subdivision of the profiles by the different reflectance curves of the layers, the most characteristic wavelength section of the reflectance curve was determined. This sections played the most important role during the classification of the different materials of the section. The reflectance value of individual samples, belonged to the characteristic wavelength were depicted in the function of depth and well correlated with other proxies like grain size distribution and magnetic susceptibility data. The results of the correlation showed the significance of
Development of a new two-dimensional Cartesian geometry nodal multigroup discrete-ordinates method
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Pevey, R.E.
1982-07-01
The purpose of this work is the development and testing of a new family of methods for calculating the spatial dependence of the neutron density in nuclear systems described in two-dimensional Cartesian geometry. The energy and angular dependence of the neutron density is approximated using the multigroup and discrete ordinates techniques, respectively. The resulting FORTRAN computer code is designed to handle an arbitrary number of spatial, energy, and angle subdivisions. Any degree of scattering anisotropy can be handled by the code for either external source or fission systems. The basic approach is to (1) approximate the spatial variation of the neutron source across each spatial subdivision as an expansion in terms of a user-supplied set of exponential basis functions; (2) solve analytically for the resulting neutron density inside each region; and (3) approximate this density in the basis function space in order to calculate the next iteration flux-dependent source terms. In the general case the calculation is iterative due to neutron sources which depend on the neutron density itself, such as scattering interactions.
Finite Geometries: a tool for better understanding of Euclidean Geometry
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Antonio Maturo
2014-06-01
Full Text Available An effective tool to really understand Euclidean geometry is the study of alternative models and their applications. In fact, they allow you to understand the real extent of various axioms that, when viewed from the Euclidean geometry, seem obvious or even unnecessary. The work begins with a review of Hilbert's axiomatic, starting from more general point of view adopted by Albrecht Beutelspacher and Ute Rosenbaum in their book on the fundamentals of general projective geometry (1998, defined by a system of incidence axioms. Le Geometrie Finite: uno strumento per una migliore comprensione della Geometria Euclidea Uno strumento efficace per comprendere realmente la geometria euclidea è lo studio di modelli alternativi e delle loro applicazioni. Infatti essi permettono di capire la reale portata di vari assiomi che visti dall’interno della geometria euclidea sembrerebbero scontati o addirittura inutili. Il lavoro parte da una rivisitazione dell’assiomatica di Hilbert a partire dal punto di vista più generale adottato da Albrecht Beutelspacher e Ute Rosenbaum nel loro libro del 1998 sui fondamenti della geometria proiettiva generale, definita attraverso un sistema di assiomi di incidenza. Parole Chiave: Critica dei fondamenti; Geometrie finite; Assiomi di Hilbert; Applicazioni.
The Tools of Financial Policy in the Dairy Products Subdivision of the Agroindustrial Complex
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Bielosviet Oleksandr. V.
2017-03-01
Full Text Available The article is aimed at definition and classification of tools of the State financial policy in the dairy products subdivision of the agroindustrial complex (DPS of AIC. The article considers the financial policy tools used in terms of targeted programs of the State support for the DPS of AIC: the State target program for development of Ukrainian villages, sectoral program for dairy breeding and the project of the conception of the State target program for development of dairy breeding in Ukraine for the period up to 2020. The existing tools are divided into direct and indirect action tools. As of 2016, the tasks that were relevant to the corresponding targeted programs have not been implemented on any item, except for the milk productivity of cows. Still the productivity indicator of 4500 kg/year of milk from a cow is low enough and does not correspond to the general world-wide tendencies. This suggests the need for further assessment of the existing list of tools with a view to adjusting them and defining priorities for the State support of the DPS of AIC.
Adaptive subdivision and the length and energy of Bézier curves
DEFF Research Database (Denmark)
Gravesen, Jens
1997-01-01
It is an often used fact that the control polygon of a Bézier curve approximates the curve and that the approximation gets better when the curve is subdivided. In particular, if a Bézier curve is subdivided into some number of pieces, then the arc-length of the original curve is greater than...... the sum of the chord-lengths of the pieces, and less than the sum of the polygon-lengths of the pieces. Under repeated subdivisions, the difference between this lower and upper bound gets arbitrarily small.If $L_c$ denotes the total chord-length of the pieces and $L_p$ denotes the total polygon...... combination, and it forms the basis for a fast adaptive algorithm, which determines the arc-length of a Bézier curve.The energy of a curve is half the square of the curvature integrated with respect to arc-length. Like in the case of the arc-length, it is possible to use the chord-length and polygon...
Pitra, C; Lieckfeldt, D; Alonso, J C
2000-08-01
A continent-wide survey of sequence variation in mitochondrial (mt) and nuclear (n) DNA of the endangered great bustard (Otis tarda) was conducted to assess the extent of phylogeographic structure in a morphologically monotypic bird. DNA sequence variation in a combined 809 bp segment of the mtDNA genome from 66 individuals from the last six breeding regions showed relatively low levels of intraspecific sequence diversity (n = 0.32%) but significant differences in the regional distribution of 11 haplotypes (phiST = 0.49). Despite their exceptional potential for dispersal, a complete and long-term historical separation between the populations from the Iberian Peninsula (Spain) and mainland Europe (Hungary, Slovakia, Germany, and Russia) was demonstrated. Divergence between populations based on a 3-bp insertion-deletion polymorphism within the intron region of the nuclear CHD-Z gene was geographically concordant with the primary subdivision identified within the mtDNA sequences. Inferred aspects of phylogeography were used to formulate conservation recommendations for this endangered species.
Medically Important Parasites Carried by Cockroaches in Melong Subdivision, Littoral, Cameroon
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R. J. Atiokeng Tatang
2017-01-01
Full Text Available Cockroaches have been recognized as mechanical vectors of pathogens that can infest humans or animals. A total of 844 adult cockroaches (436 males and 408 females were caught. In the laboratory, cockroaches were first washed in saturated salt solution to remove ectoparasites and then rinsed with 70% alcohol, dried, and dissected for endoparasites. An overall transport rate of 47.39% was recorded. Six genera of parasites were identified. These were Ascaris (33.76%, Trichuris (11.97%, Capillaria (6.16%, Toxocara (4.86%, Hook Worm (4.86%, and Eimeria (2.73%. The parasites were more recorded on the external surface (54.27% of cockroaches than in the internal surface (GIT, 38.51%. The same tendency was obtained between sexes with female cockroaches having a higher transport rate (36.69%. Cockroaches caught in toilets carried more parasites (31.99% as compared to those from kitchens (22.63% and houses (11.14%. Almost all encountered parasites were recognized as responsible of zoonosis and they can be consequently released in nature by hosts and easily disseminated by cockroaches as mechanical vectors. Sanitary education, reenforcement of worms’ eradication programs, and the fight against these insects remain a necessity in the Mélong Subdivision.
Hepatitis A outbreak in Ba subdivision, Fiji, October–December 2013
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Aneley Getahun
2015-06-01
Full Text Available Objective: A cluster of suspected hepatitis A cases was notified to the Fiji Ministry of Health on 22 October 2013. An outbreak investigation team was mobilized to confirm the existence of an outbreak of hepatitis A and advise appropriate public health interventions. Methods: A case definition for the outbreak investigation was established, and standardized data collection tools were used to collect information on clinical presentation and risk factors. An environmental assessment was also conducted. Results: There were 160 clinical cases of hepatitis A of which 15 were laboratory-confirmed. The attack rate was 349 per 10 000 population in the Nukuloa nursing zone; there were no reported deaths. Residents of the Nukuloa settlement were 6.6 times more likely to present with symptomatic hepatitis A infection (95% confidence interval: 3.8–12.6 compared with residents of another village with a different water supply. Discussion: This is the first significant hepatitis A outbreak documented in Ba subdivision and possibly in Fiji. Enhanced surveillance of hepatitis A may reveal other clusters in the country. Improving the primary water source dramatically reduced the occurance of disease in the affected community and adjacent areas.
Hepatitis A outbreak in Ba subdivision, Fiji, October-December 2013.
Getahun, Aneley; Rafai, Eric; Tolosa, Maria Ximena; Dawainavesi, Akanisi; Tabua, Anaseini Maisema; Tabua, Josefa
2015-01-01
A cluster of suspected hepatitis A cases was notified to the Fiji Ministry of Health on 22 October 2013. An outbreak investigation team was mobilized to confirm the existence of an outbreak of hepatitis A and advise appropriate public health interventions. A case definition for the outbreak investigation was established, and standardized data collection tools were used to collect information on clinical presentation and risk factors. An environmental assessment was also conducted. There were 160 clinical cases of hepatitis A of which 15 were laboratory-confirmed. The attack rate was 349 per 10,000 population in the Nukuloa nursing zone; there were no reported deaths. Residents of the Nukuloa settlement were 6.6 times more likely to present with symptomatic hepatitis A infection (95% confidence interval: 3.8-12.6) compared with residents of another village with a different water supply. This is the first significant hepatitis A outbreak documented in Ba subdivision and possibly in Fiji. Enhanced surveillance of hepatitis A may reveal other clusters in the country. Improving the primary water source dramatically reduced the occurance of disease in the affected community and adjacent areas.
Ovenden, Jenny R; Kashiwagi, Tom; Broderick, Damien; Giles, Jenny; Salini, John
2009-02-12
The territorial fishing zones of Australia and Indonesia are contiguous to the north of Australia in the Timor and Arafura Seas and in the Indian Ocean to the north of Christmas Island. The area surrounding the shared boundary consists of a variety of bio-diverse marine habitats including shallow continental shelf waters, oceanic trenches and numerous offshore islands. Both countries exploit a variety of fisheries species, including whaler (Carcharhinus spp.) and hammerhead sharks (Sphyrna spp.). Despite their differences in social and financial arrangements, the two countries are motivated to develop complementary co-management practices to achieve resource sustainability. An essential starting point is knowledge of the degree of population subdivision, and hence fisheries stock status, in exploited species. Populations of four commercially harvested shark species (Carcharhinus obscurus, Carcharhinus sorrah, Prionace glauca, Sphyrna lewini) were sampled from northern Australia and central Indonesia. Neutral genetic markers (mitochondrial DNA control region sequence and allelic variation at co-dominant microsatellite loci) revealed genetic subdivision between Australian and Indonesian populations of C. sorrah. Further research is needed to address the possibility of genetic subdivision among C. obscurus populations. There was no evidence of genetic subdivision for P. glauca and S. lewini populations, but the sampling represented a relatively small part of their distributional range. For these species, more detailed analyses of population genetic structure is recommended in the future. Cooperative management between Australia and Indonesia is the best option at present for P. glauca and S. lewini, while C. sorrah and C. obscurus should be managed independently. On-going research on these and other exploited shark and ray species is strongly recommended. Biological and ecological similarity between species may not be a predictor of population genetic structure, so
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Giles Jenny
2009-02-01
Full Text Available Abstract Background The territorial fishing zones of Australia and Indonesia are contiguous to the north of Australia in the Timor and Arafura Seas and in the Indian Ocean to the north of Christmas Island. The area surrounding the shared boundary consists of a variety of bio-diverse marine habitats including shallow continental shelf waters, oceanic trenches and numerous offshore islands. Both countries exploit a variety of fisheries species, including whaler (Carcharhinus spp. and hammerhead sharks (Sphyrna spp.. Despite their differences in social and financial arrangements, the two countries are motivated to develop complementary co-management practices to achieve resource sustainability. An essential starting point is knowledge of the degree of population subdivision, and hence fisheries stock status, in exploited species. Results Populations of four commercially harvested shark species (Carcharhinus obscurus, Carcharhinus sorrah, Prionace glauca, Sphyrna lewini were sampled from northern Australia and central Indonesia. Neutral genetic markers (mitochondrial DNA control region sequence and allelic variation at co-dominant microsatellite loci revealed genetic subdivision between Australian and Indonesian populations of C. sorrah. Further research is needed to address the possibility of genetic subdivision among C. obscurus populations. There was no evidence of genetic subdivision for P. glauca and S. lewini populations, but the sampling represented a relatively small part of their distributional range. For these species, more detailed analyses of population genetic structure is recommended in the future. Conclusion Cooperative management between Australia and Indonesia is the best option at present for P. glauca and S. lewini, while C. sorrah and C. obscurus should be managed independently. On-going research on these and other exploited shark and ray species is strongly recommended. Biological and ecological similarity between species may
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Thaler Andrew D
2011-12-01
Full Text Available Abstract Background Deep-sea hydrothermal vents provide patchy, ephemeral habitats for specialized communities of animals that depend on chemoautotrophic primary production. Unlike eastern Pacific hydrothermal vents, where population structure has been studied at large (thousands of kilometres and small (hundreds of meters spatial scales, population structure of western Pacific vents has received limited attention. This study addresses the scale at which genetic differentiation occurs among populations of a western Pacific vent-restricted gastropod, Ifremeria nautilei. Results We used mitochondrial and DNA microsatellite markers to infer patterns of gene flow and population subdivision. A nested sampling strategy was employed to compare genetic diversity in discrete patches of Ifremeria nautilei separated by a few meters within a single vent field to distances as great as several thousand kilometres between back-arc basins that encompass the known range of the species. No genetic subdivisions were detected among patches, mounds, or sites within Manus Basin. Although I. nautilei from Lau and North Fiji Basins (~1000 km apart also exhibited no evidence for genetic subdivision, these populations were genetically distinct from the Manus Basin population. Conclusions An unknown process that restricts contemporary gene flow isolates the Manus Basin population of Ifremeria nautilei from widespread populations that occupy the North Fiji and Lau Basins. A robust understanding of the genetic structure of hydrothermal vent populations at multiple spatial scales defines natural conservation units and can help minimize loss of genetic diversity in situations where human activities are proposed and managed.
Quantum geometry and gravitational entropy
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Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Variable geometry Darrieus wind machine
Pytlinski, J. T.; Serrano, D.
1983-08-01
A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
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Irkham Ulil Albab
2014-10-01
Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews
Geometry, topology, and string theory
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Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Teaching Activity-Based Taxicab Geometry
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
Sex, Subdivision, and Domestic Dispersal of Trypanosoma cruzi Lineage I in Southern Ecuador
Ocaña-Mayorga, Sofía; Llewellyn, Martin S.; Costales, Jaime A.; Miles, Michael A.; Grijalva, Mario J.
2010-01-01
Background Molecular epidemiology at the community level has an important guiding role in zoonotic disease control programmes where genetic markers are suitably variable to unravel the dynamics of local transmission. We evaluated the molecular diversity of Trypanosoma cruzi, the etiological agent of Chagas disease, in southern Ecuador (Loja Province). This kinetoplastid parasite has traditionally been a paradigm for clonal population structure in pathogenic organisms. However, the presence of naturally occurring hybrids, mitochondrial introgression, and evidence of genetic exchange in the laboratory question this dogma. Methodology/Principal Findings Eighty-one parasite isolates from domiciliary, peridomiciliary, and sylvatic triatomines and mammals were genotyped across 10 variable microsatellite loci. Two discrete parasite populations were defined: one predominantly composed of isolates from domestic and peridomestic foci, and another predominantly composed of isolates from sylvatic foci. Spatial genetic variation was absent from the former, suggesting rapid parasite dispersal across our study area. Furthermore, linkage equilibrium between loci, Hardy-Weinberg allele frequencies at individual loci, and a lack of repeated genotypes are indicative of frequent genetic exchange among individuals in the domestic/peridomestic population. Conclusions/Significance These data represent novel population-level evidence of an extant capacity for sex among natural cycles of T. cruzi transmission. As such they have dramatic implications for our understanding of the fundamental genetics of this parasite. Our data also elucidate local disease transmission, whereby passive anthropogenic domestic mammal and triatomine dispersal across our study area is likely to account for the rapid domestic/peridomestic spread of the parasite. Finally we discuss how this, and the observed subdivision between sympatric sylvatic and domestic/peridomestic foci, can inform efforts at Chagas disease
Coyote movements and social structure along a cryptic population genetic subdivision.
Sacks, Benjamin N; Mitchell, Brian R; Williams, Christen L; Ernest, Holly B
2005-04-01
A recent region-wide study determined that the central California coyote (Canis latrans) population was genetically subdivided according to habitat bioregions, supporting the hypothesis that coyotes exhibit a dispersal bias toward their natal habitat type. Here, we further investigated this hypothesis using radio-collared coyotes captured on a 150-km(2) study site on the border of (i.e. overlapping) two bioregions (Great Valley and Cascade Mountains). As predicted, most coyotes were assigned (based on a priori genetic criteria) to genetic clusters corresponding to one of these two bioregions. All of those assigned to the Great Valley genetic cluster were caught in (and for the most part, remained in) the Great Valley bioregion. However, contrary to expectations, the coyotes assigned to the Cascades genetic cluster occurred commonly in both bioregions. Nearly all resident individuals on the study site, regardless of the particular bioregion, were assigned to the Cascades genetic cluster, whereas a sizable fraction of nonresident (transient or dispersing) coyotes caught in the Great Valley bioregion were assigned to the Great Valley cluster. Even among resident coyotes, interrelatedness of packs was greater within than between bioregions, and packs with territories overlapping both bioregions were more closely related to those with territories completely within the Cascades bioregion than territories completely within the Great Valley bioregion. Finally, direct estimates indicated that gene flow was twice as high from the Cascades bioregion to the Great Valley bioregion than in the reverse direction. Collectively, these findings reveal the anatomy of the genetic subdivision as beginning abruptly at the bioregion boundary and ending diffusely within the Great Valley bioregion.
Directory of Open Access Journals (Sweden)
Eve Gazave
Full Text Available BACKGROUND: Homoscleromorpha is the fourth major sponge lineage, recently recognized to be distinct from the Demospongiae. It contains <100 described species of exclusively marine sponges that have been traditionally subdivided into 7 genera based on morphological characters. Because some of the morphological features of the homoscleromorphs are shared with eumetazoans and are absent in other sponges, the phylogenetic position of the group has been investigated in several recent studies. However, the phylogenetic relationships within the group remain unexplored by modern methods. METHODOLOGY/PRINCIPAL FINDINGS: Here we describe the first molecular phylogeny of Homoscleromorpha based on nuclear (18S and 28S rDNA and complete mitochondrial DNA sequence data that focuses on inter-generic relationships. Our results revealed two robust clades within this group, one containing the spiculate species (genera Plakina, Plakortis, Plakinastrella and Corticium and the other containing aspiculate species (genera Oscarella and Pseudocorticium, thus rejecting a close relationship between Pseudocorticium and Corticium. Among the spiculate species, we found affinities between the Plakortis and Plakinastrella genera, and between the Plakina and Corticium. The validity of these clades is furthermore supported by specific morphological characters, notably the type of spicules. Furthermore, the monophyly of the Corticium genus is supported while the monophyly of Plakina is not. CONCLUSIONS/SIGNIFICANCE: As the result of our study we propose to restore the pre-1995 subdivision of Homoscleromorpha into two families: Plakinidae Schulze, 1880 for spiculate species and Oscarellidae Lendenfeld, 1887 for aspiculate species that had been rejected after the description of the genus Pseudocorticium. We also note that the two families of homoscleromorphs exhibit evolutionary stable, but have drastically distinct mitochondrial genome organizations that differ in gene content
Gazave, Eve; Lapébie, Pascal; Renard, Emmanuelle; Vacelet, Jean; Rocher, Caroline; Ereskovsky, Alexander V; Lavrov, Dennis V; Borchiellini, Carole
2010-12-14
Homoscleromorpha is the fourth major sponge lineage, recently recognized to be distinct from the Demospongiae. It contains sponges that have been traditionally subdivided into 7 genera based on morphological characters. Because some of the morphological features of the homoscleromorphs are shared with eumetazoans and are absent in other sponges, the phylogenetic position of the group has been investigated in several recent studies. However, the phylogenetic relationships within the group remain unexplored by modern methods. Here we describe the first molecular phylogeny of Homoscleromorpha based on nuclear (18S and 28S rDNA) and complete mitochondrial DNA sequence data that focuses on inter-generic relationships. Our results revealed two robust clades within this group, one containing the spiculate species (genera Plakina, Plakortis, Plakinastrella and Corticium) and the other containing aspiculate species (genera Oscarella and Pseudocorticium), thus rejecting a close relationship between Pseudocorticium and Corticium. Among the spiculate species, we found affinities between the Plakortis and Plakinastrella genera, and between the Plakina and Corticium. The validity of these clades is furthermore supported by specific morphological characters, notably the type of spicules. Furthermore, the monophyly of the Corticium genus is supported while the monophyly of Plakina is not. As the result of our study we propose to restore the pre-1995 subdivision of Homoscleromorpha into two families: Plakinidae Schulze, 1880 for spiculate species and Oscarellidae Lendenfeld, 1887 for aspiculate species that had been rejected after the description of the genus Pseudocorticium. We also note that the two families of homoscleromorphs exhibit evolutionary stable, but have drastically distinct mitochondrial genome organizations that differ in gene content and gene order.
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Math Sense: Algebra and Geometry.
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
College geometry a unified development
Kay, David C
2011-01-01
""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273
GEOMETRY AND COMPLEXITY IN ARCHITECTURE
Directory of Open Access Journals (Sweden)
RUSU Maria Ana
2015-06-01
Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Algebraic Methods in Plane Geometry
Indian Academy of Sciences (India)
Srimath
group, taxicab number, Carmi- chael number. Algebraic Methods in Plane Geometry. 2. Cubic Curves. Shailesh A Shirali. Shailesh Shirali heads a. Community Mathematics. Center at Rishi Valley. School (KFI). He has a ..... Ian Stewart and David Tall, Algebraic Number Theory and Fermat's Last. Theorem, A K Peters, 2002.
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Learners engaging with transformation geometry
African Journals Online (AJOL)
able to move flexibly between the modes and who displayed a deep understanding of the concepts. ... However the strand remains in the curriculum for Grades R to 9, and will still provide rich learning opportunities ... There is limited available research on learners' understanding and learning of transformation geometry.
Optimization Problems in Elementary Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 6. Optimization Problems in Elementary Geometry. A K Mallik. General Article Volume 13 Issue 6 June 2008 pp 561-582 ... Author Affiliations. A K Mallik1. Department Of Mechanical Engineering, Indian Institute of Technology, Kanpur, India.
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
M. Deza; M. Laurent (Monique)
1997-01-01
htmlabstractCuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book offers a
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Axiomatic Differential Geometry Ⅱ-4
Nishimura, Hirokazu
2012-01-01
In our previous paper (Axiomatic Differential Geometry II-3) we havediscussed the general Jacobi identity, from which the Jacobi identity ofvector fields follows readily. In this paper we derive Jacobi-like identitiesof tangent-vector-valued forms from the general Jacobi identity.
Axiomatic Differential Geometry II-3
Nishimura, Hirokazu
2012-01-01
As the fourth paper of our series of papers concerned with axiomatic differential geometry, this paper is devoted to the general Jacobi identity supporting the Jacobi identity of vector fields. The general Jacobi identity can be regarded as one of the few fundamental results belonging properly to smootheology.
Axiomatic Differential Geometry II-4
Nishimura, Hirokazu
2012-01-01
In our previous paper (Axiomatic Differential Geometry II-3) we have discussed the general Jacobi identity, from which the Jacobi identity of vector fields follows readily. In this paper we derive Jacobi-like identities of tangent-vector-valued forms from the general Jacobi identity.
Improving Student Reasoning in Geometry
Wong, Bobson; Bukalov, Larisa
2013-01-01
In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…
Fubini theorem in noncommutative geometry
Sukochev, Fedor; Zanin, Dmitriy
2016-01-01
We discuss the Fubini formula in Alain Connes' noncommutative geometry. We present a sufficient condition on spectral triples for which a Fubini formula holds true. The condition is natural and related to heat semigroup asymptotics. We provide examples of spectral triples for which the Fubini formula fails.
Indian Academy of Sciences (India)
Limit: (of a sequence) A point such that the points of the sequence eventually approach it to within any previously specified distance. Some of the Greek mathematicians were quite confused! For example, let us take an empty cup and put it under a tap. Assume that it is half full in a minute. It is then 3/4-th full in another half.
Indian Academy of Sciences (India)
cartographer in the days before aerial travel) can determine the curvature. Hence the beauty of a surface is skin deep and yet is naturally associated with it! SERIES I ARTICLE cartographic surveys he was carrying out for the ruler of Germany) gave a new interpretation to Euler's theory. First consider the length of the vector t ...
Indian Academy of Sciences (India)
In order to utilise this Descartes devised the following scheme. By. fIXing a point, the origin, on a line it becomes possible to talk of a directed distance as a positive or negative number depending on whether the end point is to one or the other side of the origin. Similarly, he assigned a pair of numbers to every point of the.
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Geometry of area without length
Ho, Pei-Ming; Inami, Takeo
2016-01-01
To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
The geometry of celestial mechanics
Geiges, Hansjörg
2016-01-01
Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
General Relativity by Kawaguchi geometry
Directory of Open Access Journals (Sweden)
Tanaka Erico
2013-09-01
Full Text Available We construct a parameterisation invariant Lagrange theory of fields up to second order by using multivector bundles and Kawaguchi geometry. In this setup, the spacetime is an dynamical object which is a submanifold of the greater manifold, and the actual spacetime is the solution of Euler-Lagrange equations. Such theory is a reasonable mathematical foundation to describe an extended theory of Einstein’s general relativity, and is capable of being a stage for unification with other physical fields.
Geometry Dependence of Stellarator Turbulence
Energy Technology Data Exchange (ETDEWEB)
H.E. Mynick, P. Xanthopoulos and A.H. Boozer
2009-08-10
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Origin and plasticity of the subdivisions of the inferior olivary complex.
Hidalgo-Sánchez, Matías; Backer, Stéphanie; Puelles, Luis; Bloch-Gallego, Evelyne
2012-11-15
The precerebellar nuclei (PCN) originate from the rhombic lip, a germinal neuroepithelium adjacent to the roof plate of the fourth ventricle. We first report here that, in chicken, the Brn3a-expressing postmitotic medullary cells that produce the inferior olive (ION, the source of cerebellar climbing fibres) originate from a dorso-ventral domain roughly coinciding with the hindbrain vestibular column. Whereas Foxd3 expression labels the whole mature ION but is only detected in a subpopulation of ION neuroblasts initiating their migration, we report that Brn3a allows the visualization of the whole population of ION neurons from the very beginning of their migration. We show that Brn3a-positive neurons migrate tangentially ventralwards through a characteristic dorso-ventral double submarginal stream. Cath1 expressing progenitors lying just dorsal to the ION origin correlated dorso-ventral topography with the prospective cochlear column (caudal to it) and generate precerebellar nuclei emitting mossy-fiber cerebellar afferents. We used the chick-quail chimaera technique with homotopic grafts at HH10 to determine the precise fate map of ION precursors across the caudal cryptorhombomeric subdivisions of the medullary hindbrain (r8-r11). We demonstrate that each crypto-rhombomere contributes to two lamellae of the ION, while each ION sub-nucleus originates from at least two contiguous crypto-rhombomeres. We then questioned how rhombomere identity is related to the plasticity of cell type specification in the dorsal hindbrain. The potential plasticity of ectopically HH10 grafted ION progenitors to change their original fate in alternative rostrocaudal environments was examined. Heterotopic grafts from the presumptive ION territory to the pontine region (r4-r5) caused a change of fate, since the migrated derivatives adopted a pontine phenotype. The reverse experiment caused pontine progenitors to produce derivatives appropriately integrated into the ION complex. Grafts of
A new subdivision of the central Sesia Zone (Aosta Valley, Italy)
Giuntoli, Francesco; Engi, Martin; Manzotti, Paola; Ballèvre, Michel
2015-04-01
The Sesia Zone in the Western Alps is a continental terrane probably derived from the NW-Adriatic margin and polydeformed at HP conditions during Alpine convergence. Subdivisions of the Sesia Zone classically have been based on the dominant lithotypes: Eclogitic Micaschist Complex, Seconda Zona Diorito-Kinzigitica, and Gneiss Minuti Complex. However, recent work (Regis et al., 2014) on what was considered a single internal unit has revealed that it comprises two or more tectonic slices that experienced substantially different PTDt-evolutions. Therefore, detailed regional petrographic and structural mapping (1:3k to 1:10k) was undertaken and combined with extensive sampling for petrochronological analysis. Results allow us to propose a first tectonic scheme for the Sesia Zone between the Aosta Valley and Val d'Ayas. A set of field criteria was developed and applied, aiming to recognize and delimit the first order tectonic units in this complex structural and metamorphic context. The approach rests on three criteria used in the field: (1) Discontinuously visible metasedimentary trails (mostly carbonates) considered to be monocyclic (Permo-Mesozoic protoliths); (2) mappable high-strain zones; and (3) visible differences in the metamorphic imprint. None of these key features used are sufficient by themselves, but in combination they allow us to propose a new map that delimits main units. We propose an Internal Complex with three eclogitic sheets, each 0.5-3 km thick. Dominant lithotypes include micaschists associated with mafic rocks and minor orthogneiss. The main foliation is of HP, dipping moderately NW. Each of these sheets is bounded by (most likely monometamorphic) sediments, glaucophane, and garnet occur as relics. Towards the SW, the width of the Intermediate Complex is reduced from 0.5 km to a few meters. In the External Complex several discontinuous lenses occur; these comprise 2DK-lithotypes and are aligned with greenschist facies shear zones mapped within
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Introduction to geometry and relativity
2013-01-01
This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: Detailed solutions are provided to the Exercises in each chapter; Many of the missing steps that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand; A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area; In its treatment of modern differential geometry, the book employs both a modern, c...
Aspects of differential geometry II
Gilkey, Peter
2015-01-01
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Geometry success in 20 minutes a day
LLC, LearningExpress
2014-01-01
Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr
Uysal, Tancan; Kurt, Gokmen; Ramoglu, Sabri Ilhan
2009-01-01
To compare the degree of intra- and interarch dentoalveolar asymmetry among patients with a normal occlusion, Class II Division 1 malocclusion, and Class II subdivision malocclusion. The sample comprised dental casts of 150 (72 males [ages 22. 1 +/- 3.11 and 78 females [ages 21.1 +/- 2.1]) normal occlusion subjects, 106 (45 males [ages 17.8 +/- 1.8] and 61 females [ages 16.5 +/- 2.91) Class II Division 1 patients, and 40 (18 males [ages 15.8 +/- 2.8] and 22 females [ages 15.2 +/- 3.3]) Class II subdivision malocclusions. Maxillary and mandibular reference lines were constructed and used for the intraarch asymmetry measurements. Thirty-six width measurements were performed on the dental casts of each subject. Analysis of variance (ANOVA) was used for comparisons of the groups, and Pearson's correlation coefficients were computed to determine the interarch associations. No statistically significant intra-arch asymmetry was found for maxillary and mandibular dental arch and alveolar width in any of the three groups. All variables were larger on the right side in the normal occlusion subjects. Further, the left side maxillary dental and alveolar arch width measurements were larger in the Class II Division 1 group. None of these differences, however, were statistically significant. In the Class II subdivision group, only the Class II sides' mandibular dental arch measurements were larger (P dental arch and alveolar width dimensions differed among the groups (P dental and alveolar landmarks were significantly correlated with the transverse dimensions. Although some landmarks in the current study showed statistically significant and insignificant differences, the mean arithmetic differences were small, inconsistent, and not likely clinically important.
Blow-Ups in Generalized Complex Geometry
van der Leer Duran, J.L.
2016-01-01
Generalized complex geometry is a theory that unifies complex geometry and symplectic geometry into one single framework. It was introduced by Hitchin and Gualtieri around 2002. In this thesis we address the following question: given a generalized complex manifold together with a submanifold, does
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
Directory of Open Access Journals (Sweden)
Bruchholz U. E.
2009-10-01
Full Text Available The geometry of the space-time is deduced from gravitational and electromagnetic fields. We have to state that Rainich's "already unified field theory" is the ground work of the proposed theory. The latter is deduced independently on Rainich. Rainich's analogies are brilliantly validated. His formulae are verified this way. Further reaching results and insights demonstrate that Rainich's theory is viable. In final result, we can formulate an enhanced equivalence principle. It is the equivalence of Newton's force with the Lorentz force.
The Geometry Of Preposition Meanings
Directory of Open Access Journals (Sweden)
Peter Gärdenfors
2015-12-01
Full Text Available This article presents a unified approach to the semantics of prepositions based on the theory of conceptual spaces. Following the themes of my recent book The Geometry of Meaning, I focus on the convexity of their meanings and on which semantic domains are expressed by prepositions. As regards convexity, using polar coordinates turns out to provide the most natural representation. In addition to the spatial domain, I argue that for many prepositions, the force domain is central. In contrast to many other analyses, I also defend the position that prepositions have a central meaning and that other meanings can be derived via a limited class of semantic transformations.
The geometry of musical chords.
Tymoczko, Dmitri
2006-07-07
A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Integral geometry and representation theory
Gel'fand, I M; Vilenkin, N Ya
1966-01-01
Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one.This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of comp
Projective differential geometry of submanifolds
Akivis, M A
1993-01-01
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are s
An invitation to noncommutative geometry
Marcolli, Matilde
2008-01-01
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Number Theory, Analysis and Geometry
Goldfeld, Dorian; Jones, Peter
2012-01-01
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, th
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
Exceptional geometry and Borcherds superalgebras
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Palmkvist, Jakob [Mitchell Institute for Fundamental Physics and Astronomy, Texas A& M University,College Station, TX 77843 (United States)
2015-11-05
We study generalized diffeomorphisms in exceptional geometry with U-duality group E{sub n(n)} from an algebraic point of view. By extending the Lie algebra e{sub n} to an infinite-dimensional Borcherds superalgebra, involving also the extension to e{sub n+1}, the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n≤7. The closure of the transformations then follows from the Jacobi identity and the grading of e{sub n+1} with respect to e{sub n}.
Exceptional geometry and Borcherds superalgebras
Palmkvist, Jakob
2015-11-01
We study generalized diffeomorphisms in exceptional geometry with U-duality group E n( n) from an algebraic point of view. By extending the Lie algebra {e}_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to {e}_{n+1} , the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n ≤ 7. The closure of the transformations then follows from the Jacobi identity and the grading of {e}_{n+1} with respect to {e}_n.
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Gesik, Nicole Y; Tan, Sabrina K G; Prentiss, Gale T; Fitzsimmons, Sean; Nichols, Andrew W
2013-11-01
To determine the frequency of pregame intravenous fluid hyperhydration (PIVFH) usage, administration protocols, indications, complications, and perceived efficacy by National Collegiate Athletic Association Football Bowl Subdivision (NCAA-FBS) teams. Cross-sectional survey study. National Collegiate Athletic Association Football Bowl Subdivision. Head athletic trainers from NCAA-FBS institutions. Voluntary, anonymous 15-item validated online survey instrument. Number of teams reporting use of PIVFH. The survey response rate was 64% (77 of 120). Thirty percent of respondents reported the utilization of PIVFH, administered to an average of 2 to 3 players. The most common reasons cited for using PIVFH were to prevent muscle cramps (95%), heat illness (79%), and dehydration (68%). Additionally, 47% of programs used PIVFH to improve player exercise tolerance and 47% per player request. Twenty-four percent of programs that used PIVFH reported the occurrence of associated complications. Only 15% of respondents believed that PIVFH improved their teams' overall performance. PIVFH is a common practice among NCAA-FBS teams. PIVFH is used most often to prevent muscle cramps, dehydration, and heat illness. The relatively few numbers of players per team who receive PIVFH suggest that higher risk individuals were targeted for administration.
Szucs, Kimberly A; Molnar, Megan
2017-04-01
The aim of this study was to provide a description of gender differences of the activation patterns of the four subdivisions of the trapezius (clavicular, upper, middle, lower) following a 60min computer work task. Surface EMG was collected from these subdivisions from 21 healthy subjects during bilateral arm elevation pre-/post- task. Subjects completed a standardized 60min computer work task at a standard, ergonomic workstation. Normalized activation and activation ratios of each trapezius subdivision were compared between genders and condition with repeated measures ANOVAs. The interaction effect of Gender×Condition for upper trapezius% activation approached significance at p=0.051with males demonstrating greater activation post-task. The main effect of Condition was statistically significant for% activation of middle and lower trapezius (pcomputer typing task. Imbalances in muscle activation and activation ratios following computer work may affect total shoulder kinematics and should be further explored. Copyright © 2017 Elsevier B.V. All rights reserved.
Computational geometry algorithms and applications
de Berg, Mark; Overmars, Mark; Schwarzkopf, Otfried
1997-01-01
Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can ...
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Entanglement classification with algebraic geometry
Sanz, M.; Braak, D.; Solano, E.; Egusquiza, I. L.
2017-05-01
We approach multipartite entanglement classification in the symmetric subspace in terms of algebraic geometry, its natural language. We show that the class of symmetric separable states has the structure of a Veronese variety and that its k-secant varieties are SLOCC invariants. Thus SLOCC classes gather naturally into families. This classification presents useful properties such as a linear growth of the number of families with the number of particles, and nesting, i.e. upward consistency of the classification. We attach physical meaning to this classification through the required interaction length of parent Hamiltonians. We show that the states W N and GHZ N are in the same secant family and that, effectively, the former can be obtained in a limit from the latter. This limit is understood in terms of tangents, leading to a refinement of the previous families. We compute explicitly the classification of symmetric states with N≤slant4 qubits in terms of both secant families and its refinement using tangents. This paves the way to further use of projective varieties in algebraic geometry to solve open problems in entanglement theory.
Foundations of arithmetic differential geometry
Buium, Alexandru
2017-01-01
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Directory of Open Access Journals (Sweden)
Julia Ganz
2014-12-01
Full Text Available Background: The telencephalon shows a remarkable structural diversity among vertebrates. In particular, the everted telencephalon of ray-finned fishes has a markedly different morphology compared to the evaginated telencephalon of all other vertebrates. This difference in development has hampered the comparison between different areas of the pallium of ray-finned fishes and the pallial nuclei of all other vertebrates. Various models of homology between pallial subdivisions in ray-finned fishes and the pallial nuclei in tetrapods have been proposed based on connectional, neurochemical, gene expression and functional data. However, no consensus has been reached so far. In recent years, the analysis of conserved developmental marker genes has assisted the identification of homologies for different parts of the telencephalon among several tetrapod species. Results: We have investigated the gene expression pattern of conserved marker genes in the adult zebrafish (Danio rerio pallium to identify pallial subdivisions and their homology to pallial nuclei in tetrapods. Combinatorial expression analysis of ascl1a, eomesa, emx1, emx2, emx3, and Prox1 identifies four main divisions in the adult zebrafish pallium. Within these subdivisions, we propose that Dm is homologous to the pallial amygdala in tetrapods and that the dorsal subdivision of Dl is homologous to part of the hippocampal formation in mouse. We have complemented this analysis be examining the gene expression of emx1, emx2 and emx3 in the zebrafish larval brain. Conclusions: Based on our gene expression data, we propose a new model of subdivisions in the adult zebrafish pallium and their putative homologies to pallial nuclei in tetrapods. Pallial nuclei control sensory, motor, and cognitive functions, like memory, learning and emotion. The identification of pallial subdivisions in the adult zebrafish and their homologies to pallial nuclei in tetrapods will contribute to the use of the zebrafish
Directory of Open Access Journals (Sweden)
Silas Arandas Monteiro e Silva
2013-12-01
Full Text Available Os frutos de cacau (Theobroma cacao são conhecidos mundialmente pela sua riqueza em ácidos graxos e compostos fenólicos com poder antioxidante, sendo que em sua constituição é possível relatar mais de 50% em ácidos graxos de cadeia média que o torna matéria-prima passível de ser explorada pela indústria alimentícia, farmacêutica e cosmética. Este trabalho teve como objetivo estudar o poder antioxidante do extrato seco de cacau orgânico, obter formulações cosméticas acrescidas deste extrato, promovendo os estudos de estabilidade, ensaios reológicos e a investigação de cristais-líquidos, bem como realizar o teste de aceitação das mesmas. O extrato vegetal foi avaliado quanto seu poder antioxidante pelo método de sequestro radicalar DPPH. Formulações cosméticas foram obtidas e amostras foram submetidas a ensaios físico-químicos de estabilidade (caracterização organoléptica, teste de centrífuga e determinação dos valores de pH, caracterização reológica, assim como análises em microscopia de luz polarizada. As preparações estáveis também foram avaliadas quanto a sua aceitabilidade por provadores. A partir dos resultados apresentados pôde-se constatar a atividade antioxidante do extrato seco de cacau orgânico e obter preparações cosméticas, constituídas deste ativo a 5%, com comportamento pseudoplástico associado à tixotropia e providas de cristais líquidos lamelares. Verificou-se também que a concentração de cera autoemulsionante interferiu na aceitação do produto cosmético.
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Serra-Negra, Júnia Maria Cheib
2006-01-01
Full Text Available O objetivo do presente trabalho foi verificar o relacionamento entre os hábitos bucais das mães e os hábitos bucais dos filhos. Desenvolveu-se um estudo epidemiológico retrospectivo transversal com a entrevista, através de formulário pré-testado, de 208 mães na sala de espera das clínicas coordenadas pelo Departamento de Odontopediatria e Ortodontia da FOUFMG. Os dados coletados foram submetidos a análise estatística, sendo o qui-quadrado e odds ratio os testes escolhidos. Observou-se que a chupeta foi o hábito mais prevalente na infância tanto das mães quanto das crianças (46,6% e 65,4% respectivamente. A onicofagia foi o hábito atual mais prevalente nos dois grupos (38,7% mães e 32,7% crianças. Verificou-se que filhos de mães que utilizaram a chupeta na infância apresentaram um risco de 3,4 vezes maior (OR = 3,4 de também apresentarem o hábito de sucção de chupeta comparados aos filhos de mães que não apresentaram este hábito. Constatou-se que filhos de mães com hábito de onicofagia apresentaram quase quatro vezes mais chance de também apresentarem este costume (OR = 3,9. Dentre as portadoras de hábitos, 72,6% considera que estes as prejudicaram ou a seus filhos em algum fator, sendo a desarmonia dos dentes o item mais citado pelas mães (71,9%. Encontrou-se associação entre os hábitos bucais das mães e das crianças, havendo uma tendência de repetição destes pelos filhos. A maioria das mães tem conhecimento de que os hábitos bucais deletérios trazem prejuízos à conformação das arcadas dentárias, porém a repetição destes costumes pelos filhos foi freqüente
Some Progress in Conformal Geometry
Directory of Open Access Journals (Sweden)
Sun-Yung A. Chang
2007-12-01
Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.
Kinematic dynamos in spheroidal geometries
Ivers, D. J.
2017-10-01
The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤a/c≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Hue geometry and horizontal connections.
Ben-Shahar, Ohad; Zucker, Steven W
2004-01-01
Primate visual systems support an elaborate specialization for processing color information. Concentrating on the hue component, we observe that, contrary to Mondrian-like assumptions, hue varies in a smooth manner for ecologically important natural imagery. To represent these smooth variations, and to support those information processing tasks that utilize hue, a piecewise smooth hue field is postulated. The geometry of hue-patch interactions is developed analogously to orientation-patch interactions in texture. The result is a model for long-range (horizontal) interactions in the color domain, the power of which is demonstrated on a number of examples. Implications for computer image processing, computer vision, visual neurophysiology and psychophysics are discussed.
Spinors in Physics and Geometry
Trautman, A.; Furlan, G.
1988-11-01
The Table of Contents for the full book PDF is as follows: * Preface * Killing Spinors According to O. Hijazi and Applications * Self-Duality Conditions Satisfied by the Spin Connections on Spheres * Maslov Index and Half - Forms * Spin - 3/2 Fields on Black Hole Spacetimes * Indecomposable Conformal Spinors and Operator Product Expansions in a Massless QED Model * Nonlinear Spinor Representations * Nonlinear Wave Equations for Intrinsic Spinor Coordinates * Twistors - "Spinors" of SU(2,2), Their Generalizations and Achievements * Spinors, Reflections and Clifford Algebras: A Review * overline {SL}(n, R) Spinors for Particles, Gravity and Superstrings * Spinors on Compact Riemann Surfaces * Simple Spinors as Urfelder * Applications of Cartan Spinors to Differential Geometry in Higher Dimensions * Killing Spinors on Spheres and Projective Spaces * Spinor Structures on Homogeneous Riemannian Spaces * Classical Strings and Minimal Surfaces * Representing Spinors with Differential Forms * Inequalities for Spinors Norms in Clifford Algebras * The Importance of Spin * The Theory of World Spinors * Final List of Participants
The geometry of dynamical triangulations
Ambjørn, Jan; Marzuoli, Annalisa
1997-01-01
We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.
Conformal geometry and quasiregular mappings
Vuorinen, Matti
1988-01-01
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook an...
Dialogues about geometry and light
Bermudez, David; Leonhardt, Ulf
2015-01-01
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to what was later known as optics. On the other hand, geometry is a branch of mathematics that was born from practical studies concerning lengths, areas and volumes in the early cultures, although it was not put into axiomatic form until the 3rd century BC. In this work, we will discuss the connection between these two timeless topics and show some new things in old things". There has been several works in this direction, but taking into account the didactic approach of the Enrico Fermi Summer School, we would like to address the subject and our audience in a new light.
Integrable systems, geometry, and topology
Terng, Chuu-Lian
2006-01-01
The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of ...
Noncommutative geometry of multicore bions
Karczmarek, Joanna L.; Sibilia, Ariel
2013-01-01
We find new BPS solutions to the nonabelian theory on a world-volume of parallel D1-branes. Our solutions describe two parallel, separated bundles of N D1-branes expanding out to form a single orthogonal D3-brane. This configuration corresponds to two charge N magnetic monopoles in the world-volume of a single D3-brane, deforming the D3-brane into two parallel spikes. We obtain the emergent surface corresponding to our nonabelian D1-brane configuration and demonstrate, at finite N , a surprisingly accurate agreement with the shape of the D3-brane world-volume as obtained from the abelian Born-Infeld action. Our solution provides an explicit realization of topology change in noncommutative geometry at finite N.
Digital breast tomosynthesis geometry calibration
Wang, Xinying; Mainprize, James G.; Kempston, Michael P.; Mawdsley, Gordon E.; Yaffe, Martin J.
2007-03-01
Digital Breast Tomosynthesis (DBT) is a 3D x-ray technique for imaging the breast. The x-ray tube, mounted on a gantry, moves in an arc over a limited angular range around the breast while 7-15 images are acquired over a period of a few seconds. A reconstruction algorithm is used to create a 3D volume dataset from the projection images. This procedure reduces the effects of tissue superposition, often responsible for degrading the quality of projection mammograms. This may help improve sensitivity of cancer detection, while reducing the number of false positive results. For DBT, images are acquired at a set of gantry rotation angles. The image reconstruction process requires several geometrical factors associated with image acquisition to be known accurately, however, vibration, encoder inaccuracy, the effects of gravity on the gantry arm and manufacturing tolerances can produce deviations from the desired acquisition geometry. Unlike cone-beam CT, in which a complete dataset is acquired (500+ projections over 180°), tomosynthesis reconstruction is challenging in that the angular range is narrow (typically from 20°-45°) and there are fewer projection images (~7-15). With such a limited dataset, reconstruction is very sensitive to geometric alignment. Uncertainties in factors such as detector tilt, gantry angle, focal spot location, source-detector distance and source-pivot distance can produce several artifacts in the reconstructed volume. To accurately and efficiently calculate the location and angles of orientation of critical components of the system in DBT geometry, a suitable phantom is required. We have designed a calibration phantom for tomosynthesis and developed software for accurate measurement of the geometric parameters of a DBT system. These have been tested both by simulation and experiment. We will present estimates of the precision available with this technique for a prototype DBT system.
N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
Lerche, Wolfgang; Warner, Nicholas P
2002-01-01
We study the superpotential of a certain class of N=1 supersymmetric type II compactifications with fluxes and D-branes. We show that it has an important two-dimensional meaning in terms of a chiral ring of the topologically twisted theory on the world-sheet. In the open-closed string B-model, this chiral ring is isomorphic to a certain relative cohomology group V, which is the appropriate mathematical concept to deal with both the open and closed string sectors. The family of mixed Hodge structures on V then implies for the superpotential to have a certain geometric structure. This structure represents a holomorphic, N=1 supersymmetric generalization of the well-known N=2 special geometry. It defines an integrable connection on the topological family of open-closed B-models, and a set of special coordinates on the space \\cal M of vev's in N=1 chiral multiplets. We show that it can be given a very concrete and simple realization for linear sigma models, which leads to a powerful and systematic method for comp...
Automorphisms in Birational and Affine Geometry
Ciliberto, Ciro; Flenner, Hubert; McKernan, James; Prokhorov, Yuri; Zaidenberg, Mikhail
2014-01-01
The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference high...
Subsectors, Dynkin diagrams and new generalised geometries
Strickland-Constable, Charles
2017-08-01
We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups Spin( d, d) × ℝ + for which the generalised tangent space transforms in a spinor representation of the group. In low dimensions these all appear in subsectors of maximal supergravity theories. The case d = 8 provides a geometry for eight-dimensional backgrounds of M theory with only seven-form flux, which have not been included in any previous geometric construction. This geometry is also one of a series of "half-exceptional" geometries, which "geometrise" a six-form gauge field. In the appendix, we consider exam-ples of other algebras appearing in gravitational theories and give a method to derive the Dynkin labels for the "section condition" in general. We argue that generalised geometry can describe restrictions and subsectors of many gravitational theories.
Connections between algebra, combinatorics, and geometry
Sather-Wagstaff, Sean
2014-01-01
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...
Classical geometry Euclidean, transformational, inversive, and projective
Leonard, I E; Liu, A C F; Tokarsky, G W
2014-01-01
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p
A vector space approach to geometry
Hausner, Melvin
2010-01-01
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
This report documents the activities performed and the results obtained from the arsenic removal treatment technology demonstration project at the Geneseo Hills Subdivision in Geneseo, IL. The main objective of the project was to evaluate the effectiveness of AdEdge Technologies...
Sinninghe Damsté, J.S.; Rijpstra, W.I.C.; Hopmans, E.C.; Weijers, J.W.H.; Foesel, B.U.; Overmann, J.; Dedysh, S.N.
2011-01-01
The distribution of membrane lipids of 17 different strains representing 13 species of subdivisions 1 and 3 of the phylum Acidobacteria, a highly diverse phylum of the Bacteria, were examined by hydrolysis and gas chromatography-mass spectrometry (MS) and by high-performance liquid
Omori, O; Umetani, T; Sugioka, K
1997-02-01
Differential projections from the subdivisions of the fastigial nucleus to the vestibular complex and the prepositus hypoglossal nucleus were investigated by an anterograde tracing method using biocytin in the albino rat. The caudomedial subdivision of the nucleus projected ipsilaterally to the dorsal and medial parts of the superior vestibular nucleus (Su Ve), the dorsomedial part of the lateral vestibular nucleus (LVe), and the dorsal parts of the medial (MVe) and spinal (Sp Ve) vestibular nuclei, and projected contralaterally to the ventrolateral corners of the Su Ve and LVe, the ventral part of the MVe, and the lateral part of the Sp Ve. The bilateral prepositus hypoglossal nuclei received sparse projections from the caudomedial subdivision. The middle subdivision of the fastigial nucleus projected ipsilaterally to the dorsal and/or ventral parts of the Su Ve, the dorsomedial pats of the LVe and Sp Ve, and the dorsolateral part of the MVe, and projected contralaterally to the dorsal margin of the Su Ve, the ventrolateral part of the LVe, and the lateral part of the Sp Ve. The dorsolateral protuberance of the fastigial nucleus projected ipsilaterally to the dorsal margin of the Su Ve, the dorsomedial part of the LVe, the dorsal or lateral parts of the Sp Ve, and the lateral part of the MVe, and projected contralaterally to the ventrolateral part of the LVe and the lateral part of the Sp Ve. The subnuclei x, y, and f, interstitial nucleus of the vestibular nerve, and the infracerebellar nucleus received bilateral or ipsilateral fastigiovestibular projections.
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false May a State, or any political subdivision thereof, certify to a disposal agency that it needs a surplus power transmission line and the right-of-way acquired for its construction to meet the requirements of a public or cooperative power project? 102-75.370 Section 102...
Applications of Affine and Weyl geometry
García-Río, Eduardo; Nikcevic, Stana
2013-01-01
Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia
Introduction to non-Euclidean geometry
Wolfe, Harold E
2012-01-01
One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Latent geometry of bipartite networks
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
The geometry of population genetics
Akin, Ethan
1979-01-01
The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele...
Linguistic geometry for technologies procurement
Stilman, Boris; Yakhnis, Vladimir; Umanskiy, Oleg; Boyd, Ron
2005-05-01
In the modern world of rapidly rising prices of new military hardware, the importance of Simulation Based Acquisition (SBA) is hard to overestimate. With SAB, DOD would be able to test, develop CONOPS for, debug, and evaluate new conceptual military equipment before actually building the expensive hardware. However, only recently powerful tools for real SBA have been developed. Linguistic Geometry (LG) permits full-scale modeling and evaluation of new military technologies, combinations of hardware systems and concepts of their application. Using LG tools, the analysts can create a gaming environment populated with the Blue forces armed with the new conceptual hardware as well as with appropriate existing weapons and equipment. This environment will also contain the intelligent enemy with appropriate weaponry and, if desired, with a conceptual counters to the new Blue weapons. Within such LG gaming environment, the analyst can run various what-ifs with the LG tools providing the simulated combatants with strategies and tactics solving their goals with minimal resources spent.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Shimizu, Kenji; Ikura, Hirohiko; Ikezoe, Junpei; Nagareda, Tomofumi; Yagi, Naoto; Umetani, Keiji; Imai, Yutaka
2004-04-01
We have previously reported a synchrotron radiation (SR) microtomography system constructed at the bending magnet beamline at the SPring-8. This system has been applied to the lungs obtained at autopsy and inflated and fixed by Heitzman"s method. Normal lung and lung specimens with two different types of pathologic processes (fibrosis and emphysema) were included. Serial SR microtomographic images were stacked to yield the isotropic volumetric data with high-resolution (12 μm3 in voxel size). Within the air spaces of a subdivision of the acinus, each voxel is segmented three-dimensionally using a region growing algorithm ("rolling ball algorithm"). For each voxel within the segmented air spaces, two types of voxel coding have been performed: single-seeded (SS) coding and boundary-seeded (BS) coding, in which the minimum distance from an initial point as the only seed point and all object boundary voxels as a seed set were calculated and assigned as the code values to each voxel, respectively. With these two codes, combinations of surface rendering and volume rendering techniques were applied to visualize three-dimensional morphology of a subdivision of the acinus. Furthermore, sequentially filling process of air into a subdivision of the acinus was simulated under several conditions to visualize the ventilation procedure (air flow and diffusion). A subdivision of the acinus was reconstructed three-dimensionally, demonstrating the normal architecture of the human lung. Significant differences in appearance of ventilation procedure were observed between normal and two pathologic processes due to the alteration of the lung architecture. Three-dimensional reconstruction of the microstructure of a subdivision of the acinus and visualization of the ventilation procedure (air flow and diffusion) with SR microtomography would offer a new approach to study the morphology, physiology, and pathophysiology of the human respiratory system.
PREFACE: Water in confined geometries
Rovere, Mauro
2004-11-01
The study of water confined in complex systems in solid or gel phases and/or in contact with macromolecules is relevant to many important processes ranging from industrial applications such as catalysis and soil chemistry, to biological processes such as protein folding or ionic transport in membranes. Thermodynamics, phase behaviour and the molecular mobility of water have been observed to change upon confinement depending on the properties of the substrate. In particular, polar substrates perturb the hydrogen bond network of water, inducing large changes in the properties upon freezing. Understanding how the connected random hydrogen bond network of bulk water is modified when water is confined in small cavities inside a substrate material is very important for studies of stability and the enzymatic activity of proteins, oil recovery or heterogeneous catalysis, where water-substrate interactions play a fundamental role. The modifications of the short-range order in the liquid depend on the nature of the water-substrate interaction, hydrophilic or hydrophobic, as well as on its spatial range and on the geometry of the substrate. Despite extensive study, both experimentally and by computer simulation, there remain a number of open problems. In the many experimental studies of confined water, those performed on water in Vycor are of particular interest for computer simulation and theoretical studies since Vycor is a porous silica glass characterized by a quite sharp distribution of pore sizes and a strong capability to absorb water. It can be considered as a good candidate for studying the general behaviour of water in hydrophilic nanopores. But there there have been a number of studies of water confined in more complex substrates, where the interpretation of experiments and computer simulation is more difficult, such as in zeolites or in aerogels or in contact with membranes. Of the many problems to consider we can mention the study of supercooled water. It is
Quantum groups: Geometry and applications
Energy Technology Data Exchange (ETDEWEB)
Chu, Chong -Sun [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group; Univ. of California, Berkeley, CA (United States)
1996-05-13
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.
Algebra and Geometry of Hamilton's Quaternions
Indian Academy of Sciences (India)
IAS Admin
Inspired by the relation between the algebra of complex numbers and plane geometry, William. Rowan Hamilton sought an algebra of triples for application to three-dimensional geometry. Un- able to multiply and divide triples, he invented a non-commutative division algebra of quadru- ples, in what he considered his most ...
Cognitive Styles, Dynamic Geometry and Measurement Performance
Pitta-Pantazi, Demetra; Christou, Constantinos
2009-01-01
This paper reports the outcomes of an empirical study undertaken to investigate the effect of students' cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students' learning. A total of 49…
Reasoning by Contradiction in Dynamic Geometry
Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra
2013-01-01
This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…
Visual and Analytic Strategies in Geometry
Kospentaris, George; Vosniadou, Stella; Kazic, Smaragda; Thanou, Emilian
2016-01-01
We argue that there is an increasing reliance on analytic strategies compared to visuospatial strategies, which is related to geometry expertise and not on individual differences in cognitive style. A Visual/Analytic Strategy Test (VAST) was developed to investigate the use of visuo-spatial and analytic strategies in geometry in 30 mathematics…
Symposium on Differential Geometry and Differential Equations
Berger, Marcel; Bryant, Robert
1987-01-01
The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.
A Multivariate Model of Achievement in Geometry
Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha
2014-01-01
Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…
Making Euclidean Geometry Compulsory: Are We Prepared?
Van Putten, Sonja; Howie, Sarah; Stols, Gerrit
2010-01-01
This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…
Applications Of Nonclassical Geometry To String Theory
Zunger, Y
2003-01-01
String theory is built on a foundation of geometry. This thesis examines several applications of geometry beyond the classical Riemannian geometry of curved surfaces. The first part considers the use of extended spaces with internal dimensions to each point (“twistors”) to probe systems with a great deal of symmetry but complicated dynamics. These systems are of critical interest in understanding holographic phenomena in string theory and the origins of entropy. We develop a twistor formulation of coset spaces and use this to write simplified actions for particles and strings on anti-de Sitter space, which are easier to quantize than the ordinary (highly nonlinear) actions. In the second part, we consider two aspects of noncommutative geometry, a generalization of ordinary geometry where points are “fuzzed out” and functions of space become noncommuting operators. We first examine strings with one endpoint on a D-brane in a background magnetic field. (Strings with both ...
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS
Energy Technology Data Exchange (ETDEWEB)
Singer, Isadore M.
2008-03-04
The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis
2017-01-01
Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…
Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry
Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare
2013-01-01
A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
Mammana, M. F.; Micale, B.; Pennisi, M.
2012-01-01
We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some "the elementary particles of arithmetic" as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called "the elementary particles of physics" too. This study considers the problem of closely packing similar circles/spheres in 2D/3D space. This is in effect a discretization process of space and the allowable number in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This "number/physical" stability idea applies to bigger collections made from smaller (prime units leading to larger stable prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show convincingly that the growth of prime numbers and that of the masses of
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some “the elementary particles of arithmetic” as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called “the elementary particles of physics” too. This study considers the problem of closely packing similar circles / spheres in 2D / 3D space. This is in effect a discretization process of space and the allowable num- ber in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This “number / physical” stability idea applies to bigger collections made from smaller (prime units leading to larger sta- ble prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show con- vincingly that the growth of prime numbers and that
basement reservoir geometry and properties
Walter, bastien; Geraud, yves; Diraison, marc
2017-04-01
Basement reservoirs are nowadays frequently investigated for deep-seated fluid resources (e.g. geothermal energy, groundwater, hydrocarbons). The term 'basement' generally refers to crystalline and metamorphic formations, where matrix porosity is negligible in fresh basement rocks. Geothermal production of such unconventional reservoirs is controlled by brittle structures and altered rock matrix, resulting of a combination of different tectonic, hydrothermal or weathering phenomena. This work aims to characterize the petro-structural and petrophysical properties of two basement surface analogue case studies in geological extensive setting (the Albert Lake rift in Uganda; the Ifni proximal margin of the South West Morocco Atlantic coast). Different datasets, using field structural study, geophysical acquisition and laboratory petrophysical measurements, were integrated to describe the multi-scale geometry of the porous network of such fractured and weathered basement formations. This study points out the multi-scale distribution of all the features constituting the reservoir, over ten orders of magnitude from the pluri-kilometric scale of the major tectonics structures to the infra-millimetric scale of the secondary micro-porosity of fractured and weathered basements units. Major fault zones, with relatively thick and impermeable fault core structures, control the 'compartmentalization' of the reservoir by dividing it into several structural blocks. The analysis of these fault zones highlights the necessity for the basement reservoirs to be characterized by a highly connected fault and fracture system, where structure intersections represent the main fluid drainage areas between and within the reservoir's structural blocks. The suitable fluid storage areas in these reservoirs correspond to the damage zone of all the fault structures developed during the tectonic evolution of the basement and the weathered units of the basement roof developed during pre
Schwartz, W J; Carpino, A; de la Iglesia, H O; Baler, R; Klein, D C; Nakabeppu, Y; Aronin, N
2000-01-01
Extensive studies have established that light regulates c-fos gene expression in the suprachiasmatic nucleus, the site of an endogenous circadian clock, but relatively little is known about the expression of genes structurally related to c-fos, including fra-1, fra-2 and fosB. We analysed the photic and temporal regulation of these genes at the messenger RNA and immunoreactive protein levels in rat suprachiasmatic nucleus, and we found different expression patterns after photic stimulation and depending on location in the ventrolateral or dorsomedial subdivisions. In the ventrolateral suprachiasmatic nucleus, c-fos, fra-2 and fosB expression was stimulated after a subjective-night (but not subjective-day) light pulse. Expression of the fra-2 gene was prolonged following photic stimulation, with elevated messenger RNA and protein levels that appeared unchanged for at least a few hours beyond the c-fos peak. Unlike c-fos and fra-2, the fosB gene appeared to be expressed constitutively in the ventrolateral suprachiasmatic nucleus throughout the circadian cycle; immunohistochemical analysis suggested that delta FosB was the protein product accounting for this constitutive expression, while FosB was induced by the subjective-night light pulse. In the dorsomedial suprachiasmatic nucleus, c-fos and fra-2 expression exhibited an endogenous circadian rhythm, with higher levels during the early subjective day, although the relative abundance was much lower than that measured after light pulses in the ventrolateral suprachiasmatic nucleus. Double-label immunohistochemistry suggested that some of the dorsomedial cells responsible for the circadian expression of c-Fos also synthesized arginine vasopressin. No evidence of suprachiasmatic nucleus fra-1 expression was found. In summary, fos family genes exhibit differences in their specific expression patterns in the suprachiasmatic nucleus, including their photic and circadian regulation in separate cell populations in the
Energy Technology Data Exchange (ETDEWEB)
Nava Lara, Eric Rafael; Santos Dominguez, Martin [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico); Herrera Lavin, Jesus Xavier [Petroleos Mexicanos (Mexico)
2000-07-01
The Management System for the Budgetary Exercise (SAEP) arises from the necessity of supporting the programming processes for the budget allocation to the technological projects of the Subdivision of Technology and Profesional Development (STPD). This system allows recovering the budget partial or complete information facilitating the adjustments to this same one before integrating them to the budget assignation system (SAP). It also allows to control the expenses of the projects as well as of the exercise of the budget, and orchestrates an internal control for the technical and financial approval of the countable commitments and the budget expenses before taking the proceeding through the mechanisms of registry with the SAP. [Spanish] El Sistema de Administracion para el Ejercicio Presupuestal (SAEP) surge de la necesidad de apoyar los procesos de programacion para la asignacion del presupuesto a los proyectos tecnologicos de la Subdireccion de Tecnologia y Desarrollo Profesional (STPD). Este sistema permite recuperar la informacion parcial o completa del presupuesto facilitando las adecuaciones a este mismo antes de integrarlas al Sistema de Asignacion de Presupuesto (SAP). Tambien permite controlar los gastos, tanto de los proyectos como de los ejercicios del presupuesto e instrumenta un control interno para la aprobacion tecnica y financiera de los compromisos contables y las erogaciones del presupuesto antes de llevar el tramite a traves de los mecanismos de registro con el (SAP).
Moving KML geometry elements within Google Earth
Zhu, Liang-feng; Wang, Xi-feng; Pan, Xin
2014-11-01
During the process of modeling and visualizing geospatial information on the Google Earth virtual globe, there is an increasing demand to carry out such operations as moving geospatial objects defined by KML geometry elements horizontally or vertically. Due to the absence of the functionality and user interface for performing the moving transformation, it is either hard or impossible to interactively move multiple geospatial objects only using the existing Google Earth desktop application, especially when the data sets are in large volume. In this paper, we present a general framework and associated implementation methods for moving multiple KML geometry elements within Google Earth. In our proposed framework, we first load KML objects into the Google Earth plug-in, and then extract KML geometry elements from the imported KML objects. Subsequently, we interactively control the movement distance along a specified orientation by employing a custom user interface, calculate the transformed geographic location for each KML geometry element, and adjust geographic coordinates of the points in each KML objects. And finally, transformed KML geometry elements can be displayed in Google Earth for 3D visualization and spatial analysis. A key advantage of the proposed framework is that it provides a simple, uniform and efficient user interface for moving multiple KML geometry elements within Google Earth. More importantly, the proposed framework and associated implementations can be conveniently integrated into other customizable Google Earth applications to support interactively visualizing and analyzing geospatial objects defined by KML geometry elements.
Discrete quantum geometries and their effective dimension
Energy Technology Data Exchange (ETDEWEB)
Thuerigen, Johannes
2015-07-02
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.
Directory of Open Access Journals (Sweden)
Everton do Espírito Santo Borges
2008-09-01
Full Text Available Avaliou-se a dinâmica do fósforo no organismo de cordeiros Santa Inês alimentados com dietas com diversos níveis deste mineral, considerando as correlações entre os níveis de fósforo consumido e de fósforo no plasma; na saliva; no conteúdo ruminal; nas fezes; e na urina. Foram utilizados 18 cordeiros com 5 meses de idade e 27 kg de peso vivo. O experimento foi dividido em dois períodos de cinco semanas, cada um com nove animais. Os animais foram mantidos individualmente em gaiolas para estudo de metabolismo e receberam uma dieta basal constituída de feno de capim coast-cross (Cynodon dactylon, L. Pers. e concentrado com diferentes níveis de fósforo (1,9; 2,6; 3,3 g/dia provenientes de fosfato bicálcico. No 15º dia, iniciaram-se as coletas de saliva, plasma, conteúdo ruminal, fezes e urina para as análises de fósforo inorgânico. Observaram-se correlações positivas entre o aumento do consumo de fósforo e os teores desse mineral no plasma (r = 0,64, na saliva (r = 0,86, no conteúdo ruminal (r = 0,82, nas fezes (r = 0,92 e na urina (r = 0,37, comprovando que, quando absorvido, o fósforo é distribuído no corpo pelo plasma. Após a saturação no organismo, o excesso é secretado via saliva, segue para o rúmen e, ao chegar ao intestino, é reabsorvido em menor quantidade e excretado via fezes. À medida que se aumentaram os níveis de fósforo na dieta, verificou-se aumento expressivo dos teores desse mineral na saliva, no plasma, no conteúdo ruminal e nas fezes.The dynamics of phosphorus in the body of Santa Ines lambs fed diets with different levels of this mineral was evaluated, considering the correlations among the levels of phosphorus consumed, in plasma; in saliva, in rumen contents, in feces, and in urine. Eighteen lambs were used with five mo old and 27 kg BW. The experiment was divided into two periods of five weeks, each with nine animals. The animals were individually kept in cages of metabolism study and were
Wormhole inspired by non-commutative geometry
Energy Technology Data Exchange (ETDEWEB)
Rahaman, Farook, E-mail: rahaman@iucaa.ernet.in [Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal (India); Karmakar, Sreya, E-mail: sreya.karmakar@gmail.com [Department of Physics, Calcutta Institute of Engineering and Management, Kolkata 700040, West Bengal (India); Karar, Indrani, E-mail: indrani.karar08@gmail.com [Department of Mathematics, Saroj Mohan Institute of Technology, Guptipara, West Bengal (India); Ray, Saibal, E-mail: saibal@iucaa.ernet.in [Department of Physics, Government College of Engineering & Ceramic Technology, Kolkata 700010, West Bengal (India)
2015-06-30
In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV). A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.
Digital and discrete geometry theory and algorithms
Chen, Li
2014-01-01
This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a
Wormhole inspired by non-commutative geometry
Directory of Open Access Journals (Sweden)
Farook Rahaman
2015-06-01
Full Text Available In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV. A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.
Information geometry near randomness and near independence
Arwini, Khadiga A
2008-01-01
This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.
Fractal geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
Differential geometry and topology of curves
Animov, Yu
2001-01-01
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
Introduction into integral geometry and stereology
DEFF Research Database (Denmark)
Kiderlen, Markus
This text is the extended version of two talks held at the Summer Academy Stochastic Geometry, Spatial Statistics and Random Fields in the Soellerhaus, Germany, in September 2009. It forms (with slight modifications) a chapter of the Springer lecture notes Lectures on Stochastic Geometry, Spatial...... Statistics and Random Fields and is a self-containing introduction into integral geometry and its applications in stereology. The most important integral geometric tools for stereological applications are kinematic formulas and results of Blaschke-Petkantschin type. Therefore, Crofton's formula...
Directory of Open Access Journals (Sweden)
Karina Jerônimo Rodrigues Santiago de Lima
2005-06-01
Full Text Available O objetivo deste trabalho foi avaliar o grau de concordância entre a classificação dos dois principais tipos de Classe II, subdivisão, em fotografias e em radiografias póstero-anteriores. A amostra consistiu de 44 indivíduos que apresentavam má oclusão de Classe II, subdivisão, com idade média de 15,3 anos, apresentando os dentes permanentes superiores e inferiores, até os primeiros molares e que não haviam sido submetidos a tratamento ortodôntico. Duas examinadoras realizaram uma avaliação subjetiva das fotografias frontais, classificando a Classe II, subdivisão, como tipo 1 quando havia coincidência da linha média dentária superior com a linha média facial e desvio da linha média dentária inferior. O tipo 2 apresentava características opostas. A avaliação nas radiografias PA foi realizada por uma examinadora, analisando os desvios das linhas médias dentárias superior e inferior em relação à linha X. Avaliou-se a concordância entre os dois métodos de classificação dos tipos de Classe II, subdivisão, utilizando-se o coeficiente Kappa. Os resultados obtidos permitiram-nos concluir que, mesmo havendo a mesma tendência de distribuição dos tipos de Classe II, subdivisão, nas fotografias frontais e nas radiografias PA, a concordância entre estes dois métodos de avaliação não foi estatisticamente significante.The objective of this study was to evaluate the photographic and radiographic classification agreement of the two main types of Class II subdivision malocclusions. The sample consisted of 44 untreated Class II subdivision malocclusion subjects with a mean age of 15.3 years. All possessed a full complement of permanent teeth up to the first molars and had not been submitted to orthodontic treatment. Frontal photographic evaluation was performed by means of a subjective evaluation by two examiners. Type I Class II subdivision malocclusion presents a coincidence of the maxillary dental midline with the
Energy Technology Data Exchange (ETDEWEB)
Lozano, Juan-Andres, E-mail: lozano@din.upm.e [Departamento de Ingenieria Nuclear, Universidad Politecnica de Madrid (UPM), Jose G. Abascal, 2, 28006 Madrid (Spain); Jimenez, Javier; Garcia-Herranz, Nuria; Aragones, Jose-Maria [Departamento de Ingenieria Nuclear, Universidad Politecnica de Madrid (UPM), Jose G. Abascal, 2, 28006 Madrid (Spain)
2010-03-15
In this paper the extension of the multigroup nodal diffusion code ANDES, based on the Analytic Coarse Mesh Finite Difference (ACMFD) method, from Cartesian to hexagonal geometry is presented, as well as its coupling with the thermal-hydraulic (TH) code COBRA-IIIc for hexagonal core analysis. In extending the ACMFD method to hexagonal assemblies, triangular-Z nodes are used. In the radial plane, a direct transverse integration procedure is applied along the three directions that are orthogonal to the triangle interfaces. The triangular nodalization avoids the singularities, that appear when applying transverse integration to hexagonal nodes, and allows the advantage of the mesh subdivision capabilities implicit within that geometry. As for the thermal-hydraulics, the extension of the coupling scheme to hexagonal geometry has been performed with the capability to model the core using either assembly-wise channels (hexagonal mesh) or a higher refinement with six channels per fuel assembly (triangular mesh). Achieving this level of TH mesh refinement with COBRA-IIIc code provides a better estimation of the in-core 3D flow distribution, improving the TH core modelling. The neutronics and thermal-hydraulics coupled code, ANDES/COBRA-IIIc, previously verified in Cartesian geometry core analysis, can also be applied now to full three-dimensional VVER core problems, as well as to other thermal and fast hexagonal core designs. Verification results are provided, corresponding to the different cases of the OECD/NEA-NSC VVER-1000 Coolant Transient Benchmarks.
Structure analysis for plane geometry figures
Feng, Tianxiao; Lu, Xiaoqing; Liu, Lu; Li, Keqiang; Tang, Zhi
2013-12-01
As there are increasing numbers of digital documents for education purpose, we realize that there is not a retrieval application for mathematic plane geometry images. In this paper, we propose a method for retrieving plane geometry figures (PGFs), which often appear in geometry books and digital documents. First, detecting algorithms are applied to detect common basic geometry shapes from a PGF image. Based on all basic shapes, we analyze the structural relationships between two basic shapes and combine some of them to a compound shape to build the PGF descriptor. Afterwards, we apply matching function to retrieve candidate PGF images with ranking. The great contribution of the paper is that we propose a structure analysis method to better describe the spatial relationships in such image composed of many overlapped shapes. Experimental results demonstrate that our analysis method and shape descriptor can obtain good retrieval results with relatively high effectiveness and efficiency.
Gravity, Cartan geometry, and idealized waywisers
Westman, H F
2012-01-01
The primary aim of this paper is to provide a simple and concrete interpretation of Cartan geometry by pointing out that it is nothing but the mathematics of idealized waywisers. Waywisers, also called hodometers, are instruments traditionally used to measure distances. The mathematical representation of an idealized waywiser consists of a choice of symmetric space called a {\\em model space} and represents the `wheel' of the idealized waywiser. The geometry of a manifold is then completely characterized by a pair of variables $\\{V^A(x),A^{AB}(x)\\}$, each of which admit simple interpretations: $V^A$ is the point of contact between the waywiser's idealized wheel and the manifold whose geometry one wishes to characterize, and $A^{AB}=A_\\mu^{\\ AB}dx^\\mu$ is a connection one-form dictating how much the idealized wheel of the waywiser has rotated when rolled along the manifold. The familiar objects from differential geometry (e.g. metric $g_{\\mu\
Geometry, structure and randomness in combinatorics
Nešetřil, Jaroslav; Pellegrini, Marco
2014-01-01
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.
Homological mirror symmetry and tropical geometry
Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia
2014-01-01
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...
Track Geometry Measurement System Software Manual
1978-04-01
The Track Geometry Measurement System (TGMS) was developed through the United States Department of Transportation's, Urban Mass Transportation Administration by the Transportation Systems Center in Cambridge, Massachusetts under its Test and Evaluati...
10th China-Japan Geometry Conference
Miyaoka, Reiko; Tang, Zizhou; Zhang, Weiping
2016-01-01
Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists. The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, sympl...
The Soap-Bubble-Geometry Contest.
Morgan, Frank; Melnick, Edward R.; Nicholson, Ramona
1997-01-01
Presents an activity on soap-bubble geometry using a guessing contest, explanations, and demonstrations that allow students to mesh observation and mathematical reasoning to discover that mathematics is much more than just number crunching. (ASK)
ARC Code TI: Geometry Manipulation Protocol (GMP)
National Aeronautics and Space Administration — The Geometry Manipulation Protocol (GMP) is a library which serializes datatypes between XML and ANSI C data structures to support CFD applications. This library...
Quasi-crystalline geometry for architectural structures
DEFF Research Database (Denmark)
Weizierl, Barbara; Wester, Ture
2001-01-01
. The purpose of the paper is to investigate some possibilities for the application of Quasi-Crystal geometry for structures in architecture. The basis for the investigations is A: to use the Golden Cubes (the two different hexahedra consisting of rhombic facets where the length of the diagonals has the Golden......Artikel på CD-Rom 8 sider. The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells...... ratio) as basic elements for aperiodic 3D geometries and B: to raise aperiodic Penrose tilings and its binary substitutions from their 2D basis into 3D QC geometries and describe the structural behaviour for these spatial configurations....
Extracting Entanglement Geometry from Quantum States
Hyatt, Katharine; Garrison, James R.; Bauer, Bela
2017-10-01
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network—and hence the geometry—is largely fixed a priori by the choice of the tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of noninteracting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.
Algebra, Geometry and Mathematical Physics Conference
Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander
2014-01-01
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...
Robot Geometry and the High School Curriculum.
Meyer, Walter
1988-01-01
Description of the field of robotics and its possible use in high school computational geometry classes emphasizes motion planning exercises and computer graphics displays. Eleven geometrical problems based on robotics are presented along with the correct solutions and explanations. (LRW)
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-02-01
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
The geometry of René Descartes
Descartes, René
1954-01-01
The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." - John Stuart Mill.
The elements of non-Euclidean geometry
Sommerville, D MY
2012-01-01
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
Tame geometry with application in smooth analysis
Yomdin, Yosef
2004-01-01
The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.
De Nicola, Flavia; Baldantoni, Daniela; Maisto, Giulia; Alfani, Anna
2017-05-01
Concentrations of four heavy metals (HMs) (Cd, Cr, Fe, Pb) and four polycyclic aromatic hydrocarbons (PAHs) (fluoranthene, phenanthrene, chrysene, benzo[a]pyrene) in Quercus ilex L. leaves collected at the Campania Region (Southern Italy) in previous air biomonitoring studies were employed to (1) test the correspondence with an a priori site subdivision (remote, periurban, and urban) and (2) evaluate long temporal trends of HM (approximately 20 years) and PAH (approximately 10 years) air contaminations. Overall, Q. ilex leaf HM and PAH concentrations resulted along the gradient: remote < periurban < urban sites, reflecting the a priori subdivision based on human management. Over a long time, although a clear decrease of leaf Pb, chrysene, fluoranthene, and phenanthrene concentrations occurred at the urban sites, a high contamination level persists.
Geometry and quantization of moduli spaces
Andersen, Jørgen; Riera, Ignasi
2016-01-01
This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
Non-relativistic geometry of holographic screens
Moosa, Mudassir
2017-06-01
We propose that the intrinsic geometry of holographic screens should be described by the Newton-Cartan geometry. As a test of this proposal, we show that the evolution equations of the screen can be written in a covariant form in terms of a stress tensor, an energy current, and a momentum one-form. We derive the expressions for the stress tensor, energy density, and momentum one-form using Brown-York action formalism.
Perspectives in Analysis, Geometry, and Topology
Itenberg, I V; Passare, Mikael
2012-01-01
The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Virtanen, Risto; Oksanen, Lauri Kalervo; Oksanen, Tarja Maarit; Cohen, Juval; Forbes, Bruce C.; Johansen, Bernt; Käyhkö, Jukka; Olofsson, Johan; Pulliainen, Jouni; Tømmervik, Hans
2015-01-01
According to some treatises, arctic and alpine sub-biomes are ecologically similar, whereas others find them highly dissimilar. Most peculiarly, large areas of northern tundra highlands fall outside of the two recent subdivisions of the tundra biome. We seek an ecologically natural resolution to this long-standing and far-reaching problem. We studied broad-scale patterns in climate and vegetation along the gradient from Siberian tundra via northernmost Fennoscandia to the al...
Virtanen, Risto; Oksanen, Lauri Kalervo; Oksanen, Tarja Maarit; Cohen, Juval; Forbes, Bruce C.; Johansen, Bernt; Käyhkö, Jukka; Olofsson, Johan; Pulliainen, Jouni; Tømmervik, Hans
2015-01-01
This is the published version of the article. Published source: http://doi.org/10.1002/ece3.1837. According to some treatises, arctic and alpine sub-biomes are ecologically similar, whereas others find them highly dissimilar. Most peculiarly, large areas of northern tundra highlands fall outside of the two recent subdivisions of the tundra biome. We seek an ecologically natural resolution to this long-standing and far-reaching problem. We studied broad-scale patterns in climate...
Directory of Open Access Journals (Sweden)
O. I. Kharchenko
2014-07-01
Full Text Available Purpose. Modern transport systems are not stable and can not stand up to the destabilizing factors. Global track record in the economic and commercial management systems is the use of the concept of sustainable development. It is necessary on the basis of analysis of literary sources to define the directions of efficiency increase of functioning of railway transport subdivisions from the point of view of sustainable development. Methodology. To achieve the purpose the features of the use of sustainable development conception and its realization were investigated at a management of the complex systems. The existent models were also analyzed in the field of efficiency increase of functioning of railway transport subdivisions. Findings. On the basis of literary sources analysis, keeping up the conceptual essence of the sustainable development, the main directions of efficiency increase of subdivisions functioning were selected. They take into account the basic requirements of steady development and should be considered as a complex. Originality. New directions to consider the efficiency increase issues from position of sustainable development were offered by the author. Three components of conceptions of sustainable development (economic, ecological and social should be examined in a balanced way. Thus, the above mentioned theoretical studies can promote the forming of new economy model corresponding to the purposes and principles of sustainable development. Practical value. The conducted analysis development confirms the necessity of researches on perspective directions of development of railway transport subdivisions, which are marked by the guidance of Ukrzaliznytsia. It enables to select basic directions for further research in the area of efficiency increase.
Zhou, Zien; Chen, Zengai; Shan, Jiehui; Ma, Weiwei; Li, Lei; Zu, Jinyan; Xu, Jianrong
2015-07-25
Magnetic resonance imaging (MRI) has many advantages in the research of in vivo embryonic brain development, specifically its noninvasive aspects and ability to avoid skeletal interference. However, few studies have focused on brain development in chick, which is a traditional animal model in developmental biology. We aimed to serially monitor chick embryo brain development in vivo using 3.0 T MRI. Ten fertile Hy-line white eggs were incubated and seven chick embryo brains were monitored in vivo and analyzed serially from 5 to 20 days during incubation using 3.0 T MRI. A fast positioning sequence was pre-scanned to obtain sagittal and coronal brain planes corresponding to the established atlas. T2-weighted imaging (T2WI) was performed for volume estimation of the whole brain and subdivision (telencephalon, cerebellum, brainstem, and lateral ventricle [LV]); diffusion tensor imaging (DTI) was used to reflect the evolution of neural bundle structures. The chick embryos' whole brain and subdivision grew non-linearly over time; the DTI fractional anisotropy (FA) value within the telencephalon increased non-linearly as well. All seven scanned eggs hatched successfully. MRI avoids embryonic sacrifice in a way that allows serial monitoring of longitudinal developmental processes of a single embryo. Feasibility for analyzing subdivision of the brain during development, and adding structural information related to neural bundles, makes MRI a powerful tool for exploring brain development.
Zhao, Xixi; Yang, Ru; Wang, Kewan; Zhang, Zhongping; Wang, Junling; Tan, Xiangliang; Zhang, Jiajun; Mei, Yingjie; Chan, Queenie; Xu, Jun; Feng, Qianjin; Xu, Yikai
2017-12-20
The nucleus accumbens (NAc), an important target of deep brain stimulation for some neuropsychiatric disorders, is thought to be involved in epileptogenesis, especially the shell portion. However, little is known about the exact parcellation within the NAc, and its structural abnormalities or connections alterations of each NAc subdivision in temporal lobe epilepsy (TLE) patients. Here, we used diffusion probabilistic tractography to subdivide the NAc into core and shell portions in individual TLE patients to guide stereotactic localization of NAc shell. The structural and connection abnormalities in each NAc subdivision in the groups were then estimated. We successfully segmented the NAc in 24 of 25 controls, 14 of 16 left TLE patients, and 14 of 18 right TLE patients. Both left and right TLE patients exhibited significantly decreased fractional anisotropy (FA) and increased radial diffusivity (RD) in the shell, while there was no significant alteration in the core. Moreover, relatively distinct structural connectivity of each NAc subdivision was demonstrated. More extensive connection abnormalities were detected in the NAc shell in TLE patients. Our results indicate that neuronal degeneration and damage caused by seizure mainly exists in NAc shell and provide anatomical evidence to support the role of NAc shell in epileptogenesis. Remarkably, those NAc shell tracts with increased connectivities in TLE patients were found decreased in FA, which indicates disruption of fiber integrity. This finding suggests the regeneration of aberrant connections, a compensatory and repair process ascribed to recurrent seizures that constitutes part of the characteristic changes in the epileptic network. © 2017 Wiley Periodicals, Inc.
Geometry-induced protein pattern formation.
Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin
2016-01-19
Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.
Geometry The Language of Space and Form (Revised Edition)
Tabak, John
2011-01-01
Geometry, Revised Edition describes geometry in antiquity. Beginning with a brief description of some of the geometry that preceded the geometry of the Greeks, it takes up the story of geometry during the European Renaissance as well as the significant mathematical progress in other areas of the world. It also discusses the analytic geometry of Ren Descartes and Pierre Fermat, the alternative coordinate systems invented by Isaac Newton, and the solid geometry of Leonhard Euler. Also included is an overview of the geometry of one of the most successful mathematicians of the 19th century, Bernha
Bandyopadhyay, Ujjwal; Kundu, Dipankar; Sinha, Arijit; Banerjee, Kallol; Bandyopadhyay, Ranjana; Mandal, Tridibeshwar; Ray, Debes
2013-01-01
The ideal management of thalassemia involves a multidisciplinary therapeutic team approach and should be preferably done at a comprehensive thalassemia care center with all sorts of specialists and the backup of a well-equipped blood bank. However, in developing country like ours, these facilities are not available in rural set up. So, a situation where conservative therapy with regular blood transfusion is the only choice left to innumerable thalassemic children. To evaluate the existing conservative management protocol of Beta-thalassemia major patients in the setup of a subdivision level Government Hospital of rural West Bengal, India. The study was performed between December 2009 and December 2011. Beta-thalassemia major patients, registered in blood bank for moderate transfusion regimen, were taken in study. All the patients were screened for Transfusion Transmittable Infections at the time of registration and thereafter periodically every six months. Iron chelation therapy was given simultaneously with transfusion at a dose of 20 to 40 mg/kg/day for six days. The patients were advised to follow up with chelation therapy at home by daily infusion with a goal of maintaining serum ferritin level below 1000 ng/ml. Over this long period of study, the patients were periodically evaluated for complications. The average blood requirement (ml/kg/year) in 1-5 years, 6-10 years, and 11-15 years were 110, 150, and 180, respectively. Incidence of Hepatitis C Virus infection in 1-5 years and 6-10 years were 1.75% and 2.08%, respectively. It is well seen that serum ferritin level increase with ascending age as does the blood consumption. Conservative management may be the best alternative and at times the only hope for patients in developing country like ours. However, in order to decrease the disease load, steps need to be taken to introduce preventive measures.
Aziz, Muhammad Abdul; Adnan, Muhammad; Khan, Amir Hasan; Rehman, Atiq Ur; Jan, Rahmatullah; Khan, Jafar
2016-11-15
Medicinal flora plays a vital role in treating various types of ailments in living beings. The present study was planned to investigate and document systematically the indigenous knowledge in a scientifically little explored area of Ladha sub-division, South Waziristan agency, Pakistan. Hence, this study would contribute positively to the field of ethnopharmacology. Prior to ethnomedicinal data collection, regular field visits were conducted during the month of May and June 2015 to locate the sites and respondents from where the traditional knowledge was to be recorded. Ethno-medicinal data was collected during the month July and August 2015 through rapid appraisal approach (RAA) based on direct interaction with the indigenous communities by making group discussions, corner meetings and semi-structured interviews. Data was evaluated statistically by using the index of Use value (UV) and Frequency of citations (FC). A total of 82 medicinal plants belonging to 42 families were reported in the study. Leaves were the most frequently used plant parts. Highest use values were recorded for Peganum harmala (0.93), Punica granatum (0.91), Thymus mongolicus (0.90), Chenopodium album (0.89), Coriandrum sativum (0.87), Mentha longifolia (0.87), Lactuca serriola (0.87) and Portulaca oleracea (0.87). Medicinal plants used for the gastro intestinal complexities and respiratory diseases were more than 9% followed by skin and diarrhea (7% each), liver disorders (5%) cough and cold fever (5%). People of the area mostly still rely on traditional herbal therapies. Keeping in mind the dependence of the indigenous community for their primary health care on such herbal remedies, pharmacological and critical toxicological investigation of certain flora is necessary. Moreover, projects should be designed to analyze the existing issues and problems related with medicinal plants conservation.
Directory of Open Access Journals (Sweden)
Sun Jing-Tao
2012-02-01
Full Text Available Abstract Background Two colour forms of the two-spotted spider mite (Tetranychus urticae Koch coexist in China: a red (carmine form, which is considered to be native and a green form which is considered to be invasive. The population genetic diversity and population genetic structure of this organism were unclear in China, and there is a controversy over whether they constitute distinct species. To address these issues, we genotyped a total of 1,055 individuals from 18 red populations and 7 green populations in China using eight microsatellite loci. Results We identified 109 alleles. We found a highly significant genetic differentiation among the 25 populations (global FST = 0.506, global FST {ENA} = 0.473 and a low genetic diversity in each population. In addition, genetic diversity of the red form mites was found to be higher than the green form. Pearson correlations between statistics of variation (AR and HE and geographic coordinates (latitude and longitude showed that the genetic diversity of the red form was correlated with latitude. Using Bayesian clustering, we divided the Chinese mite populations into five clades which were well congruent with their geographic distributions. Conclusions Spider mites possess low levels of genetic diversity, limit gene flow between populations and significant and IBD (isolation by distance effect. These factors in turn contribute to the strong subdivision of genetic structure. In addition, population genetic structure results don't support the separation of the two forms of spider mite into two species. The morphological differences between the two forms of mites may be a result of epigenetic effects.
2012-01-01
Background Two colour forms of the two-spotted spider mite (Tetranychus urticae Koch) coexist in China: a red (carmine) form, which is considered to be native and a green form which is considered to be invasive. The population genetic diversity and population genetic structure of this organism were unclear in China, and there is a controversy over whether they constitute distinct species. To address these issues, we genotyped a total of 1,055 individuals from 18 red populations and 7 green populations in China using eight microsatellite loci. Results We identified 109 alleles. We found a highly significant genetic differentiation among the 25 populations (global FST = 0.506, global FST {ENA} = 0.473) and a low genetic diversity in each population. In addition, genetic diversity of the red form mites was found to be higher than the green form. Pearson correlations between statistics of variation (AR and HE) and geographic coordinates (latitude and longitude) showed that the genetic diversity of the red form was correlated with latitude. Using Bayesian clustering, we divided the Chinese mite populations into five clades which were well congruent with their geographic distributions. Conclusions Spider mites possess low levels of genetic diversity, limit gene flow between populations and significant and IBD (isolation by distance) effect. These factors in turn contribute to the strong subdivision of genetic structure. In addition, population genetic structure results don't support the separation of the two forms of spider mite into two species. The morphological differences between the two forms of mites may be a result of epigenetic effects. PMID:22348504
Kowalchuk, George A.; Naoumenko, Zinaida S.; Derikx, Piet J. L.; Felske, Andreas; Stephen, John R.; Arkhipchenko, Irina A.
1999-01-01
Although the practice of composting animal wastes for use as biofertilizers has increased in recent years, little is known about the microorganisms responsible for the nitrogen transformations which occur in compost and during the composting process. Ammonia is the principle available nitrogenous compound in composting material, and the conversion of this compound to nitrite in the environment by chemolithotrophic ammonia-oxidizing bacteria is an essential step in nitrogen cycling. Therefore, the distribution of ammonia-oxidizing members of the β subdivision of the class Proteobacteria in a variety of composting materials was assessed by amplifying 16S ribosomal DNA (rDNA) and 16S rRNA by PCR and reverse transcriptase PCR (RT-PCR), respectively. The PCR and RT-PCR products were separated by denaturing gradient gel electrophoresis (DGGE) and were identified by hybridization with a hierarchical set of oligonucleotide probes designed to detect ammonia oxidizer-like sequence clusters in the genera Nitrosospira and Nitrosomonas. Ammonia oxidizer-like 16S rDNA was detected in almost all of the materials tested, including industrial and experimental composts, manure, and commercial biofertilizers. A comparison of the DGGE and hybridization results after specific PCR and RT-PCR suggested that not all of the different ammonia oxidizer groups detected in compost are equally active. amoA, the gene encoding the active-site-containing subunit of ammonia monooxygenase, was also targeted by PCR, and template concentrations were estimated by competitive PCR. Detection of ammonia-oxidizing bacteria in the composts tested suggested that such materials may not be biologically inert with respect to nitrification and that the fate of nitrogen during composting and compost storage may be affected by the presence of these organisms. PMID:9925559
The Persistification of the ATLAS Geometry
AUTHOR|(INSPIRE)INSPIRE-00068562; The ATLAS collaboration; Bianchi, Riccardo-Maria
2016-01-01
The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the- y on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS so ware framework “Athena”, which provides the online services and the tools to retrieve the data from the database. is operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geom- etry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify and serve the geometry of HEP experiments. e new mechanism is composed by a new le format and a REST API. e new le format allows to store the whole detector description locally in a at le, and it is especially optimized to descri...
Extracting Entanglement Geometry from Quantum States.
Hyatt, Katharine; Garrison, James R; Bauer, Bela
2017-10-06
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network-and hence the geometry-is largely fixed a priori by the choice of the tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of noninteracting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.
The geometry of soil crack networks
Chertkov, V Y
2014-01-01
The subject of this work is the modification and specification of an approach to detail the estimation of soil crack network characteristics. The modification aims at accounting for the corrected soil crack volume based on the corrected shrinkage geometry factor compared to known estimates of crack volume and shrinkage geometry factor. The mode of the correction relies on recent results of the soil reference shrinkage curve. The main exposition follows the preliminary brief review of available approaches to dealing with the geometry of soil crack networks and gives a preliminary brief summary of the approach to be modified and specified. To validate and illustrate the modified approach the latter is used in the analysis of available data on soil cracking in a lysimeter.
Conference on Strings, Duality, and Geometry
Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV
2002-01-01
This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...
Geometry of curves and surfaces with Maple
Rovenski, Vladimir
2000-01-01
This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource...
Geometry and Physics of Null Infinity
Ashtekar, Abhay
2014-01-01
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups, symplectic geometry on the space of gravitational connections and geometric quantization via K\\"ahler structures. On the physical side, null infinity provides a natural home to study gravitational radiation and its structure leads to several interesting effects such as an infinite dimensional enlargement of the Poincar\\'e group, geometrical expressions of energy and momentum carried by gravitational waves, emergence of non-trivial `vacuum configurations' and an unforeseen interplay between infrared properties of the quantum gravitational field and the enlargement of the asymptotic symmetry group. The goal of this article is to present a succinct summary of this subtle and beautiful interplay.
Geometric Monte Carlo and black Janus geometries
Energy Technology Data Exchange (ETDEWEB)
Bak, Dongsu, E-mail: dsbak@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); B.W. Lee Center for Fields, Gravity & Strings, Institute for Basic Sciences, Daejeon 34047 (Korea, Republic of); Kim, Chanju, E-mail: cjkim@ewha.ac.kr [Department of Physics, Ewha Womans University, Seoul 03760 (Korea, Republic of); Kim, Kyung Kiu, E-mail: kimkyungkiu@gmail.com [Department of Physics, Sejong University, Seoul 05006 (Korea, Republic of); Department of Physics, College of Science, Yonsei University, Seoul 03722 (Korea, Republic of); Min, Hyunsoo, E-mail: hsmin@uos.ac.kr [Physics Department, University of Seoul, Seoul 02504 (Korea, Republic of); Song, Jeong-Pil, E-mail: jeong_pil_song@brown.edu [Department of Chemistry, Brown University, Providence, RI 02912 (United States)
2017-04-10
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Lectures on formal and rigid geometry
Bosch, Siegfried
2014-01-01
A first version of this work appeared in 2005 as a Preprint of the Collaborative Research Center "Geometrical Structures in Mathematics" at the University of Münster. Its aim was to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of the original preprint and has been published at the suggestion of several experts in the field.
Geometry and dynamics of integrable systems
Matveev, Vladimir
2016-01-01
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mir...
From groups to geometry and back
Climenhaga, Vaughn
2017-01-01
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering space...
Nozzle geometry variations on the discharge coefficient
Directory of Open Access Journals (Sweden)
M.M.A. Alam
2016-03-01
Full Text Available Numerical works have been conducted to investigate the effect of nozzle geometries on the discharge coefficient. Several contoured converging nozzles with finite radius of curvatures, conically converging nozzles and conical divergent orifices have been employed in this investigation. Each nozzle and orifice has a nominal exit diameter of 12.7×10−3 m. A 3rd order MUSCL finite volume method of ANSYS Fluent 13.0 was used to solve the Reynolds-averaged Navier–Stokes equations in simulating turbulent flows through various nozzle inlet geometries. The numerical model was validated through comparison between the numerical results and experimental data. The results obtained show that the nozzle geometry has pronounced effect on the sonic lines and discharge coefficients. The coefficient of discharge was found differ from unity due to the non-uniformity of flow parameters at the nozzle exit and the presence of boundary layer as well.
Early Geometry: A Visual, Intuitive Introduction to Plane Geometry for Elementary School Children.
Navarro, C. F.
Geometry is a fundamental part of the mathematics foundation provided by elementary education. Children have an intuitive understanding of geometry that they draw on when dealing with geometric concepts in activities like drawing, playing hopscotch, defending their "half of the room," and playing sports. This book offers no instruction…
Anderson, Karen L.; Casey, M. Beth; Thompson, William L.; Burrage, Marie S.; Pezaris, Elizabeth; Kosslyn, Stephen M.
2008-01-01
This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…
Guven, Bulent
2012-01-01
This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…
The organization of room geometry and object layout geometry in human memory.
Sluzenski, Julia; McNamara, Timothy P
2011-08-01
Research with humans and with nonhuman species has suggested a special role of room geometry in spatial memory functioning. In two experiments, participants learned the configuration of a room with four corners, along with the configuration of four objects within the room, while standing in a fixed position at the room's periphery. The configurations were either rectangular (Experiment 1) or irregular (Experiment 2). Room geometry was not recalled better than object layout geometry, and memories for both configurations were orientation dependent. These results suggest that room geometry and object layout geometry are represented similarly in human memory, at least in situations that promote long-term learning of object locations. There were also some differences between corners and objects in orientation dependence, suggesting that the two sources of information are represented in similar but separate spatial reference systems. [corrected
Recent topics in differential and analytic geometry
Ochiai, T
1990-01-01
Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains.Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters con
Solc filters in a reflective geometry
Messaadi, Abdelghafour; Vargas, Asticio; Sánchez-López, María M.; García-Martínez, Pascuala; Kula, Przemysław; Bennis, Noureddine; Moreno, Ignacio
2017-04-01
We present the realization of a bulk optics birefringent Solc filter in a reflective geometry. This geometry reduces by half the number of required retarders, ensures the same spectral retardance function in pairs of retarders, and helps to make more compact filters. The key element is a quarter-wave Fresnel rhomb located in between the set of retarders and a mirror. Two cases are considered: the first Solc filter uses multiple-order quartz retarders, and the second one uses two liquid-crystal retarders. The latter has the advantage of being tunable via an applied voltage. Experimental results show how to filter the spectral content of a supercontinuum laser.
Density and geometry of single component plasmas
Speck, A; Larochelle, P; Le Sage, D; Levitt, B; Kolthammer, W S; McConnell, R; Wrubel, J; Grzonka, D; Oelert, W; Sefzick, T; Zhang, Z; Comeau, D; George, M C; Hessels, E A; Storry, C H; Weel, M; Walz, J
2007-01-01
The density and geometry of p¯ and e+ plasmas in realistic trapping potentials are required to understand and optimize antihydrogen (H¯) formation. An aperture method and a quadrupole oscillation frequency method for characterizing such plasmas are compared for the first time, using electrons in a cylindrical Penning trap. Both methods are used in a way that makes it unnecessary to assume that the plasmas are spheroidal, and it is shown that they are not. Good agreement between the two methods illustrates the possibility to accurately determine plasma densities and geometries within non-idealized, realistic trapping potentials.
The VSEPR model of molecular geometry
Gillespie, Ronald J
2012-01-01
Valence Shell Electron Pair Repulsion (VSEPR) theory is a simple technique for predicting the geometry of atomic centers in small molecules and molecular ions. This authoritative reference was written by Istvan Hartiggai and the developer of VSEPR theory, Ronald J. Gillespie. In addition to its value as a text for courses in molecular geometry and chemistry, it constitutes a classic reference for professionals.Starting with coverage of the broader aspects of VSEPR, this volume narrows its focus to a succinct survey of the methods of structural determination. Additional topics include the appli
Topological gauge theory, Cartan geometry, and gravity
Wise, Derek Keith
2007-12-01
We investigate the geometry of general relativity, and of related topological gauge theories, using Cartan geometry. Cartan geometry---an 'infinitesimal' version of Klein's Erlanger Programm---allows us to view physical spacetime as tangentially approximated by a homogeneous 'model spacetime', such as de Sitter or anti de Sitter spacetime. This idea leads to a common geometric foundation for 3d Chern-Simons gravity, as studied by Witten, and 4d MacDowell-Mansouri gravity. We describe certain topological gauge theories, including BF theory---a natural generalization of 3d gravity to higher dimensions---as 'Cartan gauge theories' in which the gauge field is replaced by a 'Cartan connection' modeled on some Klein geometry G/H. Cartan-type BF theory has solutions that say spacetime is locally isometric to G/H itself; in this case Cartan geometry reduces to the theory of 'geometric structures'. This leads to generalizations of 3d gravity based on other 3d Klein geometries, including those in Thurston's classification of 3d Riemannian model geometries. In 4d gravity, we generalize MacDowell-Mansouri gravity to other Cartan geometries. For BF theory in n-dimensional spacetime, we also describe codimension-2 'branes' as topological defects. These branes---particles in 3d spacetime, strings in 4d, and so on---are shown to be classified by conjugacy classes in the gauge group G of the theory. They also obey 'exotic statistics' which are neither Bose-Einstein nor Fermi-Dirac, but are governed by representations of generalizations of the braid group known as 'motion groups'. These representations come from a natural action of the motion group on the moduli space of flat G-bundles on space. We study this in particular detail in the case of strings in 4d BF theory, where Lin has called the motion group the 'loop braid group', LBn. This makes 4d BF theory with strings into a 'loop braided quantum field theory'. We also use ideas from 'higher gauge theory' to study particles as
Geometry and conformations of benzenecarboxylic acids
Directory of Open Access Journals (Sweden)
IVAN GUTMAN
2004-11-01
Full Text Available The geometry, conformations and energy of mono-, di-, and tri-carboxylic derivatives of benzene were studied by means of the AM1 molecular-orbital method. Whereas the species having no carboxylic groups in the ortho-position (benzoic, isophthalic, terephthalic, and trimesic acids are planar in all their (stable conformations, those possessing carboxylic groups in the ortho-position (phthalic, 1,2,3-benzenetricarboxylic, and 1,2,4-benzenetricarboxylic acids assume a non-planar geometry, with one carboxyl group almost orthogonal to the plane of the benzene ring. Various rotamers of each of the studied benzenecarboxylic acids have nearly the same energy.
PODANÁ, Klára
2017-01-01
This bachelor thesis, Geometry in Art, is mainly focused on geometry in architecture during Gothic period. Its aim is to create an overview of this period and show what geometric parts were mostly used. The thesis is also introducing a few basic construction parts of a Gothic style. For the construction of the gothic windows we can use for example a homothety to which one of the chapters was also dedicated. In the connection with homothety we need to mention the Problem of Apollonius and for ...
Kinetics of Phase Separation in Confined Geometries
Puri, Sanjay
We review analytical and numerical results for the kinetics of phase separation in confined geometries. It is often the case that a confining surface has a preferential attraction for one of the components of a segregating mixture. The equilibrium surface morphology is either partially wet or completely wet, depending on the strength of the surface potential. The dynamical interplay of wetting and phase separation is referred to as surface-directed spinodal decomposition (SDSD), and is of considerable technological importance. We discuss the modeling of SDSD at both the microscopic and coarse-grained levels. We also present results for SDSD in both semi-infinite and confined geometries.
Heat diffusion in fractal geometry cooling surface
Directory of Open Access Journals (Sweden)
Ramšak Matjaz
2012-01-01
Full Text Available In the paper the numerical simulation of heat diffusion in the fractal geometry of Koch snowflake is presented using multidomain mixed Boundary Element Method. The idea and motivation of work is to improve the cooling of small electronic devices using fractal geometry of surface similar to cooling ribs. The heat diffusion is assumed as the only principle of heat transfer. The results are compared to the heat flux of a flat surface. The limiting case of infinite small fractal element is computed using Richardson extrapolation.
Thin shells joining local cosmic string geometries
Energy Technology Data Exchange (ETDEWEB)
Eiroa, Ernesto F. [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Rubin de Celis, Emilio; Simeone, Claudio [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Ciudad Universitaria Pabellon I, IFIBA-CONICET, Buenos Aires (Argentina)
2016-10-15
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)
Noncommutative Geometry, Quantum Fields and Motives
Connes, Alain
2007-01-01
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea
Thin shells joining local cosmic string geometries
Eiroa, Ernesto F; Simeone, Claudio
2016-01-01
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a standard thin shell and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters.
Thermal geometry from CFT at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Gan, Wen-Cong, E-mail: ganwencong@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: shufuwen@ncu.edu.cn [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: menghewu.physik@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)
2016-09-10
We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.
Thermal geometry from CFT at finite temperature
Directory of Open Access Journals (Sweden)
Wen-Cong Gan
2016-09-01
Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.
Architectural Geometry and Fabrication-Aware Design
Pottmann, Helmut
2013-04-27
Freeform shapes and structures with a high geometric complexity play an increasingly important role in contemporary architecture. While digital models are easily created, the actual fabrication and construction remains a challenge. This is the source of numerous research problems many of which fall into the area of Geometric Computing and form part of a recently emerging research area, called "Architectural Geometry". The present paper provides a short survey of research in Architectural Geometry and shows how this field moves towards a new direction in Geometric Modeling which aims at combining shape design with important aspects of function and fabrication. © 2013 Kim Williams Books, Turin.
Method for Determining Optimum Injector Inlet Geometry
Trinh, Huu P. (Inventor); Myers, W. Neill (Inventor)
2015-01-01
A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.
Riemannian geometry in an orthogonal frame
Cartan, Elie Joseph
2001-01-01
Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n
Effect of geometry on hydrodynamic film thickness
Brewe, D. E.; Hamrock, B. J.; Taylor, C. M.
1978-01-01
The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds boundary conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.
Project-Based Learning to Explore Taxicab Geometry
Ada, Tuba; Kurtulus, Aytac
2012-01-01
In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…
Predicting the Geometry Knowledge of Pre-Service Elementary Teachers
Duatepe Aksu, Asuman
2013-01-01
In this study, the aim was to examine the factors that predict the geometry knowledge of pre-service elementary teachers. Data was collected on 387 pre-service elementary teachers from four universities by using a geometry knowledge test, the van Hiele geometric thinking level test, a geometry self efficacy scale and a geometry attitude scale.…
Application of Analytical Geometry to the
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 9. Application of Analytical Geometry to the Form of Gear Teeth. V G A Goss. General Article Volume 18 Issue 9 September 2013 pp 817-831. Fulltext. Click here to view fulltext PDF. Permanent link:
On Ancient Babylonian Algebra and Geometry
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 8. On Ancient Babylonian Algebra and Geometry. Rahul Roy. General Article Volume 8 Issue 8 August 2003 pp 27-42. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/008/08/0027-0042. Keywords.
Causal random geometry from stochastic quantization
DEFF Research Database (Denmark)
Ambjørn, Jan; Loll, R.; Westra, W.
2010-01-01
in this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative quantum Hamiltonian of the random surface model including...... the sum over topologies. Interestingly, the generally fictitious stochastic time corresponds to proper time on the geometries...
Generalized geometry and non-symmetric gravity
Jurco, Branislav; Khoo, Fech Scen; Schupp, Peter; Vysoky, Jan
2015-01-01
Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion. The approach is related to the study of the low-energy effective closed string gravity actions.
D-instantons and asymptotic geometries
Bergshoeff, E.; Behrndt, K.
1998-01-01
The large-N limit of D-3-branes is expected to correspond to a superconformal field theory living on the boundary of the anti-de Sitter space appearing in the near-horizon geometry. Dualizing the D-3-brane to a D-instanton, we show that this limit is equivalent to a type IIB S-duality. In both cases
The Geometry of the Universe: Part 1
Francis, Stephanie
2009-01-01
This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…
Mathematics: Algebra and Geometry. GED Scoreboost.
Hoyt, Cathy
GED "Scoreboost" materials target exactly the skills one needs to pass the General Educational Development (GED) tests. This book focuses on the GED Mathematics test. To prepare for the test, the test taker needs to learn skills in number and operation sense, data and statistics, geometry and measurement, and algebra. To pass the test,…
Reshaping Mathematics for Understanding Motion Geometry.
Slovin, Hannah; Venenciano, Linda; Ishihara, Melanie; Beppu, Cynthia
This book introduces concepts of geometry that students use throughout middle-grade and higher-level mathematics courses. These concepts, presented through the study of transformations, provide a framework for other important topics such as number, measurement, proportional reasoning, and graphing on the coordinate plane. The book is designed for…
Quantum geometry of bosonic strings - revisited
Energy Technology Data Exchange (ETDEWEB)
Botelho, Luiz C.L.; Botelho, Raimundo C.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Universidade Federal Rural do Rio de Janeiro, RJ (Brazil). Dept. de Fisica
1999-07-01
We review the original paper by A.M. Polyakov (Quantum Geometry of Bosonic Strings) with corrections and improvements the concepts exposed there and following as closely as possible to the original A.M. Polyakov's paper. (author)
Foliations and the geometry of 3-manifolds
Calegari, Danny
2014-01-01
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
Fast rendering of scanned room geometries
DEFF Research Database (Denmark)
Olesen, Søren Krarup; Markovic, Milos; Hammershøi, Dorte
2014-01-01
.g. the range detection sensors used in the kinect device. This device provides a high rate of range data, which can be combined to give a very detailed map of the surrounding geometry. Such data was captured and has been presented in an earlier paper, incl. a demonstration of the principle of voxel...
Geometry and the Design of Product Packaging
Cherico, Cindy M.
2011-01-01
The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…
Size and geometry of hepatic radiofrequency lesions.
Mulier, S; Ni, Y; Miao, Y; Rosière, A; Khoury, A; Marchal, G; Michel, L
2003-12-01
To report and compare the size and geometry of hepatic radiofrequency (RF) lesions using the currently available commercial devices. A literature search was carried out for the period from January 1st 1990 to June 15th 2003. The commercial suppliers were asked to provide all available data. For each electrode and protocol, size and geometry of single-cycle thermal lesions were registered. No information at all on size and geometry of the inducible lesions was available for 17 of the 28 current commercial electrodes. Many descriptions of RF lesions are limited to the mean transverse diameter. With normal blood flow, diameter of lesions is often smaller than suggested by the length of the electrode tip or the diameter of the deployed prongs. Lesions are rarely perfect spheres but either ellipses or flattened spheres. Distortion of the RF lesion by nearby blood vessels is very common. Fusion of thermal zones between prongs of expandable electrodes can be incomplete. Blood flow interruption using a Pringle maneuver yields larger lesions that are less distorted and more complete. There is insufficient experimental data for many electrodes that are currently used in patients. RF companies should provide these data before releasing electrodes for use. For those electrodes for which data exist, coagulation lesions are often smaller, less spherical, less complete and less regular than generally presumed. Accurate knowledge of size and geometry of RF lesions is crucial to prevent local recurrence.
Geometry task sheets : grades pk-2
Rosenberg, Mary
2009-01-01
For grades PK-2, our Common Core State Standards-based resource meets the geometry concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students.
Geometry task sheets : grades 3-5
Rosenberg, Mary
2009-01-01
For grades 3-5, our Common Core State Standards-based resource meets the geometry concepts addressed by the NCTM standards and encourages the students to learn and review the concepts in unique ways. Each task sheet is organized around a central problem taken from real-life experiences of the students.
Strontium clusters: electronic and geometry shell effects
DEFF Research Database (Denmark)
Lyalin, Andrey G.; Solov'yov, Ilia; Solov'yov, Andrey V.
2008-01-01
The optimized structure and electronic properties of neutral, singly and doubly charged strontium clusters have been investigated using it ab initio theoretical methods based on density-functional theory. We have systematically calculated the optimized geometries of neutral, singly and doubly...
User Interface Design for Dynamic Geometry Software
Kortenkamp, Ulrich; Dohrmann, Christian
2010-01-01
In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch-capable DGS. We also give some hints on the educational benefits of proper user interface design.
Relating arithmetical techniques of proportion to geometry
DEFF Research Database (Denmark)
Wijayanti, Dyana
2015-01-01
The purpose of this study is to investigate how textbooks introduce and treat the theme of proportion in geometry (similarity) and arithmetic (ratio and proportion), and how these themes are linked to each other in the books. To pursue this aim, we use the anthropological theory of the didactic...
Fermoral Intercondylar Notch Geometry Of Nigerians | Didia ...
African Journals Online (AJOL)
The notch geometry had been implicated in anterior cruciate ligament (ACL) injuries and from this study we presume that the difference in incidence of ACL injuries between males and females is as a result of differences in intercondylar notch width index and the diameter of distal end of femur in both sexes. KEY WORDS: ...
Applications of Differential Geometry to Cartography
Benitez, Julio; Thome, Nestor
2004-01-01
This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…
Parametric Study Of Window Frame Geometry
DEFF Research Database (Denmark)
Zajas, Jan Jakub; Heiselberg, Per
2013-01-01
This paper describes a parametric study on window frame geometry with the goal of designing frames with very good thermal properties. Three different parametric frame models are introduced, deseribed by a number of variables. In the first part of the study, a process of sensitivity analysis...
Quasi-crystalline geometry for architectural structures
DEFF Research Database (Denmark)
Wester, Ture; Weinzieri, Barbara
The quasi-crystal (QC) type of material was discovered in 1983 by Dan Schechtman from Technion, Haifa. This new crystalline structure of material broke totally with the traditional conception of crystals and geometry introducing non-periodic close packing of cells with fivefold symmetry in 3D space...
Toric Geometry of the Regular Convex Polyhedra
Directory of Open Access Journals (Sweden)
Fiammetta Battaglia
2017-01-01
Full Text Available We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry.
Methods of algebraic geometry in control theory
Falb, Peter
1999-01-01
"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is qui...
Geometry optimization and vibrational frequencies of tetracene ...
African Journals Online (AJOL)
Tetracene is an organic semiconductor with chemical formula C18H12 used in organic field effecttransistor (OFET) and organic light emitting diode (OLED). In this work, the molecular geometry (optimized bond lengths and bond angles), vibrational frequencies and intensities, HOMO-LUMO Energy gap and Atomic charge ...
Special Relativity as a Simple Geometry Problem
de Abreu, Rodrigo; Guerra, Vasco
2009-01-01
The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…
Algebraic Geometry Solves an Old Matrix Problem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 12. Algebraic Geometry Solves an Old Matrix Problem. R Bhatia. Research News Volume 4 Issue 12 ... Author Affiliations. R Bhatia1. Statistics and Mathematics Unit, Indian Statistical Institute, 7, SJS Sansanwal Marg, New Delhi 110 016, India.
KAWA lecture notes on complex hyperbolic geometry
Rousseau, Erwan
2016-01-01
These lecture notes are based on a mini-course given at the fifth KAWA Winter School on March 24-29, 2014 at CIRM, Marseille. They provide an introduction to hyperbolicity of complex algebraic varieties namely the geometry of entire curves, and a description of some recent developments.
Determination of grain boundary geometry using TEM
Jang, H.; Farkas, D.; Hosson, J.T.M. De
An experimental method to obtain the grain boundary geometry using the transmission electron microscope is presented. The method allows Σ determination including grain boundary plane orientation. In order to determine the specialness of the grain boundary, three different criteria for maximum
Symbolic computations in applied differential geometry
Gragert, P.K.H.; Kersten, P.H.M.; Martini, Ruud
1983-01-01
The main aim of this paper is to contribute to the automatic calculations in differential geometry and its applications, with emphasis on the prolongation theory of Estabrook and Wahlquist, and the calculation of invariance groups of exterior differential systems. A large number of worked examples
Higher dimensional homogeneous cosmology in Lyra geometry
Indian Academy of Sciences (India)
Assuming a homogeneous perfect ﬂuid with ρ = ρ() and = (), we have obtained exact solutions for cosmological models in higher-dimension based on Lyra geometry. Depending on the form of metric chosen, the model is similar to FRW type. The explicit solutions of the scale factor are found via the assumption of an ...
Connecting Functions in Geometry and Algebra
Steketee, Scott; Scher, Daniel
2016-01-01
One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…
Quantity, resolution and syllable geometry | Lass | Stellenbosch ...
African Journals Online (AJOL)
Stellenbosch Papers in Linguistics. Journal Home · ABOUT · Advanced Search · Current Issue · Archives · Journal Home > Vol 10 (1983) >. Log in or Register to get access to full text downloads. Username, Password, Remember me, or Register. Quantity, resolution and syllable geometry. R Lass. Abstract. No abstract.
Magnetic resonance spectra and statistical geometry
Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints that introduce curvature into parameter space and discuss the appropriate...
On the geometry of discret Michell trusses
DEFF Research Database (Denmark)
Almegaard, Henrik
2011-01-01
given by Michell in 1904. A set of simple design rules are extracted and it is indicated how these rules can be used to construct discrete Michell truss geometries. A number of geometrical optimized discrete examples of known Michell trusses are presented and they meet these design rules very well....
Kulichevskaya, Irina S; Kostina, Lilia A; Valásková, Vendula; Rijpstra, W Irene C; Damsté, Jaap S Sinninghe; de Boer, Wietse; Dedysh, Svetlana N
2012-07-01
Two strains of subdivision 1 Acidobacteria, a pink-pigmented bacterium KA1(T) and a colourless isolate WH120(T), were obtained from acidic Sphagnum peat and wood under decay by the white-rot fungus Hyploma fasciculare, respectively. Cells of these isolates were Gram-negative-staining, non-motile, short rods, which were covered by large polysaccharide capsules and occurred singly, in pairs, or in short chains. Strains KA1(T) and WH120(T) were strictly aerobic mesophiles that grew between 10 and 33 °C, with an optimum at 22-28 °C. Both isolates developed under acidic conditions, but strain WH120(T) was more acidophilic (pH growth range 3.5-6.4; optimum, 4.0-4.5) than strain KA1(T) (pH growth range 3.5-7.3; optimum , 5.0-5.5). The preferred growth substrates were sugars. In addition, the wood-derived isolate WH120(T) grew on oxalate, lactate and xylan, while the peat-inhabiting acidobacterium strain KA1(T) utilized galacturonate, glucuronate and pectin. The major fatty acids were iso-C(15:0) and iso-C(17:1)ω8c; the cells also contained significant amounts of 13,16-dimethyl octacosanedioic acid. The quinone was MK-8. The DNA G+C contents of strains KA1(T) and WH120(T) were 54.1 and 51.7 mol%, respectively. Strains KA1(T) and WH120(T) displayed 97.8% 16S rRNA gene sequence similarity to each other. The closest recognized relatives were Acidobacterium capsulatum and Telmatobacter bradus (93.4-94.3% 16S rRNA gene sequence similarity). These species differed from strains KA1(T) and WH120(T) by their ability to grow under anoxic conditions, the absence of capsules, presence of cell motility and differing fatty acid composition. Based on these differences, the two new isolates are proposed as representing a novel genus, Acidicapsa gen. nov., and two novel species. Acidicapsa borealis gen. nov., sp. nov. is the type species for the new genus with strain KA1(T) (=DSM 23886(T)=LMG 25897(T)=VKM B-2678(T)) as the type strain. The name Acidicapsa ligni sp. nov. is proposed for
Miyazaki, Mikio; Kimiho, Chino; Katoh, Ryuhei; Arai, Hitoshi; Ogihara, Fumihiro; Oguchi, Yuichi; Morozumi, Tatsuo; Kon, Mayuko; Komatsu, Kotaro
2012-01-01
Three-dimensional dynamic geometry software has the power to enhance students' learning of spatial geometry. The purpose of this research is to clarify what potential using three-dimensional dynamic geometry software can offer us in terms of how to develop the spatial geometry curriculum in lower secondary schools. By focusing on the impacts the…
2015-12-01
Representation Geometry to Constructive Solid Geometry by Clifford W Yapp Approved for public release; distribution...US Army Research Laboratory An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to...Constructive Solid Geometry by Clifford W Yapp Survivability/Lethality Analysis Directorate, ARL Approved for public release
Classical Geometries in Modern Contexts Geometry of Real Inner Product Spaces Third Edition
Benz, Walter
2012-01-01
The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Mobius and Lie as well as geometries where Lorentz transformations play the key role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for insta
Jupri, Al
2017-04-01
In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.
College geometry an introduction to the modern geometry of the triangle and the circle
Altshiller-Court, Nathan
2007-01-01
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
The effectivnes of learning spatial geometry with 3D geometry software
Roblek, Manca
2016-01-01
In the thesis spatial ability is considered as the ability to manipulate, generate and retain well-structured visual images. Three elements of spatial ability are presented in detail: spatial visualization, spatial relations and mental rotations. Spatial ability plays an important role in school mathe- matics when students learn about space geometry. Students use different manipulatives to help them through studying. Computer programs for spa- tial geometry are not yet introduced into learnin...
AC Dielectrophoresis Using Elliptic Electrode Geometry
Directory of Open Access Journals (Sweden)
S. M. Rezaul Hasan
2011-01-01
Full Text Available This paper presents negative AC dielectrophoretic investigations using elliptic electrode geometry. Simulations of the electric field gradient variation using various ratios of the semimajor and the semiminor axis were carried out to determine the optimum elliptic geometry for the dielectrophoretic electrokinetics of specimen in an assay with laminar (low Reynolds number fluid flow. Experimental setup of the elliptic electrode assembly using PCB fabrication and electrokinetic accumulation of specimen in a dielectrophoretic cage is also being reported. Using an actuating signal between 1 kHz and 1 MHz, successful trapping of 45 μm polystyrene beads suspended in distilled water was demonstrated due to negative dielectrophoresis near 100 kHz using the novel elliptic electrode.
Geometry of Knowledge for Intelligent Systems
Resconi, Germano
2013-01-01
The book is on the geometry of agent knowledge. The important concept studied in this book is the Field and its Geometric Representation. To develop a geometric image of the gravity , Einstein used Tensor Calculus but this is very different from the knowledge instruments used now, as for instance techniques of data mining , neural networks , formal concept analysis ,quantum computer and other topics. The aim of this book is to rebuild the tensor calculus in order to give a geometric representation of agent knowledge. By using a new geometry of knowledge we can unify all the topics that have been studied in recent years to create a bridge between the geometric representation of the physical phenomena and the geometric representation of the individual and subjective knowledge of the agents.