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
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
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.
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
Analytic Geometry, A Tentative Guide.
Helwig, G. Alfred; And Others
This teacher's guide for a semester course in analytic geometry is based on the text "Analytic Geometry" by W. K. Morrill. Included is a daily schedule of suggested topics and homework assignments. Specific teaching hints are also given. The content of the course includes point and plane vectors, straight lines, point and space vectors, planes,…
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…
Trigonometry and Analytic Geometry: Curriculum Guide.
Harlandale Independent School District, San Antonio, TX. Career Education Center.
The guide (one-quarter trigonometry course; two-quarter analytic geometry course) provides both subject matter and career preparation assistance for advanced mathematics teachers. It is arranged in vertical columns relating curriculum concepts in trigonometry and analytic geometry to curriculum performance objectives, career concepts and teaching…
Higher geometry an introduction to advanced methods in analytic geometry
Woods, Frederick S
2005-01-01
For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study
Analytic Methods in Investigative Geometry.
Dobbs, David E.
2001-01-01
Suggests an alternative proof by analytic methods, which is more accessible than rigorous proof based on Euclid's Elements, in which students need only apply standard methods of trigonometry to the data without introducing new points or lines. (KHR)
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
Analytic Coleman-de Luccia Geometries
Energy Technology Data Exchange (ETDEWEB)
Dong, Xi; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC; Harlow, Daniel; /Stanford U., ITP /Stanford U., Phys. Dept.
2012-02-16
We present the necessary and sufficient conditions for a Euclidean scale factor to be a solution of the Coleman-de Luccia equations for some analytic potential V ({psi}), with a Lorentzian continuation describing the growth of a bubble of lower-energy vacuum surrounded by higher-energy vacuum. We then give a set of explicit examples that satisfy the conditions and thus are closed-form analytic examples of Coleman-de Luccia geometries.
Quantum Secret Sharing by applying Analytic Geometry
Liu, Ruilong
2010-01-01
In this paper, we investigate a novel $(2,2)$-threshold scheme and then generalize this to a $(n,n)$-threshold scheme for quantum secret sharing (QSS) which makes use of the fundamentals of Analytic Geometry. The dealer aptly selects GHZ states related to the coefficients which determine straight lines on a two-dimension plane. Then by computing each two of the lines intercept or not, we obtain a judging matrix whose rank can be used to determine the secret stored in entangled bits. Based on ...
Analytic Geometry, Student Text, Part 1. Revised Edition.
Ayre, H. Glenn; And Others
This is part one of a three-part School Mathematics Study Group (SMSG) textbook. This part contains the first five chapters including: (1) Analytic Geometry, (2) Coordinates and the Line, (3) Vectors and Their Applications, (4) Proof by Analytic Methods, and (5) Graphs and Their Equations. (MK)
Analytic Geometry. Student's Text, Unit No. 64. Revised Edition.
Ayre, H. Glenn; And Others
This text provides a one-semester study of analytic geometry for secondary school students. It is designed for use at the 12th grade level. A deliberate effort was made to tie this text to previous SMSG texts; the usual language of sets, ordered pairs, number properties, etc. are included. This flavor is what distinguishes this book from others in…
Pre-Calculus Instructional Guide for Elementary Functions, Analytic Geometry.
Montgomery County Public Schools, Rockville, MD.
This is a guide for use in semester-long courses in Elementary Functions and Analytic Geometry. A list of entry-level skills and a list of approved textbooks is provided. Each of the 18 units consists of: (1) overview, suggestions for teachers, and suggested time; (2) list of objectives; (3) cross-references guide to approved textbooks; (4) sample…
Application of Analytic Geometry to Ternary and Quaternary Diagrams.
MacCarthy, Patrick
1986-01-01
Advantages of representing ternary and quaternary composition diagrams by means of rectangular coordinates were pointed out in a previous paper (EJ 288 693). A further advantage of that approach is that analytic geometry, based on rectangular coordinates, is directly applicable as demonstrated by the examples presented. (JN)
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Miron, Radu
2012-01-01
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...
Analytic Geometry. Teacher's Commentary, Unit No. 65. Revised Edition.
Ayre, H. Glenn; And Others
This is the teacher's guide to the SMSG text ANALYTIC GEOMETRY. The text is designed to be used as a one-semester course for 12th grade students. Included in this guide are: (1) suggested length of study for each chapter; (2) discussion of each chapter that is in the student text; (3) comments keyed to the pages of the student's text to provide…
Analytic hyperbolic geometry in N dimensions an introduction
Ungar, Abraham Albert
2014-01-01
The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author's gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation la
AN ADVANCED PLACEMENT COURSE IN ANALYTIC GEOMETRY AND CALCULUS (MATHEMATICS XV X AP).
DEROLF, JOHN J.; MIENTKA, WALTER E.
THIS TEXT ON ANALYTIC GEOMETRY AND CALCULUS IS A CORRESPONDENCE COURSE DESIGNED FOR ADVANCED PLACEMENT OF HIGH SCHOOL STUDENTS IN COLLEGE. EACH OF THE 21 LESSONS INCLUDES READING ASSIGNMENTS AND LISTS OF PROBLEMS TO BE WORKED. IN ADDITION, SUPPLEMENTARY EXPLANATIONS AND COMMENTS ARE INCLUDED THAT (1) PROVIDE ILLUSTRATIVE EXAMPLES OF CONCEPTS AND…
Yildiz, Avni; Baltaci, Serdal
2016-01-01
Contextual teaching and learning can fill the gap between abstract mathematical concepts and real life practices. Analytic geometry is among the courses which constitutes a gap in this regard. Moreover, when the relevant literature is reviewed, it is seen that researches on analytic geometry mainly focus on achievement and comparing the…
Analytic solutions for seismic travel time and ray path geometry through simple velocity models.
Energy Technology Data Exchange (ETDEWEB)
Ballard, Sanford
2007-12-01
The geometry of ray paths through realistic Earth models can be extremely complex due to the vertical and lateral heterogeneity of the velocity distribution within the models. Calculation of high fidelity ray paths and travel times through these models generally involves sophisticated algorithms that require significant assumptions and approximations. To test such algorithms it is desirable to have available analytic solutions for the geometry and travel time of rays through simpler velocity distributions against which the more complex algorithms can be compared. Also, in situations where computational performance requirements prohibit implementation of full 3D algorithms, it may be necessary to accept the accuracy limitations of analytic solutions in order to compute solutions that satisfy those requirements. Analytic solutions are described for the geometry and travel time of infinite frequency rays through radially symmetric 1D Earth models characterized by an inner sphere where the velocity distribution is given by the function V (r) = A-Br{sup 2}, optionally surrounded by some number of spherical shells of constant velocity. The mathematical basis of the calculations is described, sample calculations are presented, and results are compared to the Taup Toolkit of Crotwell et al. (1999). These solutions are useful for evaluating the fidelity of sophisticated 3D travel time calculators and in situations where performance requirements preclude the use of more computationally intensive calculators. It should be noted that most of the solutions presented are only quasi-analytic. Exact, closed form equations are derived but computation of solutions to specific problems generally require application of numerical integration or root finding techniques, which, while approximations, can be calculated to very high accuracy. Tolerances are set in the numerical algorithms such that computed travel time accuracies are better than 1 microsecond.
Navau, Carles; Del-Valle, Nuria; Sanchez, Alvaro
2016-11-01
Magnetic skyrmions are candidates for a new generation of information carriers due to their nanometric size and topologically protected stability. The study of the dynamics of such skyrmions in racetrack geometries and, in general, in confined geometries becomes essential to achieve these goals. Here we present analytical expressions for the trajectories of skyrmions in confined geometries (including long tracks and squared samples) when driven by polarized electric currents. The force exerted by the borders is derived as a function of the material parameters (anisotropy, Dzyaloshinskii-Moriya, and exchange constants) and incorporated in the equation of motion of the skyrmions. We find the general expressions for the trajectories in several possible scenarios, and we also find simple expressions for the stationary position, the velocity, as well as for the threshold velocity of the driving electrons that could overcome the edge repulsion. In fully confined geometries, the geometric edges can produce a naturally oscillating movement, allowing for dynamical resonances if the driving current is an ac current with adequate frequency. Numerical micromagnetic simulations considering typical experimental parameters are used to corroborate the theory.
Kösa, Temel
2016-01-01
The purpose of this study was to investigate the effects of using dynamic geometry software on preservice mathematics teachers' spatial visualization skills and to determine whether spatial visualization skills can be a predictor of success in learning analytic geometry of space. The study used a quasi-experimental design with a control group.…
Olivares, Maria Angelica; And Others
The development of a diagnostic test at the Catholic University of Chile is described. The 50-item multiple choice test is used as an entrance and prerequisite test for students about to take a first university course in trigonometry and analytic geometry (MAT-111). Thirty items pertain to algebra and 20 to geometry. Each question corresponds to…
Sanchez-Parcerisa, D; Cortés-Giraldo, M A; Dolney, D; Kondrla, M; Fager, M; Carabe, A
2016-02-21
In order to integrate radiobiological modelling with clinical treatment planning for proton radiotherapy, we extended our in-house treatment planning system FoCa with a 3D analytical algorithm to calculate linear energy transfer (LET) in voxelized patient geometries. Both active scanning and passive scattering delivery modalities are supported. The analytical calculation is much faster than the Monte-Carlo (MC) method and it can be implemented in the inverse treatment planning optimization suite, allowing us to create LET-based objectives in inverse planning. The LET was calculated by combining a 1D analytical approach including a novel correction for secondary protons with pencil-beam type LET-kernels. Then, these LET kernels were inserted into the proton-convolution-superposition algorithm in FoCa. The analytical LET distributions were benchmarked against MC simulations carried out in Geant4. A cohort of simple phantom and patient plans representing a wide variety of sites (prostate, lung, brain, head and neck) was selected. The calculation algorithm was able to reproduce the MC LET to within 6% (1 standard deviation) for low-LET areas (under 1.7 keV μm(-1)) and within 22% for the high-LET areas above that threshold. The dose and LET distributions can be further extended, using radiobiological models, to include radiobiological effectiveness (RBE) calculations in the treatment planning system. This implementation also allows for radiobiological optimization of treatments by including RBE-weighted dose constraints in the inverse treatment planning process.
Human eye analytical and mesh-geometry models for ophthalmic dosimetry using MCNP6
Energy Technology Data Exchange (ETDEWEB)
Angelocci, Lucas V.; Fonseca, Gabriel P.; Yoriyaz, Helio, E-mail: hyoriyaz@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2015-07-01
Eye tumors can be treated with brachytherapy using Co-60 plaques, I-125 seeds, among others materials. The human eye has regions particularly vulnerable to ionizing radiation (e.g. crystalline) and dosimetry for this region must be taken carefully. A mathematical model was proposed in the past [1] for the eye anatomy to be used in Monte Carlo simulations to account for dose distribution in ophthalmic brachytherapy. The model includes the description for internal structures of the eye that were not treated in previous works. The aim of this present work was to develop a new eye model based on the Mesh geometries of the MCNP6 code. The methodology utilized the ABAQUS/CAE (Simulia 3DS) software to build the Mesh geometry. For this work, an ophthalmic applicator containing up to 24 model Amersham 6711 I-125 seeds (Oncoseed) was used, positioned in contact with a generic tumor defined analytically inside the eye. The absorbed dose in eye structures like cornea, sclera, choroid, retina, vitreous body, lens, optical nerve and optical nerve wall were calculated using both models: analytical and MESH. (author)
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
Tensors and Differential Geometry Applied to Analytic and Numerical Coordinate Generation
1981-01-01
Schild [9], Brand [10], Spain [111, Truesdell and Toupin [12], Struik [13], Sokolnikoff [14], Willmore [15], O’Neill [16], and Kreyszig [17], [18], on...Oxford, At The Clarendon Press (1959). [16] O’Neill, B., Elementary Differential Geometry, Academic Press, New York (1966). 193 [17) Kreyszig , E...Differential Geometry, Mathematical Exposition No. 11, University of Toronto Press (1959) [181 Kreyszig , E., Introduction to Differential Geometry and
关于解析几何的教学思索%Reflections on the Teaching of Analytic Geometry
Institute of Scientific and Technical Information of China (English)
姜永艳; 卜维春
2013-01-01
The teaching of analytic geometry aims at cultivating students' ability of spatial imagination, logistics and abstract. This paper discusses the main ideas, methods and teaching styles in analytic geometry teaching, and proposes new teaching method combing theory with practice.% 在解析几何的教学中，以培养学生的空间想象能力、逻辑能力、抽象能力为目的，本文通过在解析几何的主要思想、主要方法、授课方式等方面进行了论述，更对在和实践相结合上提出了新的教学方法。
Ustinov, Eugene A.
2006-01-01
In a recent publication (Ustinov, 2002), we proposed an analytic approach to evaluation of radiative and geophysical weighting functions for remote sensing of a blackbody planetary atmosphere, based on general linearization approach applied to the case of nadir viewing geometry. In this presentation, the general linearization approach is applied to the limb viewing geometry. The expressions, similar to those obtained in (Ustinov, 2002), are obtained for weighting functions with respect to the distance along the line of sight. Further on, these expressions are converted to the expressions for weighting functions with respect to the vertical coordinate in the atmosphere. Finally, the numerical representation of weighting functions in the form of matrices of partial derivatives of grid limb radiances with respect to the grid values of atmospheric parameters is used for a convolution with the finite field of view of the instrument.
A reflection on analytic geometry teaching%关于解析几何课程教学反思
Institute of Scientific and Technical Information of China (English)
赵云平
2015-01-01
In this paper, the mathematics education in normal colleges in various measures of the analytic geometry teaching, the content, method and means to reform the thinking, put forward its own views.%本文就高等师范院校数学教育各专业解析几何教学的措施、内容、方法和手段等将如何改革进行了思考，提出了自己的看法。
Approximate analytical solution for the isothermal Lane Emden equation in a spherical geometry
Soliman, Moustafa Aly; Al-Zeghayer, Yousef
2015-10-01
This paper obtains an approximate analytical solution for the isothermal Lane-Emden equation that models a self-gravitating isothermal sphere. The approximate solution is obtained by perturbation methods in terms of small and large distance parameters. The approximate solution is compared with the numerical solution. The approximate solution obtained is valid for all values of the distance parameter.
A Comparison of Two Methods of Teaching Selected Topics in Plane Analytic Geometry.
Bundrick, Charles Michael
Reported are the results of a study to determine if there is a difference in learning as measured by an achievement test between high school students who study plane analytic geometric topics via a vector approach and those who study the same topics via a traditional approach. Secondary objectives concerned the transfer to further topics in solid…
Directory of Open Access Journals (Sweden)
N. Hadadin
2011-07-01
Full Text Available The effects of basin hydrology on channel hydraulic variability for incised streams were investigated using available field data sets and models of watershed hydrology and channel hydraulics for Yazoo River Basin, USA. The study presents the hydraulic relations of bankfull discharge, channel width, mean depth, cross- sectional area, longitudinal slope, unit stream power, and runoff production as a function of drainage area using simple linear regression. The hydraulic geometry relations were developed for sixty one streams, twenty of them are classified as channel evaluation model (CEM Types IV and V and forty one of them are streams of CEM Types II and III. These relationships are invaluable to hydraulic and water resources engineers, hydrologists, and geomorphologists, involved in stream restoration and protection. These relations can be used to assist in field identification of bankfull stage and stream dimension in un-gauged watersheds as well as estimation of the comparative stability of a stream channel.
Results of this research show good fit of hydraulic geometry relationships in the Yazoo River Basin. The relations indicate that bankfull discharge, channel width, mean depth, cross-sectional area have stronger correlation to changes in drainage area than the longitudinal slope, unit stream power, and runoff production for streams CEM Types II and III. The hydraulic geometry relations show that runoff production, bankfull discharge, cross-sectional area, and unit stream power are much more responsive to changes in drainage area than are channel width, mean depth, and slope for streams of CEM Types IV and V. Also, the relations show that bankfull discharge and cross-sectional area are more responsive to changes in drainage area than are other hydraulic variables for streams of CEM Types II and III. The greater the regression slope, the more responsive to changes in drainage area will be.
MATLAB在解析几何教学中的应用%Application of MATLAB in Analytic Geometry Teaching
Institute of Scientific and Technical Information of China (English)
司凤娟
2013-01-01
In the paper, the application of Matlab software in analytic geometry is studied in depth, and the general method for the drawing of dual implicit function and ternary implicit function is discussed. The cartoon function of Matlab is applied to the teaching of analytic geometry, which makes the teaching lively and vividly, and makes the students easily understand it. The different graphics in the same coordinate system are researched, so that the students can know the position relationship of the graphics clearly, and are released from complicated calculations.%深入研究MATLAB软件在解析几何中的应用，讨论了二元隐函数和三元隐函数作图的一般方法。将MATLAB的动画功能应用于解析几何的教学中，使教学形象生动，学生易于理解。研究把不同的图形作于同一坐标系下，学生可对图形的位置关系一目了然，让学生从繁琐的计算中解脱出来。
Vieru, Andrei
2016-01-01
The renormalization of MZV was until now carried out by algebraic means. In this paper, we show that renormalization in general, and in particular of the multiple zeta functions, is more than just a pure algebraic convention. We give a simple analytic method of computing the regularized values of multiple zeta functions in any dimension for arguments of the form (1,...,1), where the series do not converge. These values happen to be the coefficients of the asymptotic expansion of the inverse G...
Ambia-Garrido, Joaquin; Pettitt, Montgomery
2008-03-01
The change in some thermodynamic quantities such as Gibbs' free energy, entropy and enthalpy of the binding of a particle tethered to a surface or particle are analytically calculated. These particles are considered ellipsoids and submerged in a liquid. The ionic strength of the media allows the linearized version of the Poisson-Boltzmann equation (from the theory of the double layer interaction) to properly describe the interactions between an ion penetrable spheroid and a hard plate. We believe that this is an adequate model for a DNA chip and the predicted electrostatic effects suggest the feasibility of electronic control and detection of DNA hybridization and design of chips underline avoiding the DNA folding problem.
You, Wei; Wang, Yuanyuan
2011-11-01
In ultrasound color flow imaging (CFI), the single-ensemble eigen-based filters can reject clutter components using each slow-time ensemble individually. They have shown excellent spatial adaptability. This article proposes a novel clutter rejection method called the single-ensemble geometry filter (SGF), which is derived from an analytic geometry perspective. If the transmitted pulse number M equals two, the clutter component distribution on a two-dimensional (2-D) plane will be similar to a tilted ellipse. Therefore, the direction of the major axis of the ellipse can be used as the first principal component of the autocorrelation matrix estimated from multiple ensembles. Then the algorithm is generalized from 2-D to a higher dimensional space by using linear algebra representations of the ellipse. Comparisons have been made with the high-pass filter (HPF), the Hankel-singular value decomposition (SVD) filter and the recursive eigen-decomposition (RED) method using both simulated and human carotid data. Results show that compared with HPF and Hankel-SVD, the proposed filter causes less bias on the velocity estimation when the clutter velocity is close to that of the blood flow. On the other hand, the proposed filter does not need to update the autocorrelation matrix and can achieve better spatial adaptability than the RED.
Institute of Scientific and Technical Information of China (English)
WANG YouYu; HUANG Tian; ZHAO XueMan; MEI JiangPing; Derek G CHETWYND
2008-01-01
Stiffness modeling is one of the most significant issues in the design of parallel kinematic machine (PKM).This paper presents a semi-analytical approach that enables the stiffness of PKM with complex machine frame geometry to be estimated effectively.This approach can be implemented by three steps:(i) decomposition of the entire system into two sub-systems associated with the parallel mechanism and the machine frame respectively;(ii) stiffness modeling of each sub-system using the analytical approach and the finite element analysis;and (iii) generation of the stiffness model of the entire system by means of linear superposition.In the modeling process of each sub-system,the virtual work princi-ple and overall deflection Jacobian are employed with special attention to the bending rigidity of the constrained passive limb and the interface stiffness of the machine frame.The stiffness distribution of a 5-DOF hybrid robot named TriVariant-B is investigated as an example to illustrate the effectivaness of this approach.The contributions of component rigidities to that of the system are evaluated using global indices.It shows that the results achieved by this approach have a good match to those obtained through finite element analysis and experiments.
Directory of Open Access Journals (Sweden)
Pablo Aguiar
2012-01-01
Full Text Available Positron emission mammography (PEM cameras are novel-dedicated PET systems optimized to image the breast. For these cameras it is essential to achieve an optimum trade-off between sensitivity and spatial resolution and therefore the main challenge for the novel cameras is to improve the sensitivity without degrading the spatial resolution. We carry out an analytical study of the effect of the different detector geometries on the photon sensitivity and the angle of incidence of the detected photons which is related to the DOI effect and therefore to the intrinsic spatial resolution. To this end, dual head detectors were compared to box and different polygon-detector configurations. Our results showed that higher sensitivity and uniformity were found for box and polygon-detector configurations compared to dual-head cameras. Thus, the optimal configuration in terms of sensitivity is a PEM scanner based on a polygon of twelve (dodecagon or more detectors. We have shown that this configuration is clearly superior to dual-head detectors and slightly higher than box, octagon, and hexagon detectors. Nevertheless, DOI effects are increased for this configuration compared to dual head and box scanners and therefore an accurate compensation for this effect is required.
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.
Energy Technology Data Exchange (ETDEWEB)
Delcey, Mickaël G. [Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala (Sweden); Freitag, Leon; González, Leticia, E-mail: leticia.gonzalez@univie.ac.at [Institut für Theoretische Chemie, Universität Wien, Währinger Straße 17, 1090 Vienna (Austria); Pedersen, Thomas Bondo [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo (Norway); Aquilante, Francesco [Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala (Sweden); Dipartimento di Chimica “G. Ciamician,” Università di Bologna, V. F. Selmi 2, 40126 Bologna (Italy); Lindh, Roland, E-mail: roland.lindh@kemi.uu.se [Department of Chemistry – Ångström, The Theoretical Chemistry Programme, Uppsala University, Box 518, 751 20 Uppsala (Sweden); Uppsala Center for Computational Chemistry - UC3, Uppsala University, Box 518, 751 20 Uppsala (Sweden)
2014-05-07
We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032 Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 Å for S{sub 0} and 0.11 Å for T{sub 1}, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.
Energy Technology Data Exchange (ETDEWEB)
Kallinikos, N.; Isliker, H.; Vlahos, L.; Meletlidou, E. [Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece)
2014-06-15
An analytical description of magnetic islands is presented for the typical case of a single perturbation mode introduced to tokamak plasma equilibrium in the large aspect ratio approximation. Following the Hamiltonian structure directly in terms of toroidal coordinates, the well known integrability of this system is exploited, laying out a precise and practical way for determining the island topology features, as required in various applications, through an analytical and exact flux surface label.
Bruce, William J; Maxwell, E A; Sneddon, I N
1963-01-01
Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions
信息技术运用与解析几何教学的整合效应%Combining Information Technology with Analytic Geometry Teaching
Institute of Scientific and Technical Information of China (English)
费谏章
2011-01-01
本文探讨如何将信息技术与解析几何教学进行整合，从而实现教学内容的呈现方式、学生的学习方式、教师的教学方式和师生的互动方式的变革发展。%This paper expounds how to combine information technology with analytic geometry teaching, thus to transform content presentation, learning process, teaching methods and interaction between teachers and students.
Energy Technology Data Exchange (ETDEWEB)
Tomaschewski, Fernanda K.; Segatto, Cynthia F., E-mail: fernandasls_89@hotmail.com, E-mail: cynthia.segatto@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional
2015-07-01
Presented here is a decomposition method based on series representation of the group angular fluxes and delayed neutron precursors in smoothly continuous functions for energy multigroups, slab-geometry discrete ordinates kinetics equations supplemented with a prescribed number of delayed neutron precursors. Numerical results to a non-reflected sub-critical slab stabilized by steady-state sources are given to illustrate the accuracy and efficiency of the o offered method. (author)
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
2014-01-01
One of the well-known problems in the curves and surfaces reconstruction theory regarding global analytic object description, besides the description of its curvature changes, inflexions and non-bijective parts, is the existence of oscillations near point discontinuities in the middle of the range and at the boundaries of the description. In the ship geometric modelling, ship hull form is usually described globally using parametric methods based on B-spline and NURB-spline, for they have ge...
Energy Technology Data Exchange (ETDEWEB)
Salama, A. [Atomic Energy Authority (AEA), Cairo (Egypt). Nuclear Research Center
2014-11-15
In this paper we implement the local analytical solution technique to the problem of heat transfer in axisymmetric annulus geometry with internal heating element. This method has shown to be very accurate in estimating the temperature field for axisymmetric problems even for coarse mesh. It is shown that this method reduces to the analytical solution for unidirectional heat transfer in the radial direction in homogeneous media. The technique is based on finding an analytical expression for the temperature field in the radial direction within each grid cell. This means that the temperature field in each cell is allowed to change in a nonlinear fashion along the radial direction. We compare this technique with the traditional finite volume technique and show that; with only few cells in the radial direction, this technique arrives at the mesh-independent solution quite accurately whereas it required denser mesh to arrive closer to this solution using traditional techniques. This method is proposed to the 1D codes that are currently being used to simulate thermalhydraulic characteristics of reactor systems. Furthermore, we also implement the experimental temperature field algorithm in which the governing equations are approximated for each cell as it would without extra manipulation to the governing equations. This technique is very simple and separates the physics from the solving part.
Chattopadhyay, Sudip; Chaudhuri, Rajat K; Freed, Karl F
2011-04-28
The improved virtual orbital (IVO) complete active space (CAS) configuration interaction (IVO-CASCI) method is a simplified CAS self-consistent field (SCF), CASSCF, method. Unlike the CASSCF approach, the IVO-CASCI method does not require iterations beyond an initial SCF calculation, rendering the IVO-CASCI scheme computationally more tractable than the CASSCF method and devoid of the convergence problems that sometimes plague CASSCF calculations as the CAS size increases, while retaining all the essential positive benefits of the CASSCF method. Earlier applications demonstrate that the IVO-CASCI energies are at least as accurate as those from the CASSCF and provide the impetus for our recent development of the analytical derivative procedures that are necessary for a wide applicability of the IVO-CASCI approach. Here we test the ability of the analytic energy gradient IVO-CASCI approach (which can treat both closed- and open-shell molecules of arbitrary spin multiplicity) to compute the equilibrium geometries of four organic radicaloid species, namely, (i) the diradicals trimethylenemethane (TMM), 2,6-pyridyne, and the 2,6-pyridynium cation and (ii) a triradical 1,2,3-tridehydrobenzene (TDB), using various basis sets and different choices for the active space. Although these systems and related molecules have fascinated theoretical chemists for many years, their strong multireference character makes their description quite difficult with most standard many-body approaches. Thus, they provide ideal tests to assess the performance of the IVO-CASCI method. The present work demonstrates consistent agreement with far more expensive benchmark state-of-the-art ab initio calculations and thereby indicates that this new gradient method is able to describe the geometries of various radicaloids very accurately, even when small, but qualitatively correct, reference spaces are used. For example, the IVO-CASCI method leads to a monocyclic structure for the 2,6-isomers of the
Geometry from Information Geometry
Caticha, Ariel
2015-01-01
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.
Modestino, Giuseppina
2016-01-01
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law. Fundamentally, three space-time amounts describe dynamics. The relationship between position and field intensity is analytic, estimable in euclidean space, and considering a linear reference system for the time parameter. The formulation shows compatibility with fundamental rules of classical mechanics, highlighting also hitherto unknown properties, as a perfect analogy between morphological and physical parameters, such as the complete correspondence between the eccentricity and the momentum in the orbital motion. Moreover, the procedure naturally contains relativistic formulation without introducing any special hypothesis on light speed isotropy, asking so the question about the actual need to introduce the concept of space-time curvature for the correct interpretation of physics ...
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Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)
2015-07-01
In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)
Institute of Scientific and Technical Information of China (English)
韦程东; 刘逸; 徐庆娟; 郭金; 陈建伟
2011-01-01
指出目前解析几何教学中存在的一些问题，讨论在解析几何的教学中融入数学建模思想的必要性，探索如何在解析几何教材、教学方法等方面融入数学建模思想的方法．%The paper points out some problems existing in the teaching of Analytic Geometry and discusses the necessity of melting mathematical modeling thought into Analytic Geometry teaching and the method of how to melt it in the teaching materials and the teaching of Analytic Geometry.
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...
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...
"The Development and Application of Analytic Geometry" of CAI Software%《解析几何》CAI软件的开发与应用
Institute of Scientific and Technical Information of China (English)
任永宏
2015-01-01
《解析几何》多媒体CAI软件在页面设计、内容导航、学习自查、答疑、以及师生交互、生生交互等方面均充分利用了网络技术的特点，便于学生进行网络学习。软件有多种应用形式，可供教师在多功能教室进行群体教学，显著提高教学质量；可供个体远程上网学习、测试、评估、互动；它是一个丰富的高校师生数学学习资源库。%"Analytic geometry" multimedia CAI software in the page design, navigation, learning self-examination, Q & A, and teacher-student interaction, student student interaction and other aspects were made full use of the characteristics of network technology, to facilitate students' learning. Various forms of application software, can be used by teachers in the multi-function classroom teaching groups, significantly improve the quality of teaching; for individual remote online learning, test, evaluation, interaction; it is a rich university students mathematics learning resource repository.
Math 1813 (PIPI): Analytic Geometry.
Oklahoma State Univ., Stillwater. Coll. of Engineering.
This study guide, designed for use at Oklahoma State University, contains lists of activities for students to perform based on the "mastery of learning" concept. The activities include readings, problems, self evaluations, and assessment tasks. The units included are: Lines in a Plane, Conics, Transformations, Polar Coordinates,…
Modern calculus and analytic geometry
Silverman, Richard A
2012-01-01
A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory - many of the answers are fo
Technical calculus with analytic geometry
Gersting, Judith L
2010-01-01
This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills.Initial chapters cover functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, using the derivative, in
Geometry for the Secondary School
Moalem, D.
1977-01-01
A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)
Bozkaya, Uğur; Sherrill, C David
2013-08-07
Orbital-optimized coupled-electron pair theory [or simply "optimized CEPA(0)," OCEPA(0), for short] and its analytic energy gradients are presented. For variational optimization of the molecular orbitals for the OCEPA(0) method, a Lagrangian-based approach is used along with an orbital direct inversion of the iterative subspace algorithm. The cost of the method is comparable to that of CCSD [O(N(6)) scaling] for energy computations. However, for analytic gradient computations the OCEPA(0) method is only half as expensive as CCSD since there is no need to solve the λ2-amplitude equation for OCEPA(0). The performance of the OCEPA(0) method is compared with that of the canonical MP2, CEPA(0), CCSD, and CCSD(T) methods, for equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions between radicals. For bond lengths of both closed and open-shell molecules, the OCEPA(0) method improves upon CEPA(0) and CCSD by 25%-43% and 38%-53%, respectively, with Dunning's cc-pCVQZ basis set. Especially for the open-shell test set, the performance of OCEPA(0) is comparable with that of CCSD(T) (ΔR is 0.0003 Å on average). For harmonic vibrational frequencies of closed-shell molecules, the OCEPA(0) method again outperforms CEPA(0) and CCSD by 33%-79% and 53%-79%, respectively. For harmonic vibrational frequencies of open-shell molecules, the mean absolute error (MAE) of the OCEPA(0) method (39 cm(-1)) is fortuitously even better than that of CCSD(T) (50 cm(-1)), while the MAEs of CEPA(0) (184 cm(-1)) and CCSD (84 cm(-1)) are considerably higher. For complete basis set estimates of hydrogen transfer reaction energies, the OCEPA(0) method again exhibits a substantially better performance than CEPA(0), providing a mean absolute error of 0.7 kcal mol(-1), which is more than 6 times lower than that of CEPA(0) (4.6 kcal mol(-1)), and comparing to MP2 (7.7 kcal mol(-1)) there is a more than 10-fold reduction in errors. Whereas the MAE for the CCSD method is
Methods for euclidean geometry
Byer, Owen; Smeltzer, Deirdre L
2010-01-01
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
The Application of Exploratory Learning Mode in Analytic Geometry Teaching%探索性学习模式在解析几何教学中的应用
Institute of Scientific and Technical Information of China (English)
李胜平; 王俊杰; 徐斌
2015-01-01
根据解析几何课程的教学实践，针对学习该课程所遇到的问题进行分析研究，改进课堂教学方法，引入探索性的学习模式，提出了问题教学方法的探索、类比推理方法的探索、联想推广定理方法的探索，以提高解析几何课程的教学质量。%According to the teaching practice of analytic geometry ,we analyze problems in the course ,improve teach‐ing methods ,and give exploratory learning mode .In order to improve the teaching quality of analytic geometry ,we give exploration of problems teaching method ,the exploration of analogical reasoning method ,the exploration of lenovo theo‐rem method .
引导学生学习解析几何中的平面几何原型%Lead the students to study the plane geometric prototype of analytic geometry
Institute of Scientific and Technical Information of China (English)
王占君; 吕效国
2007-01-01
通过列举一些特定的例子说明,教师如何在数学教学过程中,有意识地引导学生学习解析几何中的平面几何原型,并结合解析几何中的习题将它们彼此之间联系起来,这有助于认识它们的一些新的特性.%Cited some specific examples and revealed how the teachers,in the teaching of mathematics, should intentionally lead the students to Study the plane geometric prototype of analytic geometry,so as to interrelate them and tap the resources of exercise in analytic geometry,thus realize their new properties.
Institute of Scientific and Technical Information of China (English)
李栋红
2014-01-01
Matlab technology with powerful graphics capabilities,has great advantages in terms of design graphics. University of analytic geometry teaching process with the need graphics,but some simple graphical tools simply can not draw it. The Matlab software are insufficient to make up for the traditional drawing tools with powerful graphics capabilities in terms of analytic geometry. Matlab software can be said to be a powerful tool for teaching analytic geometry,analytic geometry graphics makes more vivid. Author from the actual teaching, combined with a number of examples to introduce the powerful Matlab software,and when to make up the advantages of traditional teaching.%Matlab技术具有强大的制图功能，在图形的设计方面具有很大的优越性。大学的解析几何教学过程中需要图形配合，但是一些简单的图形工具根本无法绘制出来。而Matlab软件正弥补了传统绘图工具的不足，在解析几何的绘图方面具有强大的功能。可以说Matlab软件是解析几何教学的得力工具，使得解析几何的图形更加生动、形象。笔者从实际的教学出发，结合一些实例来介绍Matlab软件的强大功能，以及在弥补传统教学时的优点。
Institute of Scientific and Technical Information of China (English)
李娜
2016-01-01
Through a series of teaching practice and research, this paper points out some problems existing in the current analytic geometry course. At the same time, this paper expounds the fea-sibility and necessity of integrating mathematical modeling thought into analytic geometry, further explores the methods of the integration in analytic geometry teaching and teaching mate-rials, and also illustrates that the integration is an effective method for the current teaching.%文章通过一系列的教学实践研究指出一些当下解析几何课程中存在的一些问题，同时阐述了在解析几何中融入数学建模思想的可行性和必要性，进一步探索在解析几何教学和教材等方面融入建模思想的方法，同时说明了将建模思想融入到解析几何课程中是目前教学过程中的有效方法之一。
Institute of Scientific and Technical Information of China (English)
赵丽
2015-01-01
解决立体几何问题的关键就是利用几何图形中的垂直关系,建立恰当的空间直角坐标系,运用几何图形中所涉及的点表示向量,进而解决空间立体几何问题. 本文针对高职学生在空间解析几何解题中的问题,运用空间直角坐标系分析空间几何解题思路,总结出空间直角坐标系在空间解析几何解题中的具体应用.%abstract:The key to solve the problems of solid geometry is using the geometry of the vertical relations ,setting up appropriate space rectangular coordinate system ,and using geometry point vector .To deal with the problem solving of higher vocational students in space analytic geometry ,this paper applies the space rectangular coordinate system to analyzing the space geometry problem solving ,and concludes some specific ways .
Institute of Scientific and Technical Information of China (English)
王玉华; 李建华
2013-01-01
本文结合教学实践，举实例探讨了知识系统化思想、数形结合思想、类比思想、向量法这四种数学思想方法在解析几何课堂教学中的应用。%Combining teaching practice,this paper discusses The Application of four kinds of mathematical thought and method of the knowledge system of thought,the number of application of combination of thought,thought of analogy and vector method by example in analytic geometry teaching in classroom.
Institute of Scientific and Technical Information of China (English)
崔秋珍
2012-01-01
利用MATLAB实现空间解析几何二次曲面伸缩法的设计和演示，力图从直观的、立体的和运动的角度揭示二次曲面的图像特征和方程之间的对应关系。%In this paper, we implement the design and demonstration of quadric surface expansion and contraction method in space analytic geometry using matlab, trying to reveal the corresponding relation about image characteristics and equation from the intuitive and stereo and motion view.
Relationships between "Higher Algebra" and "Analytic Geometry" by Some Examples%例谈《高等代数》与《解析几何》的关联
Institute of Scientific and Technical Information of China (English)
宋元凤; 李武明
2012-01-01
This paper elaborates the relationships between "higher algebra" and "analytic geometry" by the follow ing four aspects: determinant and vector, system of linear equations and plane, matrix and curve of second order, matrix and quadric surface.%文中从行列式与向量关系、线性方程组与面面关系、矩阵与二次曲线关系、矩阵与二次曲面关系四个方面对《高等代数》与《解析几何》相通性进行了阐述．
Students' Misconceptions and Errors in Transformation Geometry
Ada, Tuba; Kurtulus, Aytac
2010-01-01
This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The…
Institute of Scientific and Technical Information of China (English)
覃桂茳; 卢振坤
2015-01-01
Constructivist learning theory emphasizes that cognition comes from the students' independent participation of cogni-tive activity. Mathematical experiment is actually a new technique to take the place of specific activities in cognitive learning. Mathe-matical experiment is a useful supplement for traditional teaching methods of analytic geometry. This study will explore how to inte-grate analytic geometry teaching with mathematical experiment.%建构主义学习理论强调认知来源于学生对认知活动的自主参与，数学实验正是认知学习中可以替代具体活动的新技术。数学实验课对解析几何传统教学方式是一种有益的补充，该文将探讨如何把数学实验融入解析几何教学之中。
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
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
Institute of Scientific and Technical Information of China (English)
王元金; 陈萍清
2001-01-01
This artice is discussed the significan ce of combinin g higher algebra and analytic geometry as one course and its merit.And it is to give some advice and suggestion on the basic teaching requirements of higher alg ebra and analytic geometry towards 21 century.By teaching and studying the cours e,it may be organic related the two subjects.It is necessary that we remind the reciprocal utilization of the two subjects,reform the pattern of traditional tea ching,reinforce the teaching of the basic conceptions and basic theories,reinfor ce the training of the logical reasonig,stimulate the students' thirst for knowl edge,cultivate their habits of research.It make them learn to grasp the method o f higher algebra and analytic geometry to analyze the problem,solve the problem and establish the new ideas gradually.%论述了把高等代数与解析几 何合并成一门课的意义及其内在的合理性．对这两门课面向21世纪教学的基本要求提出一些 看法和建议：通过本课程教学，要把二者有机地揉合在一起．注意两门知识的交互应用，改 革传统的教学模式，加强基本概念、基本理论的教学，加强逻辑推理方面的训练，激发学生 的求知欲，培养他们的探索精神，逐步学会运用几何与代数相结合的方法分析问题，解决问 题，在潜移默化中树立和锻炼创新意识．
Phase structures in fuzzy geometries
Govindarajan, T R; Gupta, K S; Martin, X
2012-01-01
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.
Spain, Barry; Ulam, S; Stark, M
1960-01-01
Analytical Quadrics focuses on the analytical geometry of three dimensions. The book first discusses the theory of the plane, sphere, cone, cylinder, straight line, and central quadrics in their standard forms. The idea of the plane at infinity is introduced through the homogenous Cartesian coordinates and applied to the nature of the intersection of three planes and to the circular sections of quadrics. The text also focuses on paraboloid, including polar properties, center of a section, axes of plane section, and generators of hyperbolic paraboloid. The book also touches on homogenous coordi
Energy Technology Data Exchange (ETDEWEB)
Teixeira, Paulo Cleber Mendonca; Narain, Rajendra [Pernambuco Univ., Recife, PE (Brazil). Dept. de Energia Nuclear]. E-mail: clebermt@yahoo.com.br
2002-07-01
This paper presents an analytical solution for transport equation in a ring reactor with a rotating neutron source of the type S(x){delta}(x-Vt). It is an extension of the previous study of Williams carried out with source of the type S(x){delta}(t). Rotating neutron source is produced in a new concept of pulsed annular reactor for the production of high flux. The solution is obtained by opening of the annular geometry and applying transport theory in one-group, one-dimension, using applied mathematics techniques like Laplace Transforms and Complex Variables. A general solution for flux presented for the rotating source injected in the reactor. Condition for the existence of harmonics were specified depending upon the perimeter of the annular core. The solution is studied to look for flux instability of the harmonics in annular reactor. It is observed that no instability is possible the new reactor concept.(author)
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.
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
Energy Technology Data Exchange (ETDEWEB)
Ceolin, Celina
2010-07-01
The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)
Directory of Open Access Journals (Sweden)
Serdal Baltacı
2016-12-01
Full Text Available The potential of GeoGebra in teaching analytic geometry concepts was investigated in this paper. The study carried out with case study methodology and the participants were 6 pre-service mathematics teachers at 3rd grade of elementary mathematics education. All of the participants had the skill of well self-expression and they were volunteers for interview. Two participants were at high achievement levels, two participants were at medium achievement levels and two participants were low achievement levels. While carrying out each lesson, participants used worksheets which were prepared by the researchers. The data were obtained by semi-structured interviews which were carried out at the end of the courses and the data were analyzed with content analysis method. Research results showed that using dynamic mathematics software while studying on analytic geometry provides convenience for the participants and they felt more active while they were using software in the learning environment. [Bu çalışmada, analitik geometri kavramlarının öğretiminde GeoGebra’ nın potansiyeli incelenmiştir. Özel durum çalışması yöntemiyle yürütülen bu araştırmanın katılımcılarını, ilköğretim matematik öğretmenliği 3. sınıfa devam eden 6 öğretmen adayı oluşturmaktadır. Katılımcılar kendini ifade etme becerisi yüksek, mülakata gönüllü ve farklı başarı düzeyinde (yüksek, orta, düşük olan ikişer öğretmen adayından oluşmaktadır. Çalışmada analitik geometri dersleri, araştırmacılar tarafından geliştirilen çalışma yaprakları kullanılarak yürütülmüştür. Araştırmanın verileri derslerin sonunda yapılan yarı yapılandırılmış mülakatlarla toplanmıştır. Araştırmadan elde edilen veriler, içerik analizi yöntemi ile analiz edilmiştir. Araştırma sonuçları öğretmen adaylarının analitik geometri kavramlarını öğrenmede yazılımı kullanmalarının onlara kolaylık sa
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
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
Institute of Scientific and Technical Information of China (English)
侯传燕
2013-01-01
文章针对新疆双语班解析几何教学现状，提出在课堂教学中穿插美学教育、数学史教育，激发学生的学习热情和兴趣；在课件中使用数学软件，使教学变得直观生动形象；民汉学生互帮互学互助，形成轻松和谐的学习氛围，从而提高教学质量。%In teaching of Analytic Geometry in Bilingual classes, education of aesthetic and mathematics histo-ry can stimulate students. enthusiasm and interest. Using mathematics software to make teaching vividness, impro-ving class exercises efficiency;teaching and learning each other, forming relaxed and harmonious learning environ-ment, which helps to improve the teaching.
Institute of Scientific and Technical Information of China (English)
姜月萍
2014-01-01
本文针对线性代数与解析几何课程教学的现状，以及Matlab软件的特性，分析了利用Matlab软件进行教学改革的必要性。为激发学生的学习兴趣，提高学生的学习积极性，培养学生的知识应用能力，提出了教学方法改革、教学内容改革和训练方式改革三方面的教改措施。%According to the status of the curriculum of linear algebra and analytic geometry, and the characteristic of Matlab software, this paper analyzes the necessity of reform in education with Matlab software. To stimulate students' interest in learning, improve students' learning initiative, train students' application ability, three areas of education reform measures are proposed: the reform of teaching methods, the reform of teaching contents and the reform of training methods.
Descartes, R.; Rota, G.-C.; Euler, L.; Bernoulli, J. D.; Siegel, Edward Carl-Ludwig
2011-03-01
Quantum-statistics Dichotomy: Fermi-Dirac(FDQS) Versus Bose-Einstein(BEQS), respectively with contact-repulsion/non-condensation(FDCR) versus attraction/ condensationBEC are manifestly-demonstrated by Taylor-expansion ONLY of their denominator exponential, identified BOTH as Descartes analytic-geometry conic-sections, FDQS as Elllipse (homotopy to rectangle FDQS distribution-function), VIA Maxwell-Boltzmann classical-statistics(MBCS) to Parabola MORPHISM, VS. BEQS to Hyperbola, Archimedes' HYPERBOLICITY INEVITABILITY, and as well generating-functions[Abramowitz-Stegun, Handbook Math.-Functions--p. 804!!!], respectively of Euler-numbers/functions, (via Riemann zeta-function(domination of quantum-statistics: [Pathria, Statistical-Mechanics; Huang, Statistical-Mechanics]) VS. Bernoulli-numbers/ functions. Much can be learned about statistical-physics from Euler-numbers/functions via Riemann zeta-function(s) VS. Bernoulli-numbers/functions [Conway-Guy, Book of Numbers] and about Euler-numbers/functions, via Riemann zeta-function(s) MORPHISM, VS. Bernoulli-numbers/ functions, visa versa!!! Ex.: Riemann-hypothesis PHYSICS proof PARTLY as BEQS BEC/BEA!!!
Institute of Scientific and Technical Information of China (English)
高立新; 周慧会; 胡延平
2009-01-01
The kinematics analysis of the McPherson front independent suspension is made based on spatial analytic geometry. The calculation equations are deduced,and they are convenient for programming by Visual C+ + and effective in the practical design of the suspension. The simulation results show that the visible interface designed for analyzing the McPherson suspension is feasible in practice.%文章利用空间解析几何的方法对麦弗逊式前独立悬架进行了运动学分析,由此方法推导出了运动特性参数的计算公式,这些计算公式易于实现软件编程,便于在悬架设计过程中实际应用;在此基础上,利用Visual C++编程设计了可视化麦弗逊式悬架特性分析界面,通过实例仿真表明,此界面易于用户操作,有较好的实际应用价值.
Kreyszig, Erwin
1991-01-01
An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
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 ...
General Geometry and Geometry of Electromagnetism
Shahverdiyev, Shervgi S.
2002-01-01
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...
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
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
Energy Technology Data Exchange (ETDEWEB)
Leal, Andre Luiz do Carmo
2008-07-01
In this work we evaluate polynomial approximations to obtain the transfer functions that appear in SGF auxiliary equations (Green's Functions) for monoenergetic linearly anisotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use Lagrange Polynomials in order to compare the numerical results with the ones generated by the standard SGF method applied to SN problems in heterogeneous domains. This work is a preliminary investigation of a new proposal for handling the transverse leakage terms that appear in the transverse-integrated one-dimensional SN equations when we use the SGF - exponential nodal method (SGF-ExpN) in multidimensional rectangular geometry. (author)
Digital Differential Geometry Processing
Institute of Scientific and Technical Information of China (English)
Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng
2006-01-01
The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.
Institute of Scientific and Technical Information of China (English)
GUO Enli; MO Xiaohuan
2006-01-01
In this paper,a survey on Riemann-Finsler geometry is given.Non-trivial examples of Finsler metrics satisfying different curvature conditions are presented.Local and global results in Finsler geometry are analyzed.
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...
Veronese geometry and the electroweak vacuum moduli space
Energy Technology Data Exchange (ETDEWEB)
He, Yang-Hui, E-mail: hey@maths.ox.ac.uk [Department of Mathematics, City University, London, Northampton Square, London EC1V 0HB (United Kingdom); School of Physics, NanKai University, Tianjin 300071 (China); Merton College, University of Oxford, Oxford OX1 4JD (United Kingdom); Jejjala, Vishnu, E-mail: vishnu@neo.phys.wits.ac.za [Centre for Theoretical Physics, NITheP, and School of Physics, University of the Witwatersrand, Johannesburg, WITS 2050 (South Africa); Matti, Cyril, E-mail: Cyril.Matti.1@city.ac.uk [Department of Mathematics, City University, London, Northampton Square, London EC1V 0HB (United Kingdom); Nelson, Brent D., E-mail: b.nelson@neu.edu [Department of Physics, Northeastern University, Boston, MA 02115 (United States); ICTP, Strada Costiera 11, Trieste 34014 (Italy)
2014-09-07
We explain the origin of the Veronese surface in the vacuum moduli space geometry of the MSSM electroweak sector. While this result appeared many years ago using techniques of computational algebraic geometry, it has never been demonstrated analytically. Here, we present an analytical derivation of the vacuum geometry of the electroweak theory by understanding how the F- and D-term relations lead to the Veronese surface. We moreover give a detailed description of this geometry, realising an extra branch as a zero-dimensional point when quadratic Higgs lifting deformations are incorporated into the superpotential.
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
Symplectic geometries on supermanifolds
Lavrov, P M
2007-01-01
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with an non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of different symplectic geometries on supermanifolds.
Gualtieri, Marco
2010-01-01
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory. We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.
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...
Fields with Analytic Structure
Cluckers, Raf
2009-01-01
We present a unifying theory of fields with certain classes of analytic functions, called fields with analytic structure. Both real closed fields and Henselian valued fields are considered. For real closed fields with analytic structure, o-minimality is shown. For Henselian valued fields, both the model theory and the analytic theory are developed. We give a list of examples that comprises, to our knowledge, all principal, previously studied, analytic structures on Henselian valued fields, as well as new ones. The b-minimality is shown, as well as other properties useful for motivic integration on valued fields. The paper is reminiscent of [Denef, van den Dries, "p-adic and real subanalytic sets" Ann. of Math. (2) 128 (1988) 79--138], of [Cohen, Paul J. "Decision procedures for real and p-adic fields" Comm. Pure Appl. Math. 22 (1969) 131--151, and of [Fresnel, van der Put, "Rigid analytic geometry and its applications" Progress in Mathematics, 218 Birkhauser (2004)], and unifies work by van den Dries, Haskell...
Bates, Desiree M; Smith, Joshua R; Tschumper, Gregory S
2011-09-13
The structures of more than 70 low-lying water clusters ranging in size from (H2O)3 to (H2O)10 have been fully optimized with several different quantum mechanical electronic structure methods, including second-order Møller-Plesset perturbation theory (MP2) in conjunction with correlation consistent triple-ζ basis sets (aug-cc-pVTZ for O and cc-pVTZ for H, abbreviated haTZ). Optimized structures obtained with less demanding computational procedures were compared to the MP2/haTZ ones using both MP2/haTZ single point energies and the root-mean-square (RMS) deviations of unweighted Cartesian coordinates. Based on these criteria, B3LYP/6-31+G(d,2p) substantially outperforms both HF/haTZ and MP2/6-31G*. B3LYP/6-31+G(d,2p) structures never deviate from the MP2/haTZ geometries by more than 0.44 kcal mol(-1) on the MP2/haTZ potential energy surface, whereas the errors associated with the HF/haTZ and MP2/6-31G* structures grow as large as 12.20 and 2.98 kcal mol(-1), respectively. The most accurate results, however, were obtained with the two-body:many-body QM:QM fragmentation method for weakly bound clusters, in which all one- and two-body interactions are calculated at the high-level, while a low-level calculation is performed on the entire cluster to capture the cooperative effects (nonadditivity). With the haTZ basis set, the MP2:HF two-body:many-body fragmentation method generates structures that deviate from the MP2/haTZ ones by 0.01 kcal mol(-1) on average and not by more than 0.03 kcal mol(-1).
Geometry and scaling of cosmic voids
Gaite, Jose
2008-01-01
CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. AIMS: Our objective is to understand the geometry of cosmic voids in relation to a fractal structure of matter. We intend to distinguish monofractal voids from multifractal voids, regarding their scaling properties. We plan to analyse voids in the distributions of mass concentrations (halos) in a multifractal and their relation to galaxy voids. METHODS: We make a statistical analysis of point distributions based on the void probability function and correlation functions. We assume that voids are spherical and devise a simple spherical void finder. For continuous mass distributions, we employ the methods of fractal geometry. We confirm the analytical predictions with numerical simula...
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.
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.
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
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.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
Milton, Graeme W
2016-01-01
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer $p$. If $p$ takes its maximum value then we have a complete analytic material. Otherwise it is incomplete analytic material of rank $p$. For two-dimensional materials further progress can be made in the identification of analytic materials by using the well-known fact that a $90^\\circ$ rotation applied to a divergence free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.
Federal Laboratory Consortium — The Analytical Labspecializes in Oil and Hydraulic Fluid Analysis, Identification of Unknown Materials, Engineering Investigations, Qualification Testing (to support...
Euclidean Geometry via Programming.
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
Supersymmetric Sigma Model geometry
Lindström, Ulf
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
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
Ulf Lindström
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
Bergshoeff, Eric A.; Riccioni, Fabio; Alvarez-Gaumé, L.
2011-01-01
We probe doubled geometry with dual fundamental branes. i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundam
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.
Planar Ion Trap Geometry for Microfabrication
Madsen, M J; Stick, D; Rabchuk, J A; Monroe, C
2004-01-01
We describe a novel high aspect ratio radiofrequency linear ion trap geometry that is amenable to modern microfabrication techniques. The ion trap electrode structure consists of a pair of stacked conducting cantilevers resulting in confining fields that take the form of fringe fields from parallel plate capacitors. The confining potentials are modeled both analytically and numerically. This ion trap geometry may form the basis for large scale quantum computers or parallel quadrupole mass spectrometers. PACS: 39.25.+k, 03.67.Lx, 07.75.+h, 07.10+Cm
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.
Riemann-Finsler Geometry with Applications to Information Geometry
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce RiemannFinsler geometry, by which we establish Information Geometry on a much broader base,so that the potential applications of Information Geometry will be beyond statistics.
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
Bonola, Roberto
2010-01-01
This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well a
Santo, J
1999-01-01
The ALICE Geometry Database project consists of the development of a set of data structures to store the geometrical information of the ALICE Detector. This Database will be used in Simulation, Reconstruction and Visualisation and will interface with existing CAD systems and Geometrical Modellers.At the present time, we are able to read a complete GEANT3 geometry, to store it in our database and to visualise it. On disk, we store different geometry files in hierarchical fashion, and all the nodes, materials, shapes, configurations and transformations distributed in this tree structure. The present status of the prototype and its future evolution will be presented.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Federal Laboratory Consortium — NETL’s analytical laboratories in Pittsburgh, PA, and Albany, OR, give researchers access to the equipment they need to thoroughly study the properties of materials...
Derived logarithmic geometry I
Steffen, Sagave; Timo, Schurg; Gabriele, Vezzosi
2016-01-01
In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \\'etale maps and use this to define derived log stacks.
Facilitating Understandings of Geometry.
Pappas, Christine C.; Bush, Sara
1989-01-01
Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)
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...
Hohmann, Manuel
2014-01-01
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.
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...
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
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...
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.......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....
Schreiber, Urs
2016-01-01
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey examples and problems of interest. In section 3 we survey the abstract cohesive homotopy theory that serves to make all this precise and tractable.
Punzi, Raffaele; Wohlfarth, Mattias N R
2008-01-01
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Energy Technology Data Exchange (ETDEWEB)
Punzi, Raffaele [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: raffaele.punzi@desy.de; Schuller, Frederic P. [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)], E-mail: fps@aei.mpg.de; Wohlfarth, Mattias N.R. [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: mattias.wohlfarth@desy.de
2008-12-11
We reveal the non-metric geometry underlying {omega}{yields}0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Compaction of granular material inside confined geometries
Marks, Benjy; Sandnes, Bjornar; Dumazer, Guillaume; Eriksen, Jon Alm; Måløy, Knut Jørgen
2015-06-01
In both nature and the laboratory, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We use the discrete element method to investigate the stress distribution developed within the granular packing as a result of compaction due to the displacement of a rigid piston. We observe that the stress within the packing increases exponentially with the length of accumulated grains, and show an extension to current analytic models which fits the measured stress. The micromechanical behaviour is studied for a range of system parameters, and the limitations of existing analytic models are described. In particular, we show the smallest sized systems which can be treated using existing models. Additionally, the effects of increasing piston rate, and variations of the initial packing fraction, are described.
Update on Scroll Compressor Chamber Geometry
Bell, Ian; Groll, Eckhard; Braun, James; King, Galen
2010-01-01
The geometry of the scroll compressor determines the efficiency of the scroll compressor and controls all elements of its operation. It is therefore critical to be able to accurately model the volumes of the compressor over the course of a revolution. This paper proposes a novel quasi-analytic formulation of the suction, compression and discharge chambers based on a change of variables from involute angle to polar integration angle. This solution has been compared against a reference polyg...
Energy Technology Data Exchange (ETDEWEB)
2006-06-01
In the Analytical Microscopy group, within the National Center for Photovoltaic's Measurements and Characterization Division, we combine two complementary areas of analytical microscopy--electron microscopy and proximal-probe techniques--and use a variety of state-of-the-art imaging and analytical tools. We also design and build custom instrumentation and develop novel techniques that provide unique capabilities for studying materials and devices. In our work, we collaborate with you to solve materials- and device-related R&D problems. This sheet summarizes the uses and features of four major tools: transmission electron microscopy, scanning electron microscopy, the dual-beam focused-ion-beam workstation, and scanning probe microscopy.
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...
Integral Geometry and Holography
Czech, Bartlomiej; McCandlish, Samuel; Sully, James
2015-01-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we...
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...
Emergent Complex Network Geometry
Wu, Zhihao; Rahmede, Christoph; Bianconi, Ginestra
2014-01-01
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 geo...
Supersymmetry and noncommutative geometry
Beenakker, Wim; Suijlekom, Walter D van
2016-01-01
In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far. The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model. This book is ...
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.
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…
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
The Geometry of Conventionality
Weatherall, James Owen
2013-01-01
Hans Reichenbach famously argued that the geometry of spacetime is conventional in relativity theory, in the sense that one can freely choose the spacetime metric so long as one is willing to postulate a "universal force field". Here we make precise a sense in which the field Reichenbach defines fails to be a "force". We then argue that there is an interesting and perhaps tenable sense in which geometry is conventional in classical spacetimes. We conclude with a no-go result showing that the variety of conventionalism available in classical spacetimes does not extend to relativistic spacetimes.
Bowyer, Adrian
1983-01-01
A Programmer's Geometry provides a guide in programming geometric shapes. The book presents formulas and examples of computer representation and coding of geometry. Each of the nine chapters of the text deals with the representation and solution of a specific geometrical problem, such as areas, vectors, and volumes. The last chapter provides a brief discussion on generating image through a computer. The codes presented in the book are written in FORTRAN 77. The text will be of great use to programmers who are working on projects that involve geometric calculations.
DEFF Research Database (Denmark)
Seif El-Nasr, Magy; Drachen, Anders; Canossa, Alessandro
2013-01-01
Game Analytics has gained a tremendous amount of attention in game development and game research in recent years. The widespread adoption of data-driven business intelligence practices at operational, tactical and strategic levels in the game industry, combined with the integration of quantitative...
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.
Spacetime and Euclidean Geometry
Brill, D R; Brill, Dieter; Jacobson, Ted
2004-01-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Universal correlators from geometry
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Temuerhan, Mine; Sinkovics, Annamaria [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)]. E-mail: sinkovic@science.uva.nl
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion. (author)
Universal Correlators from Geometry
Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Universal Correlators from Geometry
Dijkgraaf, R; Temurhan, M; Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-01-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
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
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…
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
Advanced geometries and regimes
Energy Technology Data Exchange (ETDEWEB)
Bulanov, S. S. [Univeristy of California, Berkeley, CA, 94720 (United States); Bulanov, S. V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Turchetti, G. [Dipartimento di Fisica, Università di Bologna and INFN Sezione di Bologna, Via Irnerio, 46-I-40126 Bologna (Italy); Limpouch, J.; Klimo, O.; Psikal, J. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague, Czech Republic and Czech Technical University in Prague, FNSPE, Brehova 7, 115 19 Prague (Czech Republic); Antici, P. [Dipartimento di Energetica ed INFM, Università di Roma, La Sapienza, 00165 Roma (Italy); Margarone, D.; Korn, G. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague (Czech Republic)
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
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.
An introduction to Minkowski geometries
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
DEFF Research Database (Denmark)
include: re-identification, consumer behavior analysis, utilizing pupillary response for task difficulty measurement, logo detection, saliency prediction, classification of facial expressions, face recognition, face verification, age estimation, super-resolution, pose estimation, and pain recognition......This book collects the papers presented at two workshops during the 23rd International Conference on Pattern Recognition (ICPR): the Third Workshop on Video Analytics for Audience Measurement (VAAM) and the Second International Workshop on Face and Facial Expression Recognition (FFER) from Real...
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Spectral Geometry and Causality
Kopf, T
1996-01-01
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of...
Lee, Jeongseog; Safdi, Benjamin R
2014-01-01
Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
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
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
Krauss, L M; Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
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....
Hilbert, completeness and geometry
Directory of Open Access Journals (Sweden)
Giorgio Venturi
2011-11-01
Full Text Available This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory.
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...
Integral geometry and holography
Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.
Generalised Geometry and Flux Vacua
Larfors, Magdalena
2015-01-01
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.
Holographic free energy and thermodynamic geometry
Ghorai, Debabrata
2016-01-01
We analytically obtain the free energy and thermodynamic geometry of holographic superconductors in $2+1$-dimensions. The gravitational theory in the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the $3+1$-dimensions and is that of a charged $AdS$ black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.
LEARNING GEOMETRY THROUGH MIMESIS AND DIGITAL CONSTRUCT
Directory of Open Access Journals (Sweden)
Maria Mion POP
2015-12-01
Full Text Available The theme proposed by us is useful to teachers and students for mathematics in the compulsory school cycle. The issues faced by school teachers/parents are the difficulty with which students read and understand the lessons/examples/synthesis in order to assimilate technical terms. The echoic and iconic memory facilitates the learning of the specific curriculum of linear, spatial and analytical geometry by the students using digital platform designed by us; it facilitates the acquiring of the theoretical elements of applied geometry by encoding-decoding, so that the teacher's role becomes the one of the advisor and not only a person who transmits the information. The utility of the program extends from mainstream schools to special schools.
Linear connections on matrix geometries
Madore, J; Mourad, J; Madore, John; Masson, Thierry; Mourad, Jihad
1994-01-01
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.
Introductory non-Euclidean geometry
Manning, Henry Parker
1963-01-01
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
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.
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
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.
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
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
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
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
Helrich, Carl S
2017-01-01
This advanced undergraduate textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations, with constraints incorporated through Lagrange multipliers. Hamilton's Principle and the canonical equations remain the basis of the remainder of the text. Topics considered for applications include small oscillations, motion in electric and magnetic fields, and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally the text has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance. The text is enriched with an outline of the history of mechanics, which particularly outlines the importance of the work of Euler, Lagrange, Hamilton and Jacobi. Numerous exercises with solutions support the exceptionally clear and concise treatment...
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…
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V.; Clemente-Gallardo, J.; van der Schaft, A. J.
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure—in doing so we try to bring together various fundamental concepts...
ORDERED ANALYTIC REPRESENTATION OF PDES BY HAMILTONIAN CANONICAL SYSTEM
Institute of Scientific and Technical Information of China (English)
ZhengYu; ChenYong
2002-01-01
Based on the method of symplectic geometry and variational calculation,the method for some PDEs to be ordered and analytically represented by Hamiltonian canonical system is discussed. Meanwhile some related necessary and sufficient conditions are obtained.
Institute of Scientific and Technical Information of China (English)
朱克莲; 王静
2014-01-01
To guide students' thinking duplication training and focus on the cultivation of their thinking quality can effectively develop their problem-solving ability. This paper first introduced the theoretical basis of thinking duplication, and then explored how to use thinking duplication training to develop students' problem-solving ability in analytic geometry teaching.%引导学生进行思维复制训练，注重思维品质的培养，可以有效地发展学生问题解决能力。本文首先介绍了思维复制的理论依据，进而探讨了如何在解析几何教学中运用思维复制训练来发展学生的问题解决能力。
Tool Neck Geometry Design to Improve Stiffness of Micro Endmills
Li, P.; Rozing, M.; Oosterling, J.A.J.; Hoogstrate, A.M.; Langen, H.H.
2008-01-01
Due to the scaling effect, micro endmills have low stiffness in nature, which will result in lose of form accuracy in workpiece and vibration of micro tools during micromilling process. Through analytical modeling, it is found that the neck geometry of the micro endmill has a big influence on the to
Resistive drift wave turbulence in a three-dimensional geometry
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Naulin, V.
1999-01-01
The Hasegawa-Wakatani model describing resistive drift waves is investigated analytically and numerically in a three-dimensional periodic geometry. After an initial growth of the energy the drift waves couple nonlinearly to convective cells, which eventually dominate the system completely...
Mužík, Zbyněk
2006-01-01
Práce se zabývá problematikou měření ukazatelů souvisejících s provozem webových stránek a aplikací a technologickými prostředky k tomu sloužícími ? Web Analytics (WA). Hlavním cílem práce je otestovat a porovnat vybrané zástupce těchto nástrojů a podrobit je srovnání podle objektivních kriterií, dále také kritické zhodnocení možností WA nástrojů obecně. V první části se práce zaměřuje na popis různých způsobů měření provozu na WWW a definuje související metriky. Poskytuje také přehled dostup...
Simulating arbitrary-geometry ultrasound transducers using triangles
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt
1996-01-01
-echo field. The spatial impulse response has only been determined analytically for a few geometries and using apodization over the transducer surface generally makes it impossible to find the response analytically. A popular approach to find the general field is thus to split the aperture into small...... focused at different zones. The time-integrated spatial impulse response is used in the program to minimize the effect of the sharp edges of the spatial impulse response in a sampled signal. Since the integrated response from a triangular element cannot be analytically evaluated, a simple numerical...
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.
Covariant Macroscopic Quantum Geometry
Hogan, Craig J
2012-01-01
A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Stockem, A.; Fiuza, F.; Silva, L. O.; Antici, P.; Margarone, D.; Korn, G.
2013-08-01
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project. At the request of the Proceedings Editors and Dr. Stepan Bulanov, University of California, Berkeley, the above article has been updated to include three additional authors: A. Stockem, F. Fiuza, and L. O. Silva. All additional authors have consented to their name being added to the paper. Furthermore, the updated article PDF contains amendments to a number of references as detailed within the pages attached to the end of the updated article PDF file. The updated article was re-published on 8 August 2013.
Critique of information geometry
Energy Technology Data Exchange (ETDEWEB)
Skilling, John, E-mail: skilling@eircom.net [Maximum Entropy Data Consultants Ltd, Kenmare (Ireland)
2014-12-05
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.
Byron, S.
1985-03-01
The low pressure gas-filled thyratron is scalable in the long dimension. Internally the tube is formed as a tetrode, with an auxiliary grid placed between the cathode and the control grid. A dc or pulsed power source drives the auxiliary grid both to insure uniform cathode emission and to provide a grid-cathode plasma prior to commutation. The high voltage holdoff structure consists of the anode, the control grid and its electrostatic shielding baffles, and a main quartz insulator. A small gas flow supply and exhaust system is used that eliminates the need for a hydrogen reservoir and permits other gases, such as helium, to be used. The thyratron provides a low inductance, high current, long lifetime switch configuration: useful for switch-on applications involving large scale lasers and other similar loads that are distributed in a linear geometry.
A new approach to two-charge fuzzball geometries
Indian Academy of Sciences (India)
Rui-Yan Yu
2009-04-01
A few years ago, Mathur proposed a `fuzzball' conjecture to give a microscopic description of black hole entropy. In the fuzzball scenario, the entropy in a two-charge black hole corresponds to microstates of a two-charge string (brane) system, e.g., a winding fundamental string with momentum modes. The geometry of such a two-charge system is fuzzy near the horizon, and is very difficult to get analytically in general. In this paper, we show a new method to get geometries of two-charge fuzzball. Our method is based on the multipole expansion. We find that the method is powerful enough to get a clean analytic form of metric of the fuzzball with one-momentum mode. It is expected to get multi-mode geometries using this method in the near future.
Magnetism in curved geometries
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Klein geometries, parabolic geometries and differential equations of finite type
Abadoglu, Ender
2009-01-01
We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M defines a differential equation of order M+1 on G/H whose global solution space is G (Proposition 18).
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...
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
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......, 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...
Finding Proofs in Tarskian Geometry
Beeson, Michael; Wos, Larry
2016-01-01
We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski's axioms of Hilbert's 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some \\Otter proofs in Tarskian geometry (solving challenges issued in Wos's 1998...
Linear algebra and projective geometry
Baer, Reinhold
2005-01-01
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra
Digital geometry in image processing
Mukhopadhyay, Jayanta
2013-01-01
Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing. The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of
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
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...
Functional integration over geometries
Mottola, E
1995-01-01
The geometric construction of the functional integral over coset spaces {\\cal M}/{\\cal G} is reviewed. The inner product on the cotangent space of infinitesimal deformations of \\cal M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber \\cal G, the functional measure on the coset space {\\cal M}/{\\cal G} is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev-Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where \\cal G is the group of coordinate reparametrizations of spacetime, the continuum functional integral over geometries, {\\it i.e.} metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the me...
Geometries from field theories
Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
2015-10-01
We propose a method to define a d+1-dimensional geometry from a d-dimensional quantum field theory in the 1/N expansion. We first construct a d+1-dimensional field theory from the d-dimensional one via the gradient-flow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-N limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the large-N factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
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.
Geometry with Coordinates, Student's Text, Part II, Unit 48. Revised Edition.
Allen, Frank B.; And Others
This is part two of a two-part SMSG geometry text for high school students. One of the goals of the text is the development of analytic geometry hand-in-hand with synthetic geometry. The authors emphasize that both are deductive systems and that it is useful to have more than one mode of attack in solving problems. The text begins the development…
Geometry with Coordinates, Student's Text, Part I, Unit 47. Revised Edition.
Allen, Frank B.; And Others
This is part one of a two-part SMSG geometry text for high school students. One of the goals of the text is the development of analytic geometry hand-in-hand with synthetic geometry. The authors emphasize that both are deductive systems and that it is useful to have more than one mode of attack in solving problems. The text begins the development…
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....
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...
Index Theorems on Torsional Geometries
Kimura, Tetsuji
2007-01-01
We study various topological invariants on a differential geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH=0. By using the identification between the Clifford algebra on a geometry and the canonical quantization condition of fermion in the quantum mechanics, we construct the N=1 quantum mechanical sigma model in the Hamiltonian formalism and extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We improve the formulation of the Dirac index on the torsional geometry which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional geometry.
Ionization coefficient approach to modeling breakdown in nonuniform geometries.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Nicolaysen, Scott D.
2003-11-01
This report summarizes the work on breakdown modeling in nonuniform geometries by the ionization coefficient approach. Included are: (1) fits to primary and secondary ionization coefficients used in the modeling; (2) analytical test cases for sphere-to-sphere, wire-to-wire, corner, coaxial, and rod-to-plane geometries; a compilation of experimental data with source references; comparisons between code results, test case results, and experimental data. A simple criterion is proposed to differentiate between corona and spark. The effect of a dielectric surface on avalanche growth is examined by means of Monte Carlo simulations. The presence of a clean dry surface does not appear to enhance growth.
Transmission through metallic chains: Role of distortions and contact geometry
Energy Technology Data Exchange (ETDEWEB)
Wunderlich, Thomas; Akgenc, Berna; Schuster, Cosima; Eckern, Ulrich [Institut fuer Physik, Universitaet Augsburg, 86135 (Germany)
2010-07-01
We present results of electronic structure and transport calculations for metallic chains, based on density functional theory and scattering theory combined with the the non-equilibrium Green's function technique. Starting from a simple model system of monovalent metallic chains we investigate the influence of distortions on the electronic structure and the transport properties of H and Li chains. Furthermore we calculate the electronic structure of Au chains which are contacted to leads via different geometries, and study the influence of the contact geometry on the transmission coefficient. In particular, we compare chains, pyramides and planes in the contact region. A comparison with analytical results is given.
Controlling Electromagnetic Fields at Boundaries of Arbitrary Geometries
Teo, Jonathon Yi Han; Molardi, Carlo; Genevet, Patrice
2015-01-01
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realise coatings to achieve exotic effects like optical illusions and anomalous diffraction behaviour. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.
Controlling electromagnetic fields at boundaries of arbitrary geometries
Teo, Jonathon Yi Han; Wong, Liang Jie; Molardi, Carlo; Genevet, Patrice
2016-08-01
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary optics: a design theory that determines the optical response for designer input and output fields at such interfaces. Given any object, we can realize coatings to achieve exotic effects like optical illusions and anomalous diffraction behavior. This approach is relevant to a broad range of applications from conventional refractive optics to the design of the next-generation of wearable optical components. This concept can be generalized to other fields of research where designer interfaces with nontrivial geometries are encountered.
The Geometry Description Markup Language
Institute of Scientific and Technical Information of China (English)
RadovanChytracek
2001-01-01
Currently,a lot of effort is being put on designing complex detectors.A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier.A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment.However,no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files,source code (C/C++/FORTRAN),to XML and database solutions.The XML(Extensible Markup Language)has proven to provide an interesting approach for describing detector geometries,with several different but incompatible XML-based solutions existing.Therefore,interoperability and geometry data exchange among different frameworks is not possible at present.This article introduces a markup language for geometry descriptions.Its aim is to define a common approach for sharing and exchanging of geometry description data.Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML.
Hamilton geometry: Phase space geometry from modified dispersion relations
Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2015-01-01
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
Hull, C. M.
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Ho...
Linear algebra, geometry and transformation
Solomon, Bruce
2014-01-01
Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear SystemThe Augmented Matrix and RRE Form Homogeneous Systems in RRE Form Inhomogeneous Systems in RRE Form The Gauss-Jordan Algorithm Two Mapping Answers Linear Geometry Geometric Vectors Geometric/Numeric Duality Dot-Product Geometry Lines, Planes, and Hyperplanes System Geometry and Row/Column Duality The Algebra of Matrices Matrix Operations Special Matrices Matrix Inversion A Logical Digression The Logic of the Inversion Alg
Quantum Consequences of Parameterizing Geometry
Wanas, M. I.
2002-12-01
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
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
Adler, Irving
1967-01-01
This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text proves many significant theorems and employs several important techniques. Chapters on non- Euclidean geometry and projective geometry form brief, self-contained treatments.More than 100 exercises with answers and 200 diagrams illuminate the text. Teachers, students (particularly those majoring in mathematics educa
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
Hull, C M
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Hopkins Workshop on Current Problems in Particle Theory, Gothenborg, 1992.)
Thermal Phase in Bubbling Geometries
Institute of Scientific and Technical Information of China (English)
LIU Chang-Yong
2008-01-01
We use matrix model to study thermal phase in bubbling half-BPS type IIB geometries with SO(4)×SO(4) symmetry.Near the horizon limit,we find that thermal vacua of bubbling geometries have disjoint parts,and each part is one kind of phase of the thermal system.We connect the thermal dynamics of bubbling geometries with one-dimensional fermions thermal system.Finally,we try to give a new possible way to resolve information loss puzzle.
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.
Scattering Amplitudes via Algebraic Geometry Methods
Søgaard, Mads; Damgaard, Poul Henrik
This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of ...
Classical geometry from the quantum Liouville theory
Hadasz, L; Piatek, M; Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin
2005-01-01
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl
2005-09-26
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Geometry and mechanics of thin growing bilayers.
Pezzulla, Matteo; Smith, Gabriel P; Nardinocchi, Paola; Holmes, Douglas P
2016-05-11
We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourths the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude.
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Siddharth Gautam; S Mitra; R Mukhopadhyay
2008-10-01
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations: An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
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, ...
Geometry, mechanics, and electronics of singular structures and wrinkles in graphene.
Pereira, Vitor M; Castro Neto, A H; Liang, H Y; Mahadevan, L
2010-10-01
As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity, and electronics at the limits of their validity. We describe the transport and electronic structure in the neighborhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene. We use a combination of atomistic mechanical simulations, analytical geometry, and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport, and mobility in suspended samples, and how the geometry-generated pseudomagnetic and pseudoelectric fields might disrupt Landau quantization.
Courant Algebroids in Parabolic Geometry
Armstrong, Stuart
2011-01-01
To a smooth manifold $M$, a parabolic geometry associates a principal bundle, which has a parabolic subgroup of a semisimple Lie group as its structure group, and a Cartan connection. We show that the adjoint tractor bundle of a regular normal parabolic geometry can be endowed with the structure of a Courant algebroid. This gives a class of examples of transitive Courant algebroids that are not exact.
Higgs mass in noncommutative geometry
Energy Technology Data Exchange (ETDEWEB)
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)
Paper Interfaces for Learning Geometry
Bonnard, Quentin; Verma, Himanshu; Kaplan, Frédéric; Dillenbourg, Pierre
2012-01-01
Paper interfaces offer tremendous possibilities for geometry education in primary schools. Existing computer interfaces designed to learn geometry do not consider the integration of conventional school tools, which form the part of the curriculum. Moreover, most of computer tools are designed specifically for individual learning, some propose group activities, but most disregard classroom-level learning, thus impeding their adoption. We present an augmented reality based tabletop system with ...
Topology and geometry for physicists
Nash, Charles
2011-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Differential Geometry Applied to Rings and Möbius Nanostructures
DEFF Research Database (Denmark)
Lassen, Benny; Willatzen, Morten; Gravesen, Jens
2014-01-01
Nanostructure shape effects have become a topic of increasing interest due to advancements in fabrication technology. In order to pursue novel physics and better devices by tailoring the shape and size of nanostructures, effective analytical and computational tools are indispensable....... In this chapter, we present analytical and computational differential geometry methods to examine particle quantum eigenstates and eigenenergies in curved and strained nanostructures. Example studies are carried out for a set of ring structures with different radii and it is shown that eigenstate and eigenenergy...... at bending radii above 50 nm. In the second part of the chapter, a more complicated topological structure, the Möbius nanostructure, is analyzed and geometry effects for eigenstate properties are discussed including dependencies on the Möbius nanostructure width, length, thickness, and strain....
MacNeill, Sheila; Campbell, Lorna M.; Hawksey, Martin
2014-01-01
This article presents an overview of the development and use of analytics in the context of education. Using Buckingham Shum's three levels of analytics, the authors present a critical analysis of current developments in the domain of learning analytics, and contrast the potential value of analytics research and development with real world…
NUMERICAL SIMULATION OF THE GEOMETRY OF LOGS FOR SAWING INDUSTRIES
Directory of Open Access Journals (Sweden)
R. DANWE,
2011-02-01
Full Text Available Currently, the majority of wood sawing industries in Cameroun have as a concern the search for an optimization of the production. It is a question of having a good output matter during the cutting up. Thisproblem passes by knowledge of the geometry of the wood log, the strategies of cutting up and the quality of output. In this paper we develop a tool able to represent the log geometry with an aim at carrying out an optimal cutting up. We used representation by the analytical equations of the geometry of the external structure of the log ; that enables us to obtain an algorithm which helps to numerically generate the external structure of the wood.
System theory as applied differential geometry. [linear system
Hermann, R.
1979-01-01
The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.
Flow of viscoplastic fluids in eccentric annular geometries
DEFF Research Database (Denmark)
Szabo, Peter; Hassager, Ole
1992-01-01
A classification of flowfields for the flow of a Bingham fluid in general eccentric annular geometries is presented. Simple arguments show that a singularity can exist in the stress gradient on boundaries between zones with yielded and un-yielded fluid respectively. A Finite Element code is used...... to verify this property of the Bingham fluid. An analytical solution for the flowfield in case of small eccentricities is derived....
Holomorphic Cartan geometries and rational curves
Biswas, Indranil
2010-01-01
We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.
When to carry out analytic continuation?
Zuo, J M
1998-01-01
This paper discusses the analytic continuation in the thermal field theory by using the theory of $\\eta-\\xi$ spacetime. Taking a simple model as example, the $2\\times 2$ matrix real-time propagator is solved from the equation obtained through continuation of the equation for the imaginary-time propagator. The geometry of the $\\eta-\\xi$ spacetime plays important role in the discussion.
Design and analysis of an intelligent controller for active geometry suspension systems
Goodarzi, Avesta; Oloomi, Ehsan; Esmailzadeh, Ebrahim
2011-02-01
An active geometry suspension (AGS) system is a device to optimise suspension-related factors such as toe angle and roll centre height by controlling vehicle's suspension geometry. The suspension geometry could be changed through control of suspension mounting point's position. In this paper, analysis and control of an AGS system is addressed. First, the effects of suspension geometry change on roll centre height and toe angle are studied. Then, based on an analytical approach, the improvement of the vehicle's stability and handling due to the control of suspension geometry is investigated. In the next section, an eight-degree-of-freedom handling model of a sport utility vehicle equipped with an AGS system is introduced. Finally, a self-tuning proportional-integral controller has been designed, using the fuzzy control theory, to control the actuator that changes the geometry of the suspension system. The simulation results show that an AGS system can improve the handling and stability of the vehicle.
General Construction of Tubular Geometry
Mukhopadhyay, Partha
2016-01-01
We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction.
Wave propagation on microstate geometries
Keir, Joseph
2016-01-01
Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two and three charge supersymmetric microstate geometries, finding a number of surprising results. In both cases we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three charge microstates possess an ergoregion; these geometries therefore avoid Friedman's "ergosphere instability". In fact, in the three charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although this data must have nontrivial dependence on the Kaluza-Klein coordinate. In the two charge case we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform dec...
Quantum geometry and gravitational entropy
Energy Technology Data Exchange (ETDEWEB)
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.
Conventionalism and integrable Weyl geometry
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Geometry of black hole spacetimes
Andersson, Lars; Blue, Pieter
2016-01-01
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
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...
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
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
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
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday
2003-07-10
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.
Geometry Design of Wooden Barrels
Directory of Open Access Journals (Sweden)
Ivan CISMARU
2010-12-01
Full Text Available The aim of this paper is to present a design methodology of the wooden barrel geometry, as an algorithm of successive calculations. Thus, starting from the required elements (volume, length, shape, maximum height of storage space the user will be able to define the geometry which must be obtained by processing. Based on these calculations, one can define the structure, size and shape of the staves in order to establish the processing technology of both components and subassemblies (jacket and bottoms which are to form the final product by their assembling using metal circles.
Lectures on classical differential geometry
Struik, Dirk J
1988-01-01
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student.Writ
Gauging Geometry: A Didactic Lecture
Kannenberg, L
2016-01-01
Local inertial frame invariance is taken as the fundamental principle of physical geometry, where a local inertial frame is represented by a verbein. Invariance of the vierbein with respect to local Lorentz transformations then expresses local inertial frame invariance. The dynamics of physical geometry develops as a gauge theory of the verbein that is closely analogous to the Yang-Mills field provided the verbein connection and curvature correspond to the geometric potential and field respectively. The resulting theory is shown to be equivalent to Einstein's tensor form of relativistic gravitation.
Energy Technology Data Exchange (ETDEWEB)
Benabbassi, A. [Centre Universitaire de Bechar (Algeria)
2001-07-01
The paper describes computer investigation on improving of performance engine parameters by limiting heat losses into walls and utilizing exhaust gases energy in power turbine connected to crank-shaft. Heat losses limitation improves indicated efficiency, if air - fuel ratio is provided high and if diesel has a sophisticated level of air - fuel mixing and combustion processes. The disadvantage for in - cylinder surfaces temperature growth is degradation in filling efficiency. Sufficient air - fuel ratio may be provided by employing higher exhaust gases temperature associated with heat losses limitation and by implementing a variable geometry turbine. (author)
Clustering in analytical chemistry.
Drab, Klaudia; Daszykowski, Michal
2014-01-01
Data clustering plays an important role in the exploratory analysis of analytical data, and the use of clustering methods has been acknowledged in different fields of science. In this paper, principles of data clustering are presented with a direct focus on clustering of analytical data. The role of the clustering process in the analytical workflow is underlined, and its potential impact on the analytical workflow is emphasized.
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…
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
Energy Technology Data Exchange (ETDEWEB)
Byrd, M.
1997-10-01
The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.
Differential geometry meets the cell.
Marshall, Wallace F
2013-07-18
A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.
Loop groups and noncommutative geometry
Carpi, Sebastiano
2015-01-01
We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group LG. The construction is based on certain supersymmetric conformal field theory models associated with LG.
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.
Signature geometry and quantum engineering
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
Data Imprecision in Computational Geometry
Löffler, M.
2009-01-01
The field of computational geometry is concerned with the design and analysis of geometric algorithms. For such algorithms, correctness and efficiency proofs are constructed, or problems are proven to be hard when no correct and efficient algorithms exist. In order to be able to do this, several ass
Foucault pendulum through basic geometry
von Bergmann, Jens; von Bergmann, HsingChi
2007-10-01
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.
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...
Casimir effects for classical and quantum liquids in slab geometry: A brief review
Energy Technology Data Exchange (ETDEWEB)
Biswas, Shyamal, E-mail: sbsp@uohyd.ac.in [School of Physics, University of Hyderabad, C.R. Rao Road, Gachibowli, Hyderabad-500046 (India)
2015-05-15
We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over {sup 4}He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.
Holographic entanglement entropy of anisotropic minimal surfaces in LLM geometries
Kim, Chanju; Kim, Kyung Kiu; Kwon, O.-Kab
2016-08-01
We calculate the holographic entanglement entropy (HEE) of the Zk orbifold of Lin-Lunin-Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern-Simons level k. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and k up to μ02 -order where μ0 is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the F-theorem. Except the multiplication factor and to all orders in μ0, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with Zk orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to μ04 -order for the symmetric droplet case.
Holographic entanglement entropy of anisotropic minimal surfaces in LLM geometries
Directory of Open Access Journals (Sweden)
Chanju Kim
2016-08-01
Full Text Available We calculate the holographic entanglement entropy (HEE of the Zk orbifold of Lin–Lunin–Maldacena (LLM geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern–Simons level k. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and k up to μ02-order where μ0 is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the F-theorem. Except the multiplication factor and to all orders in μ0, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with Zk orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to μ04-order for the symmetric droplet case.
Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries
Kim, Chanju; Kwon, O-Kab
2016-01-01
We calculate the holographic entanglement entropy (HEE) of the $\\mathbb{Z}_k$ orbifold of Lin-Lunin-Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern-Simons level $k$. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and $k$ up to $\\mu_0^2$-order where $\\mu_0$ is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the $F$-theorem. Except the multiplication factor and to all orders in $\\mu_0$, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with $\\mathbb{Z}_k$ orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to $...
Mardoukhi, Yousof; Jeon, Jae-Hyung; Metzler, Ralf
2015-11-28
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T(-h) with h fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
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...
Differential geometry and mathematical physics
Rudolph, Gerd
2013-01-01
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...
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...
Gear geometry of cycloid drives
Institute of Scientific and Technical Information of China (English)
CHEN BingKui; FANG TingTing; LI ChaoYang; WANG ShuYan
2008-01-01
According to differential geometry and gear geometry,the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion.The correct meshing condition,contact line,contact ratio,calculating method for pin tooth's maximum contact point are developed.Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1,2,3 and -1,respectively.A general method called enveloping method to generate hypocycloid and epicycloid is put forward.The correct mesh-ing condition for cycloid pin wheel gearing is provided,and the contact line and the contact ratio are also discussed.
Geometry of polycrystals and microstructure
Directory of Open Access Journals (Sweden)
Ball John M.
2015-01-01
Full Text Available We investigate the geometry of polycrystals, showing that for polycrystals formed of convex grains the interior grains are polyhedral, while for polycrystals with general grain geometry the set of triple points is small. Then we investigate possible martensitic morphologies resulting from intergrain contact. For cubic-totetragonal transformations we show that homogeneous zero-energy microstructures matching a pure dilatation on a grain boundary necessarily involve more than four deformation gradients. We discuss the relevance of this result for observations of microstructures involving second and third-order laminates in various materials. Finally we consider the more specialized situation of bicrystals formed from materials having two martensitic energy wells (such as for orthorhombic to monoclinic transformations, but without any restrictions on the possible microstructure, showing how a generalization of the Hadamard jump condition can be applied at the intergrain boundary to show that a pure phase in either grain is impossible at minimum energy.
Geometry of Membrane Sigma Models
Vysoky, Jan
2015-01-01
String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are described by an action functional extremalising the volume of a manifold swept by a propagating membrane. This and related field theories are collectively called membrane sigma models. Differential geometry is an important mathematical tool in the study of string theory. It turns out that string and membrane backgrounds can be conveniently described using objects defined on a direct sum of tangent and cotangent bundles of the spacetime manifold. Mathematical field studying such object is called generalized geometry. Its integral part is the theory of Leibniz algebroids, vector bundles with a Leibniz algebra bracket on its module of smooth sections. Special cases of Leibniz algebroids are better ...
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...
The geometry of surfaces contact
Directory of Open Access Journals (Sweden)
Siegl J.
2007-11-01
Full Text Available This contribution deals with a geometrical exact description of contact between two given surfaces which are defined by the vector functions. These surfaces are substituted at a contact point by approximate surfaces of the second order in accordance with the Taylor series and consequently there is derived a differential surface of these second order surfaces. Knowledge of principal normal curvatures, their directions and the tensor (Dupin indicatrix of this differential surface are necessary for description of contact of these surfaces. For description of surface geometry the first and the second surface fundamental tensor and a further methods of the differential geometry are used. A geometrical visualisation of obtained results of this analysis is made. Method and results of this study will be applied to contact analysis of tooth screw surfaces of screw machines.
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...
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.
Gear geometry of cycloid drives
Institute of Scientific and Technical Information of China (English)
2008-01-01
According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion. The correct meshing condition, contact line, contact ratio, calculating method for pin tooth’s maximum contact point are developed. Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1, 2, 3 and ?1, respectively. A general method called enveloping method to generate hypocycloid and epicycloid is put forward. The correct meshing condition for cycloid pin wheel gearing is provided, and the contact line and the contact ratio are also discussed.
Core foundations of abstract geometry.
Dillon, Moira R; Huang, Yi; Spelke, Elizabeth S
2013-08-27
Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.
Geometry for the accelerating universe
Punzi, R; Wohlfarth, M N R; Punzi, Raffaele; Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2006-01-01
The Lorentzian spacetime metric is replaced by an area metric which naturally emerges as a generalized geometry in quantum string and gauge theory. Employing the area metric curvature scalar, the gravitational Einstein-Hilbert action is re-interpreted as dynamics for an area metric. Without the need for dark energy or fine-tuning, area metric cosmology explains the observed small acceleration of the late Universe.
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.
Black Holes as Effective Geometries
Balasubramanian, Vijay; El-Showk, Sheer; Messamah, Ilies
2008-01-01
Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective t...
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...
A Conserved Energy Integral for Perturbation Equations in the Kerr-de Sitter Geometry
Umetsu, H
2000-01-01
The analytic proof of mode stability of the Kerr black hole was provided by Whiting. In his proof, the construction of a conserved quantity for unstable mode was crucial. We extend the method of the analysis for the Kerr-de Sitter geometry. The perturbation equations of massless fields in the Kerr-de Sitter geometry can be transformed into Heun's equations which have four regular singularities. In this paper we investigate differential and integral transformations of solutions of the equations. Using those we construct a conserved quantity for unstable modes in the Kerr-de Sitter geometry, and discuss its property.
Analytical Chemistry in Russia.
Zolotov, Yuri
2016-09-06
Research in Russian analytical chemistry (AC) is carried out on a significant scale, and the analytical service solves practical tasks of geological survey, environmental protection, medicine, industry, agriculture, etc. The education system trains highly skilled professionals in AC. The development and especially manufacturing of analytical instruments should be improved; in spite of this, there are several good domestic instruments and other satisfy some requirements. Russian AC has rather good historical roots.
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Towards a Nano Geometry? Geometry and Dynamics on Nano Scale
Booss-Bavnbek, Bernhelm
2012-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elaborated - in contrast to the familiar Newtonian mechanics and the more recent, but by now also rather well established quantum field theories. Examples are given originating from the systems biology of insulin secreting pancreatic beta-cells and the mathematical challenges of an envisioned non-invasive control of magnetic nanoparticles.
Cerebral blood flow simulations in realistic geometries
Directory of Open Access Journals (Sweden)
Szopos Marcela
2012-04-01
Full Text Available The aim of this work is to perform the computation of the blood flow in all the cerebral network, obtained from medical images as angiographies. We use free finite elements codes as FreeFEM++. We first test the code on analytical solutions in simplified geometries. Then, we study the influence of boundary conditions on the flow and we finally perform first computations on realistic meshes. L’objectif est ici de simuler l’écoulement sanguin dans tout le réseau cérébral (artériel et veineux obtenu à partir d’angiographies cérébrales 3D à l’aide de logiciels d’éléments finis libres, comme FreeFEM++. Nous menons d’abord une étude détaillée des résultats sur des solutions analytiques et l’influence des conditions limites à imposer dans des géométries simplifiées avant de travailler sur les maillages réalistes.
Analytical Electron Microscope
Federal Laboratory Consortium — The Titan 80-300 is a transmission electron microscope (TEM) equipped with spectroscopic detectors to allow chemical, elemental, and other analytical measurements to...
Science Update: Analytical Chemistry.
Worthy, Ward
1980-01-01
Briefly discusses new instrumentation in the field of analytical chemistry. Advances in liquid chromatography, photoacoustic spectroscopy, the use of lasers, and mass spectrometry are also discussed. (CS)
Theory of diffusion-influenced reactions in complex geometries
Galanti, Marta; Fanelli, Duccio; Traytak, Sergey D.; Piazza, Francesco
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DI reactions, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DI reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases.
Geometry-dependent viscosity reduction in sheared active fluids
Słomka, Jonasz
2016-01-01
We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of previously intractable higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, geometry-dependent viscosity reduction and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of non-equilibrium fluids by tuning confinement geometry and pattern scale selection.
Geometry of shoot apical dome and distribution of growth rates
Directory of Open Access Journals (Sweden)
Jerzy Nakielski
2014-01-01
Full Text Available The distribution of the relative elementary rate of growth (RERG in apical domes of various shapes and patterns of displacement lines can be analytically examined. The geometry of these domes may be described by parabolas of n-th order, the variant of the distribution of linear growth rate should be established along any displacement line (e.g. along the axis and then the RERG can be studied as the function depending on the position coordinates and the parameter n. Such investigations of several aplical domes of various shapes have been performed. The results confirm the occurrence of the minimum of relative, elementary growth rate (in volume in the subapical region of the dome independently of the type of geometry (n parabola order.
Theory of diffusion-influenced reactions in complex geometries
Galanti, Marta; Piazza, Francesco
2015-01-01
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment's geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DI reactions, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory able to describe the environment's "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DI reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical form...
A Whirlwind Tour of Computational Geometry.
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Analytical stiffness matrices with Green-Lagrange strain measure
DEFF Research Database (Denmark)
Pedersen, Pauli
2005-01-01
Separating the dependence on material and stress/strain state from the dependence on initial geometry, we obtain analytical secant and tangent stiffness matrices. For the case of a linear displacement triangle with uniform thickness and uniform constitutive behaviour closed-form results are listed...
Generalised Complex Geometry in Thermodynamical Fluctuation Theory
Directory of Open Access Journals (Sweden)
P. Fernández de Córdoba
2015-08-01
Full Text Available We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simplified version of the Unruh effect: the thermalising effect of gravitational fields on the Schroedinger wavefunction.
Exceptional geometry and Borcherds superalgebras
Palmkvist, Jakob
2015-01-01
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 less than 8. The closure of the transformations then follows from the Jacobi identity and the grading of e_{n+1} with respect to e_n.
Bondi accretion in trumpet geometries
Miller, August J.; Baumgarte, Thomas W.
2017-02-01
The Bondi solution, which describes the radial inflow of a gas onto a non-rotating black hole, provides a powerful test for numerical relativistic codes. However, the Bondi solution is usually derived in Schwarzschild coordinates, which are not well suited for dynamical spacetime evolutions. Instead, many current numerical relativistic codes adopt moving-puncture coordinates, which render black holes in trumpet geometries. Here we transform the Bondi solution into trumpet coordinates, which result in regular expressions for the fluid flow extending into the black-hole interior. We also evolve these solutions numerically and demonstrate their usefulness for testing and calibrating numerical codes.
Complexity and Shock Wave Geometries
Stanford, Douglas
2014-01-01
In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge to the computational complexity of the of the dual quantum state. Our refinement states that the complexity is proportional to the spatial volume of the ERB. More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by $G_N l_{AdS}$. We test this conjecture against a wide variety of spherically symmetric shock wave geometries in different dimensions. We find detailed agreement.
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
Loop quantum geometry: a primer
Energy Technology Data Exchange (ETDEWEB)
Corichi, Alejandro [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico)
2005-01-15
This is the written version of a lecture given at the 'VI Mexican School of Gravitation and Mathematical Physics' (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a friendly guide to the existing pedagogical literature on the subject. This account is geared towards graduate students and non-experts interested in learning the basics of the subject.
Adding momentum to supersymmetric geometries
Energy Technology Data Exchange (ETDEWEB)
Lunin, Oleg, E-mail: olunin@albany.edu [Department of Physics, University at Albany (SUNY), Albany, NY 12222 (United States); Mathur, Samir D., E-mail: mathur.16@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States); Turton, David, E-mail: turton.7@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States)
2013-03-11
We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a traveling wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T{sup 4}. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.
Adding momentum to supersymmetric geometries
Lunin, Oleg; Turton, David
2012-01-01
We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a travelling-wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T^4. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.
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.
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
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
Generalised geometry for string corrections
Coimbra, André; Triendl, Hagen; Waldram, Daniel
2014-01-01
We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a well-defined effective action require a precise choice of the (generalised) connection. The action takes a universal form given by a generalised Lichnerowitz--Bismut theorem. As examples of this construction we discuss the corrections linear in $\\alpha'$ in heterotic strings and the absence of such corrections for type II theories.
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
Quanta of geometry and unification
Chamseddine, Ali H.
2016-11-01
This is a tribute to Abdus Salam’s memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.
Quanta of Geometry and Unification
Chamseddine, Ali H
2016-01-01
This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.
Isosurfaces geometry, topology, and algorithms
Wenger, Rephael
2013-01-01
Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. In color throughout, the book covers the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolutio
Some Heterodox Analytic Philosophy
Directory of Open Access Journals (Sweden)
Guillermo E. Rosado Haddock
2013-04-01
Full Text Available Analytic philosophy has been the most influential philosophical movement in 20th century philosophy. It has surely contributed like no other movement to the elucidation and demarcation of philosophical problems. Nonetheless, the empiricist and sometimes even nominalist convictions of orthodox analytic philosophers have served them to inadequately render even philosophers they consider their own and to propound very questionable conceptions.
The Analytical Hierarchy Process
DEFF Research Database (Denmark)
Barfod, Michael Bruhn
2007-01-01
The technical note gathers the theory behind the Analytical Hierarchy Process (AHP) and present its advantages and disadvantages in practical use.......The technical note gathers the theory behind the Analytical Hierarchy Process (AHP) and present its advantages and disadvantages in practical use....
Jackson, Brian
2010-01-01
Using a survey of 138 writing programs, I argue that we must be more explicit about what we think students should get out of analysis to make it more likely that students will transfer their analytical skills to different settings. To ensure our students take analytical skills with them at the end of the semester, we must simplify the task we…
DEFF Research Database (Denmark)
Andersen, Jens Enevold Thaulov; Karlberg, Bo
2009-01-01
The EuCheMS Division of Analytical Chemistry (DAC) maintains a website with informations on groups of analytical chemistry at European universities (www.dac-euchems. org). Everyone may contribute to the database and contributors are responsible for an annual update of the information. The service...
Learning Analytics Considered Harmful
Dringus, Laurie P.
2012-01-01
This essay is written to present a prospective stance on how learning analytics, as a core evaluative approach, must help instructors uncover the important trends and evidence of quality learner data in the online course. A critique is presented of strategic and tactical issues of learning analytics. The approach to the critique is taken through…
Understanding Business Analytics
2015-01-05
language are the limits of my mind. All I know is what I have words for.” - Ludwig Wittgenstein Defining Business Analytics The following are examples of...Michael Porter Figure 2: The analytic Process Step 2: Now that the problem statement has been defined, this needs to be reformulated into an
Energy Technology Data Exchange (ETDEWEB)
1990-01-01
This 43rd Annual Summer Symposium on Analytical Chemistry was held July 24--27, 1990 at Oak Ridge, TN and contained sessions on the following topics: Fundamentals of Analytical Mass Spectrometry (MS), MS in the National Laboratories, Lasers and Fourier Transform Methods, Future of MS, New Ionization and LC/MS Methods, and an extra session. (WET)
Analytical mass spectrometry. Abstracts
Energy Technology Data Exchange (ETDEWEB)
1990-12-31
This 43rd Annual Summer Symposium on Analytical Chemistry was held July 24--27, 1990 at Oak Ridge, TN and contained sessions on the following topics: Fundamentals of Analytical Mass Spectrometry (MS), MS in the National Laboratories, Lasers and Fourier Transform Methods, Future of MS, New Ionization and LC/MS Methods, and an extra session. (WET)
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.
Global continuation for distance geometry problems
Energy Technology Data Exchange (ETDEWEB)
More, J.J.; Wu, Zhijun
1995-03-01
Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. The authors formulate the distance geometry problem as a global minimization problem with special structure, and show the global smoothing techniques and a continuation approach for global optimization can be used to determine solutions of distance geometry problems with a nearly 100% probability of success.
Effects of Magnet Size and Geometry on Magnetic Levitation Force
Institute of Scientific and Technical Information of China (English)
M. K. Alqadi; H. M. Al-khateeb; F. Y. Alzoubi; N. Y. Ayoub
2007-01-01
We obtain analytical relations for the levitation force as a function of dimensions of the superconductor-magnet system. The force has been calculated on the basis of the dipole-dipole interaction model.The effect of thickness of the superconductor on the levitation force is investigated. The results show that the influence of geometry and thickness of the magnet becomes significantly large at small levitation distances. Furthermore, approximating the permanent magnet as a point dipole results in an inaccurate estimation of the levitation force.
The influence of the nanostructure geometry on the thermoelectric properties
AL-Badry, Lafy F.
2016-09-01
We discuss the influence of nanostructure geometry on the thermoelectric properties in quantum ring consists of one QD in each arm, each QD connects with side QD. The calculations are based on the time-dependent Hamiltonian model, the steady state is considered to obtain an analytical expression for the transmission probability as a function of system energies. We employed the transmission probability to calculate the thermoelectric properties. We investigate thermoelectric properties through three configurations of this nanostructure. Figure of merit enhanced in configuration (II) when side QD connected to upper arm of quantum ring. The magnetic flux threads quantum ring. The effect of magnetic flux on the thermoelectric properties is examined.
The Casimir effect in the sphere-plane geometry
Canaguier-Durand, Antoine; Neto, Paulo A Maia; Lambrecht, Astrid; Reynaud, Serge
2012-01-01
We present calculations of the Casimir interaction between a sphere and a plane, using a multipolar expansion of the scattering formula. This configuration enables us to study the nontrivial dependence of the Casimir force on the geometry, and its correlations with the effects of imperfect reflection and temperature. The accuracy of the Proximity Force Approximation (PFA) is assessed, and is shown to be affected by imperfect reflexion. Our analytical and numerical results at ambient temperature show a rich variety of interplays between the effects of curvature, temperature, finite conductivity, and dissipation.
The advanced geometry of plane curves and their applications
Zwikker, C
2005-01-01
""Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating."" - British Journal of Applied PhysicsThis study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves.Informativ
Geometry dependence of 2-dimensional space-charge-limited currents
De Visschere, Patrick
2016-01-01
The space-charge-limited current in a zero thickness planar thin film depends on the geometry of the electrodes. We present a theory which is to a large extent analytical and applicable to many different lay-outs. We show that a space-charge-limited current can only be sustained if the emitting electrode induces a singularity in the field and if the singularity induced by the collecting electrode is not too strong. For those lay-outs where no space-charge-limited current can be sustained for a zero thickness film, the real thickness of the film must be taken into account using a numerical model.
Quo vadis, analytical chemistry?
Valcárcel, Miguel
2016-01-01
This paper presents an open, personal, fresh approach to the future of Analytical Chemistry in the context of the deep changes Science and Technology are anticipated to experience. Its main aim is to challenge young analytical chemists because the future of our scientific discipline is in their hands. A description of not completely accurate overall conceptions of our discipline, both past and present, to be avoided is followed by a flexible, integral definition of Analytical Chemistry and its cornerstones (viz., aims and objectives, quality trade-offs, the third basic analytical reference, the information hierarchy, social responsibility, independent research, transfer of knowledge and technology, interfaces to other scientific-technical disciplines, and well-oriented education). Obsolete paradigms, and more accurate general and specific that can be expected to provide the framework for our discipline in the coming years are described. Finally, the three possible responses of analytical chemists to the proposed changes in our discipline are discussed.
DEFF Research Database (Denmark)
Karlberg, B.; Grasserbauer, M.; Andersen, Jens Enevold Thaulov
2009-01-01
The European Analytical Column has once more invited a guest columnist to give his views on various matters related to analytical chemistry in Europe. This year, we have invited Professor Manfred Grasserbauer of the Vienna University of Technology to present some of the current challenges...... for European analytical chemistry. During the period 2002–07, Professor Grasserbauer was Director of the Institute for Environment and Sustainability, Joint Research Centre of the European Commission (EC), Ispra, Italy. There is no doubt that many challenges exist at the present time for all of us representing...... a major branch of chemistry, namely analytical chemistry. The global financial crisis is affecting all branches of chemistry, but analytical chemistry, in particular, since our discipline by tradition has many close links to industry. We have already noticed decreased industrial commitment with respect...
Geometry and the Quantum: Basics
Chamseddine, Ali H; Mukhanov, Viatcheslav
2014-01-01
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these represen...
Warped Geometry of Brane Worlds
Felder, G; Kofman, L A; Felder, Gary; Frolov, Andrei; Kofman, Lev
2002-01-01
We study the dynamical equations for a warp factor and a bulk scalar in 5d brane world scenarios. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4d cosmology, but with the sign of the scalar field potential reversed. Based on this analogy, we introduce two novel methods for studying the warped geometry. First, we construct the full phase portraits of the warp factor/scalar system for several examples of the bulk potential. This allows us to view the global properties of the warped geometry. For flat branes, the phase portrait is two dimensional. Moving along typical phase trajectories, the warp factor is initially increasing and finally decreasing. All trajectories have timelike gradient-dominated singularities at one or both of their ends, which are reachable in a finite distance and must be screened by the branes. For curved branes, the phase portrait is three dimensional. However, as the warp factor increases the phase trajectories tend towards the tw...
Weyl gravity and Cartan geometry
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Ring polymers in confined geometries
Usatenko, Z; Kuterba, P
2016-01-01
The investigation of a dilute solution of phantom ideal ring polymers and ring polymers with excluded volume interactions (EVI) in a good solvent confined in a slit geometry of two parallel repulsive walls and in a solution of colloidal particles of big size were performed. Taking into account the correspondence between the field theoretical $\\phi^4$ $O(n)$-vector model in the limit $n\\to 0$ and the behavior of long-flexible polymer chains in a good solvent the correspondent depletion interaction potentials, depletion forces and the forces which exert phantom ideal ring and ring polymer chains with EVI on the walls were obtained in the framework of the massive field theory approach at fixed space dimensions d=3 up to one-loop order. Additionally, the investigation of a dilute solution of phantom ideal ring polymers in a slit geometry of two inert walls and mixed walls with one repulsive and other one inert wall were performed and correspondent depletion interaction potentials and the depletion forces were cal...
Weyl gravity and Cartan geometry
Attard, Jeremy; Lazzarini, Serge
2015-01-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned by two theories: the first one will be the associated Yang-Mills-like Lagrangian, while the second, inspired by~\\cite{Wheeler2014}, will be a slightly more general one which will relax the conformal Cartan geometry. The corresponding gauge symmetry is treated within the BRST language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the `normal conformal Cartan connection'. Finally, we provide in a Lagrangian framework a justification of the identification, in dimension $4$, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in ...
Fuzzy Logic for Incidence Geometry.
Tserkovny, Alex
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.
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
The geometry of singularities and the black hole information paradox
Stoica, Ovidiu Cristinel
2015-01-01
The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have {\
Hageneder, Simone; Bauch, Martin; Dostalek, Jakub
2016-08-15
This paper investigates plasmonic amplification in two commonly used optical configurations for fluorescence readout of bioassays - epifluorescence (EPF) and total internal reflection fluorescence (TIRF). The plasmonic amplification in the EPF configuration was implemented by using crossed gold diffraction grating and Kretschmann geometry of attenuated total reflection method (ATR) was employed in the TIRF configuration. Identical assay, surface architecture for analyte capture, and optics for the excitation, collection and detection of emitted fluorescence light intensity were used in both TIRF and EPF configurations. Simulations predict that the crossed gold diffraction grating (EPF) can amplify the fluorescence signal by a factor of 10(2) by the combination of surface plasmon-enhanced excitation and directional surface plasmon-coupled emission in the red part of spectrum. This factor is about order of magnitude higher than that predicted for the Kretschmann geometry (TIRF) which only took advantage of the surface plasmon-enhanced excitation. When applied for the readout of sandwich interleukin 6 (IL-6) immunoassay, the plasmonically amplified EPF geometry designed for Alexa Fluor 647 labels offered 4-times higher fluorescence signal intensity compared to TIRF. Interestingly, both geometries allowed reaching the same detection limit of 0.4pM despite of the difference in the fluorescence signal enhancement. This is attributed to inherently lower background of fluorescence signal for TIRF geometry compared to that for EPF which compensates for the weaker fluorescence signal enhancement. The analysis of the inflammation biomarker IL-6 in serum at medically relevant concentrations and the utilization of plasmonic amplification for the fluorescence measurement of kinetics of surface affinity reactions are demonstrated for both EPF and TIRF readout.
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
Proofs Produced by Secondary School Students Learning Geometry in a Dynamic Computer Environment.
Marrades, Ramon; Gutierrez, Angel
2000-01-01
Presents an analytic framework to describe and analyze students' answers to proof problems. Employs the framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and improve their proof skills. (Author/MM)
Waisberg, Daniel
2015-01-01
A roadmap for turning Google Analytics into a centralized marketing analysis platform With Google Analytics Integrations, expert author Daniel Waisberg shows you how to gain a more meaningful, complete view of customers that can drive growth opportunities. This in-depth guide shows not only how to use Google Analytics, but also how to turn this powerful data collection and analysis tool into a central marketing analysis platform for your company. Taking a hands-on approach, this resource explores the integration and analysis of a host of common data sources, including Google AdWords, AdSens
Energy Technology Data Exchange (ETDEWEB)
Scholtz, Jean; Burtner, Edwin R.; Cook, Kristin A.
2016-06-13
This course will introduce the field of Visual Analytics to HCI researchers and practitioners highlighting the contributions they can make to this field. Topics will include a definition of visual analytics along with examples of current systems, types of tasks and end users, issues in defining user requirements, design of visualizations and interactions, guidelines and heuristics, the current state of user-centered evaluations, and metrics for evaluation. We encourage designers, HCI researchers, and HCI practitioners to attend to learn how their skills can contribute to advancing the state of the art of visual analytics
The noncommutative geometry of Zitterbewegung
Eckstein, Michał; Miller, Tomasz
2016-01-01
Based on the mathematics of noncommutative geometry, we model a 'classical' Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of the model encodes the possibility of Zitterbewegung - the 'trembling motion' of the fermion. We recover the well-known frequency of Zitterbewegung as the highest possible speed of change in the fermion's 'internal space'. Furthermore, we show that the latter does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Higgs-like field. We discuss a table-top experiment in the domain of quantum simulation to test the predictions of the model and outline the consequences of our model for quantum gauge theories.
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2002-01-01
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Dijkgraaf, Robbert; Vafa, Cumrun
2002-11-01
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large- N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large- N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert E-mail: rhd@science.uva.nl; Vafa, Cumrun
2002-11-11
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large-N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large-N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Walking droplets in confined geometries
Filoux, Boris; Mathieu, Olivier; Vandewalle, Nicolas
2014-11-01
When gently placing a droplet onto a vertically vibrated bath, coalescence may be avoided: the drop bounces permanently. Upon increasing forcing acceleration, a drop interacts with the wave it generates, and becomes a ``walker'' with a well defined velocity. In this work, we investigate the confinement of a walker in a mono-dimensional geometry. The system consists of linear submarine channels used as waveguides for a walker. By studying the dynamics of walkers in those channels, we discover some 1D-2D transition. We also propose a model based on an analogy with ``Quantum Wires.'' Finally, we consider the situation of a walker in a circular submarine channel, and examine the behavior of several walking droplets in this system. We show the quantization of the drop distances, and correlate it to their bouncing modes.
Hofstadter's Butterfly in Quantum Geometry
Hatsuda, Yasuyuki; Tachikawa, Yuji
2016-01-01
We point out that the recent conjectural solution to the spectral problem for the Hamiltonian $H=e^{x}+e^{-x}+e^{p}+e^{-p}$ in terms of the refined topological invariants of a local Calabi-Yau geometry has an intimate relation with two-dimensional non-interacting electrons moving in a periodic potential under a uniform magnetic field. In particular, we find that the quantum A-period, determining the relation between the energy eigenvalue and the Kahler modulus of the Calabi-Yau, can be found explicitly when the quantum parameter $q=e^{i\\hbar}$ is a root of unity, that its branch cuts are given by Hofstadter's butterfly, and that its imaginary part counts the number of states of the Hofstadter Hamiltonian. The modular double operation, exchanging $\\hbar$ and $4\\pi^2/\\hbar$, plays an important role.
Hopf algebras in noncommutative geometry
Varilly, J C
2001-01-01
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of noncommutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups.
The Distance Geometry of Music
Demaine, Erik D; Meijer, Henk; Rappaport, David; Taslakian, Perouz; Toussaint, Godfried T; Winograd, Terry; Wood, David R
2007-01-01
We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms which encompass over forty timelines (\\emph{ostinatos}) from traditional world music. We prove that these \\emph{Euclidean rhythms} have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of \\emph{evenness}. We also show that essentially all Euclidean rhythms are \\emph{deep}: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicies form an interval $1,2,...,k-1$. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful prop...
Interactive graphics for geometry modeling
Wozny, M. J.
1984-01-01
An interactive vector capability to create geometry and a raster color shaded rendering capability to sample and verify interim geometric design steps through color snapshots is described. The development is outlined of the underlying methodology which facilitates computer aided engineering and design. At present, raster systems cannot match the interactivity and line-drawing capability of refresh vector systems. Consequently, an intermediate step in mechanical design is used to create objects interactively on the vector display and then scan convert the wireframe model to render it as a color shaded object on a raster display. Several algorithms are presented for rendering such objects. Superquadric solid primitive extend the class of primitives normally used in solid modelers.
Geometry of Spinning Ellis Wormholes
Chew, Xiao Yan; Kunz, Jutta
2016-01-01
We give a detailed account of the properties of spinning Ellis wormholes, supported by a phantom field. The general set of solutions depends on three parameters, associated with the size of the throat, the rotation and the symmetry of the solutions. For symmetric wormholes the global charges possess the same values in both asymptotic regions, while this is no longer the case for non-symmetric wormholes. We present mass formulae for these wormholes, study their quadrupole moments, and discuss the geometry of their throat and their ergoregion. We demonstrate, that these wormholes possess limiting configurations corresponding to an extremal Kerr black hole. Moreover, we analyze the geodesics of these wormholes, and show that they possess bound orbits.
Holographic thermalization in noncommutative geometry
Zeng, Xiao-Xiong; Liu, Wen-Biao
2014-01-01
Gravitational collapse of a dust shell in noncommutative geometry is probed by the renormalized geodesic length and minimal area surface, which are dual to the two-point correlation function and expectation value of Wilson loop in the dual conformal field theory. For the spacetime without a horizon, we find the shell will not collapse all the time but will stop in a stable state. For the spacetime with a horizon, we investigate how the noncommutative parameter affects the thermalization process in detail. From the numeric results, we find that larger the noncommutative parameter is, longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. From the fitted functions of the thermalization curve, we find for both thermalization probes, there is a phase transition point during the thermalization process, which divides the thermalization into an acceleration phase and a deceleration phase. During the acceleration phase, the acceleration is found to ...
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.
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.
Amoeboid motion in confined geometry
Wu, Hao; Hu, Wei-Fan; Farutin, Alexander; Rafaï, Salima; Lai, Ming-Chih; Peyla, Philippe; Misbah, Chaouqi
2015-01-01
Cells of the immune system, as well as cancer cells, migrating in confined environment of tissues undergo frequent shape changes (described as amoeboid motion) that enable them to move forward through these porous media without the assistance of adhesion sites. In other words, they perform amoeboid swimming (AS) while using extracellular matrices and cells of tissues as support. We introduce a simple model of AS in a confined geometry solved by means of 2D numerical simulations. We find that confinement promotes AS, unless being so strong that it restricts shape change amplitude. A straight AS trajectory in the channel is found to be unstable, and ample lateral excursions of the swimmer prevail. For weak confinement, these excursions are symmetric, while they become asymmetric at stronger confinement, whereby the swimmer is located closer to one of the two walls. This is a spontaneous symmetry-breaking bifurcation. We find that there exists an optimal confinement for migration. We provide numerical results as...
Hessian geometry and entanglement thermodynamics
Matsueda, Hiroaki
2015-01-01
We reconstruct entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of entanglement thermodynamics, we derive that a proper choice of the Hessian potential leads to both of the entanglement entropy scaling for quantum critical systems and hyperbolic metric (or AdS space with imaginary time). We also derive geometric representation of the entanglement entropy in which the entropy is described as integration of local conserved current of information flowing across an entangling surface. We find that the entangling surface is equivalent to the domain boundary of the Hessian potential. This feature originates in a special property of critical systems in which we can identify the entanglement entropy with the Hessian potential after the second derivative by the canonical parameters, and this identification guarantees violation of extensive nature of ...
Analytic theory of curvature effects for wave problems with general boundary conditions
DEFF Research Database (Denmark)
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found...
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Enzymes in Analytical Chemistry.
Fishman, Myer M.
1980-01-01
Presents tabular information concerning recent research in the field of enzymes in analytic chemistry, with methods, substrate or reaction catalyzed, assay, comments and references listed. The table refers to 128 references. Also listed are 13 general citations. (CS)
Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry
2014-01-01
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...
Metoda Analytic Network Process
2010-01-01
The thesis is concerned with Multi-Criteria Decision Making, in particular the Analytic Network Process method. The introductory part is dedicated to compile all the theory necessary to understand the method and utilized throughout the paper. The Analytic Hierarchy Process method is described and later generalized in the form of the ANP. Part of the paper is a description of available software products that are able to solve the ANP models. The main focus is on the application of the method, ...
Encyclopedia of analytical surfaces
Krivoshapko, S N
2015-01-01
This encyclopedia presents an all-embracing collection of analytical surface classes. It provides concise definitions and description for more than 500 surfaces and categorizes them in 38 classes of analytical surfaces. All classes are cross references to the original literature in an excellent bibliography. The encyclopedia is of particular interest to structural and civil engineers and serves as valuable reference for mathematicians.
Extreme Scale Visual Analytics
Energy Technology Data Exchange (ETDEWEB)
Steed, Chad A [ORNL; Potok, Thomas E [ORNL; Pullum, Laura L [ORNL; Ramanathan, Arvind [ORNL; Shipman, Galen M [ORNL; Thornton, Peter E [ORNL; Potok, Thomas E [ORNL
2013-01-01
Given the scale and complexity of today s data, visual analytics is rapidly becoming a necessity rather than an option for comprehensive exploratory analysis. In this paper, we provide an overview of three applications of visual analytics for addressing the challenges of analyzing climate, text streams, and biosurveilance data. These systems feature varying levels of interaction and high performance computing technology integration to permit exploratory analysis of large and complex data of global significance.
Nagin, Gleb
2011-01-01
Business analytics refers to the skills, technologies, applications and practisies for continuous iterative exploration and investigation of past business performance to gain insight and drive business planning. Business analytics focuses on developing new insights and understanding of business performance based on data and statistical methods. Business intelligence traditionally focuses on using a consistent set of metrics to both measure past performance and guide business planning, which i...
Solving the Vlasov equation in complex geometries
Directory of Open Access Journals (Sweden)
Sonnendrücker E.
2011-11-01
Full Text Available This paper introduces an isoparametric analysis to solve the Vlasov equation with a semi-Lagrangian scheme. A Vlasov-Poisson problem modeling a heavy ion beam in an axisymmetric configuration is considered. Numerical experiments are conducted on computational meshes targeting different geometries. The impact of the computational grid on the accuracy and the computational cost are shown. The use of analytical mapping or Bézier patches does not induce a too large computational overhead and is quite accurate. This approach successfully couples an isoparametric analysis with a semi-Lagrangian scheme, and we expect to apply it to a gyrokinetic Vlasov solver. Nous présentons ici une analyse isoparamétrique pour résoudre l’équation de Vlasov à l’aide d’un schéma Semi-Lagrangien. Le cas test d’un faisceau axisymétrique d’ions lourds est étudié dans le cadre du système Vlasov-Poisson. Des tests numériques sont effectués sur différents maillages a fin d’étudier diverses géométries. L’impact du choix de maillage sur la précision numérique et le coût de calcul est quantifié. L’utilisation de mapping analytique ou de patches de Bézier ne semble pas trop coûteux et permet une précision numérique suffisante. Le couplage de l’analyse isoparamétrique au schéma Semi-Lagrangien est donc réeussi, nous espérons pouvoir appliquer cette méthode à des solveurs de l’équation de Vlasov gyrocinétique.
Convection in Slab and Spheroidal Geometries
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Interplay between geometry and temperature in the Casimir effect
Energy Technology Data Exchange (ETDEWEB)
Weber, Alexej
2010-06-23
In this thesis, we investigate the interplay between geometry and temperature in the Casimir effect for the inclined-plates, sphere-plate and cylinder-plate configurations. We use the worldline approach, which combines the string-inspired quantum field theoretical formalism with Monte Carlo techniques. The approach allows the precise computation of Casimir energies in arbitrary geometries. We analyze the dependence of the Casimir energy, force and torque on the separation parameter and temperature T, and find Casimir phenomena which are dominated by long-range fluctuations. We demonstrate that for open geometries, thermal energy densities are typically distributed on scales of thermal wavelengths. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates, such as the proximity-force approximation, are found to become unreliable even at small surface-separations. Whereas the hightemperature behavior is always found to be linear in T, richer power-law behaviors at small temperatures emerge. In particular, thermal forces can develop a non-monotonic behavior. Many novel numerical as well as analytical results are presented. (orig.)
Verification of a magnetic island in gyro-kinetics by comparison with analytic theory
Energy Technology Data Exchange (ETDEWEB)
Zarzoso, D., E-mail: david.zarzoso-fernandez@polytechnique.org; Casson, F. J.; Poli, E. [Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Hornsby, W. A. [Theoretical Physics V, Department of Physics, Universitaet Bayreuth, Bayreuth, Germany D-95447 (Germany); Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Peeters, A. G. [Theoretical Physics V, Department of Physics, Universitaet Bayreuth, Bayreuth, Germany D-95447 (Germany)
2015-02-15
A rotating magnetic island is imposed in the gyrokinetic code GKW, when finite differences are used for the radial direction, in order to develop the predictions of analytic tearing mode theory and understand its limitations. The implementation is verified against analytics in sheared slab geometry with three numerical tests that are suggested as benchmark cases for every code that imposes a magnetic island. The convergence requirements to properly resolve physics around the island separatrix are investigated. In the slab geometry, at low magnetic shear, binormal flows inside the island can drive Kelvin-Helmholtz instabilities which prevent the formation of the steady state for which the analytic theory is formulated.
Effect of geometry on concentration polarization in realistic heterogeneous permselective systems
Green, Yoav; Yossifon, Gilad
2014-01-01
This study extends previous analytical solutions of concentration-polarization occurring solely in the depleted region, to the more realistic geometry consisting of a three dimensional (3D) heterogeneous ion-permselective medium connecting two opposite microchambers (i.e. 3 layers system). Under the local electro-neutrality approximation, the separation of variable methods is used to derive an analytical solution of the electro-diffusive problem for the two opposing asymmetric microchambers. Assuming an ideal permselective medium allows for the analytic calculation of the 3D concentration and electric potential distributions as well as a current-voltage relation. It is shown that any asymmetry in the microchamber geometries will result in current rectification. Moreover, it is demonstrated that for non-negligible microchamber resistances the conductance does not exhibit the expected saturation at low concentrations but instead shows a continuous decrease. The results are intended to facilitate a more direct c...
Croatian Analytical Terminology
Directory of Open Access Journals (Sweden)
Kastelan-Macan; M.
2008-04-01
Full Text Available Results of analytical research are necessary in all human activities. They are inevitable in making decisions in the environmental chemistry, agriculture, forestry, veterinary medicine, pharmaceutical industry, and biochemistry. Without analytical measurements the quality of materials and products cannot be assessed, so that analytical chemistry is an essential part of technical sciences and disciplines.The language of Croatian science, and analytical chemistry within it, was one of the goals of our predecessors. Due to the political situation, they did not succeed entirely, but for the scientists in independent Croatia this is a duty, because language is one of the most important features of the Croatian identity. The awareness of the need to introduce Croatian terminology was systematically developed in the second half of the 19th century, along with the founding of scientific societies and the wish of scientists to write their scientific works in Croatian, so that the results of their research may be applied in economy. Many authors of textbooks from the 19th and the first half of the 20th century contributed to Croatian analytical terminology (F. Rački, B. Šulek, P. Žulić, G. Pexidr, J. Domac, G. Janeček , F. Bubanović, V. Njegovan and others. M. DeŢelić published the first systematic chemical terminology in 1940, adjusted to the IUPAC recommendations. In the second half of 20th century textbooks in classic analytical chemistry were written by V. Marjanović-Krajovan, M. Gyiketta-Ogrizek, S. Žilić and others. I. Filipović wrote the General and Inorganic Chemistry textbook and the Laboratory Handbook (in collaboration with P. Sabioncello and contributed greatly to establishing the terminology in instrumental analytical methods.The source of Croatian nomenclature in modern analytical chemistry today are translated textbooks by Skoog, West and Holler, as well as by Günnzler i Gremlich, and original textbooks by S. Turina, Z.
Filippov, A. V.; Tarasov, S. Yu; Podgornyh, O. A.; Shamarin, N. N.; Filippova, E. O.
2017-01-01
Automatization of engineering processes requires developing relevant mathematical support and a computer software. Analysis of metal cutting kinematics and tool geometry is a necessary key task at the preproduction stage. This paper is focused on developing a procedure for determining the geometry of oblique peakless round-nose tool lathe machining with the use of vector/matrix transformations. Such an approach allows integration into modern mathematical software packages in distinction to the traditional analytic description. Such an advantage is very promising for developing automated control of the preproduction process. A kinematic criterion for the applicable tool geometry has been developed from the results of this study. The effect of tool blade inclination and curvature on the geometry-dependent process parameters was evaluated.
Second International workshop Geometry and Symbolic Computation
Walczak, Paweł; Geometry and its Applications
2014-01-01
This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...
A Relationship between Geometry and Algebra
Bejarano, Jose Ricardo Arteaga
2011-01-01
The three key documents for study geometry are: 1) "The Elements" of Euclid, 2) the lecture by B. Riemann at G\\"ottingen in 1854 entitled "\\"Uber die Hypothesen welche der Geometrie zu Grunde liegen" (On the hypotheses which underlie geometry) and 3) the "Erlangen Program", a document written by F. Klein (1872) on his income as professor at the Faculty of Philosophy and the Senate of the Erlangen University. The latter document F. Klein introduces the concept of group as a tool to study geometry. The concept of a group of transformations of space was known at the time. The purpose of this informative paper is to show a relationship between geometry and algebra through an example, the projective plane. Erlangen program until today continues being a guideline of how to study geometry.
Riemannian geometry of fluctuation theory: An introduction
Velazquez, Luisberis
2016-05-01
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dpξ(x|θ). This theory states a connection among geometry notions and statistical properties: separation distance as a measure of relative probabilities, curvature as a measure about the existence of irreducible statistical correlations, among others. In statistical mechanics, fluctuation geometry arises as the mathematical apparatus of a Riemannian extension of Einstein fluctuation theory, which is also closely related to Ruppeiner geometry of thermodynamics. Moreover, the curvature tensor allows to express some asymptotic formulae that account for the system fluctuating behavior beyond the gaussian approximation, while curvature scalar appears as a second-order correction of Legendre transformation between thermodynamic potentials.
A transient, quadratic nodal method for triangular-Z geometry
Energy Technology Data Exchange (ETDEWEB)
DeLorey, T.F.
1993-06-01
Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.
Geometry of solar coronal rays
Filippov, B. P.; Martsenyuk, O. V.; Platov, Yu. V.; Den, O. E.
2016-02-01
Coronal helmet streamers are the most prominent large-scale elements of the solar corona observed in white light during total solar eclipses. The base of the streamer is an arcade of loops located above a global polarity inversion line. At an altitude of 1-2 solar radii above the limb, the apices of the arches sharpen, forming cusp structures, above which narrow coronal rays are observed. Lyot coronagraphs, especially those on-board spacecrafts flying beyond the Earth's atmosphere, enable us to observe the corona continuously and at large distances. At distances of several solar radii, the streamers take the form of fairly narrow spokes that diverge radially from the Sun. This radial direction displays a continuous expansion of the corona into the surrounding space, and the formation of the solar wind. However, the solar magnetic field and solar rotation complicate the situation. The rotation curves radial streams into spiral ones, similar to water streams flowing from rotating tubes. The influence of the magnetic field is more complex and multifarious. A thorough study of coronal ray geometries shows that rays are frequently not radial and not straight. Coronal streamers frequently display a curvature whose direction in the meridional plane depends on the phase of the solar cycle. It is evident that this curvature is related to the geometry of the global solar magnetic field, which depends on the cycle phase. Equatorward deviations of coronal streamers at solar minima and poleward deviations at solar maxima can be interpreted as the effects of changes in the general topology of the global solar magnetic field. There are sporadic temporal changes in the coronal rays shape caused by remote coronal mass ejections (CMEs) propagating through the corona. This is also a manifestation of the influence of the magnetic field on plasma flows. The motion of a large-scale flux rope associated with a CME away from the Sun creates changes in the structure of surrounding field
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.
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
Generalized Kahler Geometry from supersymmetric sigma models
Bredthauer, A; Persson, J; Zabzine, M; Bredthauer, Andreas; Lindstrom, Ulf; Persson, Jonas; Zabzine, Maxim
2006-01-01
We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.
Recent developments and some open problems in Finsler geometry
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Finsler geometry is just Riemannian geometry without the quadratic restriction. Recent studies on Finsler geometry have taken on a new look. In this article, we will briefly discuss recent developments and some open problems in Finsler geometry.
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
Disformal transformation in Newton-Cartan geometry
Energy Technology Data Exchange (ETDEWEB)
Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)
2016-08-15
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)
Foliations dynamics, geometry and topology
Nicolau, Marcel
2014-01-01
This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods arising and used in the study of foliations. The lectures by A. El Kacimi Alaoui offer an introduction to Foliation Theory, with emphasis on examples and transverse structures. S. Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations, like limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, stable manifolds, Pesin Theory, and hyperbolic, parabolic, and elliptic types of foliations, all of them illustrated with examples. The lectures by M. Asaoka are devoted to the computation of the leafwise cohomology of orbit foliations given by locally free actions of certain Lie groups, and its application to the description of the deformation of those actions. In the lectures by K. Richardson, he studies the geometric and analytic properties ...
Directory of Open Access Journals (Sweden)
Phillip Brooker
2016-07-01
Full Text Available In the few years since the advent of ‘Big Data’ research, social media analytics has begun to accumulate studies drawing on social media as a resource and tool for research work. Yet, there has been relatively little attention paid to the development of methodologies for handling this kind of data. The few works that exist in this area often reflect upon the implications of ‘grand’ social science methodological concepts for new social media research (i.e. they focus on general issues such as sampling, data validity, ethics, etc.. By contrast, we advance an abductively oriented methodological suite designed to explore the construction of phenomena played out through social media. To do this, we use a software tool – Chorus – to illustrate a visual analytic approach to data. Informed by visual analytic principles, we posit a two-by-two methodological model of social media analytics, combining two data collection strategies with two analytic modes. We go on to demonstrate each of these four approaches ‘in action’, to help clarify how and why they might be used to address various research questions.
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 Bourges Cathedral
Directory of Open Access Journals (Sweden)
Robert Bork
2014-09-01
Full Text Available This article presents a geometrical analysis of Bourges Cathedral, based on the application of computer-aided design (CAD techniques to the results of a recent and highly precise laser survey. This analysis reveals that the cathedral's original designer developed a tightly interlocking and strikingly unified design, in which the five-fold subdivision of the chevet ground plan set proportions that would be vertically extruded into an elevation that can be inscribed both within a square and within a series of progessively smaller equilaterial triangles. These results contribute to an ongoing debate about the use of ‘ad quadratum’ and ‘ad triangulum’ geometries in Gothic architecture, and they provide new evidence for the geometrical coherence of Gothic cathedral design. In methodological terms, meanwhile, this discussion demonstrates the potential of CAD-based geometrical analysis for the study of precisely surveyed medieval buildings. The sequence of images being analysed can be viewed as supplementary material at: http://dx.doi.org/10.5334/ah.bz.s1
Combinatorics, geometry, and mathematical physics
Energy Technology Data Exchange (ETDEWEB)
Chen, W.Y.C.; Louck, J.D.
1998-11-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.
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...
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...
Analytic QCD Binding Potentials
Fried, H M; Grandou, T; Sheu, Y -M
2011-01-01
This paper applies the analytic forms of a recent non-perturbative, manifestly gauge- and Lorentz-invariant description (of the exchange of all possible virtual gluons between quarks ($Q$) and/or anti-quarks ($\\bar{Q}$) in a quenched, eikonal approximation) to extract analytic forms for the binding potentials generating a model $Q$-$\\bar{Q}$ "pion", and a model $QQQ$ "nucleon". Other, more complicated $Q$, $\\bar{Q}$ contributions to such color-singlet states may also be identified analytically. An elementary minimization technique, relevant to the ground states of such bound systems, is adopted to approximate the solutions to a more proper, but far more complicated Schroedinger/Dirac equation; the existence of possible contributions to the pion and nucleon masses due to spin, angular momentum, and "deformation" degrees of freedom is noted but not pursued. Neglecting electromagnetic and weak interactions, this analysis illustrates how the one new parameter making its appearance in this exact, realistic formali...
Advances in analytical chemistry
Arendale, W. F.; Congo, Richard T.; Nielsen, Bruce J.
1991-01-01
Implementation of computer programs based on multivariate statistical algorithms makes possible obtaining reliable information from long data vectors that contain large amounts of extraneous information, for example, noise and/or analytes that we do not wish to control. Three examples are described. Each of these applications requires the use of techniques characteristic of modern analytical chemistry. The first example, using a quantitative or analytical model, describes the determination of the acid dissociation constant for 2,2'-pyridyl thiophene using archived data. The second example describes an investigation to determine the active biocidal species of iodine in aqueous solutions. The third example is taken from a research program directed toward advanced fiber-optic chemical sensors. The second and third examples require heuristic or empirical models.
Institute of Scientific and Technical Information of China (English)
MATHAI; Varghese
2010-01-01
We review the Reidemeister, Ray-Singer’s analytic torsion and the Cheeger-Mller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsion of invariant forms are inverse to each other for any dimension.
Mathai, Varghese
2009-01-01
We review the Reidemeister and Ray-Singer's analytic torsions and the Cheeger-M"uller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsions are inverse to each other for any dimensions.
Competing on talent analytics.
Davenport, Thomas H; Harris, Jeanne; Shapiro, Jeremy
2010-10-01
Do investments in your employees actually affect workforce performance? Who are your top performers? How can you empower and motivate other employees to excel? Leading-edge companies such as Google, Best Buy, Procter & Gamble, and Sysco use sophisticated data-collection technology and analysis to answer these questions, leveraging a range of analytics to improve the way they attract and retain talent, connect their employee data to business performance, differentiate themselves from competitors, and more. The authors present the six key ways in which companies track, analyze, and use data about their people-ranging from a simple baseline of metrics to monitor the organization's overall health to custom modeling for predicting future head count depending on various "what if" scenarios. They go on to show that companies competing on talent analytics manage data and technology at an enterprise level, support what analytical leaders do, choose realistic targets for analysis, and hire analysts with strong interpersonal skills as well as broad expertise.
Aggarwal, Charu C
2011-01-01
Social network analysis applications have experienced tremendous advances within the last few years due in part to increasing trends towards users interacting with each other on the internet. Social networks are organized as graphs, and the data on social networks takes on the form of massive streams, which are mined for a variety of purposes. Social Network Data Analytics covers an important niche in the social network analytics field. This edited volume, contributed by prominent researchers in this field, presents a wide selection of topics on social network data mining such as Structural Pr
Radioactive Materials Analytical Laboratory
Energy Technology Data Exchange (ETDEWEB)
Laing, W.R.; Corbin, L.T.
1979-01-01
The Radioactive Materials Analytical Laboratory was completed 15 years ago and has been used since as an analytical chemistry support lab for reactor, fuel development, and reprocessing programs. Additions have been made to the building on two occasions, and a third addition is planned for the future. Major maintenance items include replacement of ZnBr/sub 2/ windows, cleanup of lead glass windows, and servicing of the intercell conveyor. An upgrading program, now in progress, includes construction of new hot-cell instrumentation and the installation of new equipment such as an x-ray fluorescence analyzer and a spark source mass spectrometer.
Chen, Xiaoman
2003-01-01
The seminal 1989 work of Douglas and Paulsen on the theory of analytic Hilbert modules precipitated a number of major research efforts. This in turn led to some intriguing and valuable results, particularly in the areas of operator theory and functional analysis. With the field now beginning to blossom, the time has come to collect those results under one cover. Written by two of the most active and often-cited researchers in the field, Analytic Hilbert Modules reports on the progress made by the authors and others, including the characteristic space theory, rigidity, the equivalence problem, the Arveson modules, extension theory, and reproducing Hilbert spaces on n-dimensional complex space.
Foundations of predictive analytics
Wu, James
2012-01-01
Drawing on the authors' two decades of experience in applied modeling and data mining, Foundations of Predictive Analytics presents the fundamental background required for analyzing data and building models for many practical applications, such as consumer behavior modeling, risk and marketing analytics, and other areas. It also discusses a variety of practical topics that are frequently missing from similar texts. The book begins with the statistical and linear algebra/matrix foundation of modeling methods, from distributions to cumulant and copula functions to Cornish--Fisher expansion and o
Directory of Open Access Journals (Sweden)
Daniel Alejandro Pérez Chamorro.
2012-12-01
Full Text Available For 50 years the philosophers of the Anglo-Saxon analytic tradition (E. Anscombre, P. Geach, A. Kenny, P. Foot have tried to follow the Thomas Aquinas School which they use as a source to surpass the Cartesian Epistemology and to develop the virtue ethics. Recently, J. Haldane has inaugurated a program of “analytical thomism” which main result until the present has been his “theory of identity mind/world”. Nevertheless, none of Thomás’ admirers has still found the means of assimilating his metaphysics of being.
Quantum groups: Geometry and applications
Energy Technology Data Exchange (ETDEWEB)
Chu, C.S. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
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.
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Samiran [College of Textile Technology, Berhampore 742101, Murshidabad, West Bengal (India)]. E-mail: sran_g@yahoo.com
2005-04-11
It has been found that the dust ion acoustic solitary wave (DIASW) is governed by a modified form of Korteweg-de Vries (KdV) equation modified by the effects of ionization, particle collisions and bounded nonplanar geometry. Approximate analytical time evolution solution and also the numerical solution of modified form of KdV equation reveal that the wave amplitude grows exponentially with time due to ionization, whereas the bounded nonplanar geometry and collision reduce the instability growth rate.
Maximum likelihood molecular clock comb: analytic solutions.
Chor, Benny; Khetan, Amit; Snir, Sagi
2006-04-01
Maximum likelihood (ML) is increasingly used as an optimality criterion for selecting evolutionary trees, but finding the global optimum is a hard computational task. Because no general analytic solution is known, numeric techniques such as hill climbing or expectation maximization (EM), are used in order to find optimal parameters for a given tree. So far, analytic solutions were derived only for the simplest model--three taxa, two state characters, under a molecular clock. Four taxa rooted trees have two topologies--the fork (two subtrees with two leaves each) and the comb (one subtree with three leaves, the other with a single leaf). In a previous work, we devised a closed form analytic solution for the ML molecular clock fork. In this work, we extend the state of the art in the area of analytic solutions ML trees to the family of all four taxa trees under the molecular clock assumption. The change from the fork topology to the comb incurs a major increase in the complexity of the underlying algebraic system and requires novel techniques and approaches. We combine the ultrametric properties of molecular clock trees with the Hadamard conjugation to derive a number of topology dependent identities. Employing these identities, we substantially simplify the system of polynomial equations. We finally use tools from algebraic geometry (e.g., Gröbner bases, ideal saturation, resultants) and employ symbolic algebra software to obtain analytic solutions for the comb. We show that in contrast to the fork, the comb has no closed form solutions (expressed by radicals in the input data). In general, four taxa trees can have multiple ML points. In contrast, we can now prove that under the molecular clock assumption, the comb has a unique (local and global) ML point. (Such uniqueness was previously shown for the fork.).
Transmission geometry laserspray ionization vacuum using an atmospheric pressure inlet.
Lutomski, Corinne A; El-Baba, Tarick J; Inutan, Ellen D; Manly, Cory D; Wager-Miller, James; Mackie, Ken; Trimpin, Sarah
2014-07-01
This represents the first report of laserspray ionization vacuum (LSIV) with operation directly from atmospheric pressure for use in mass spectrometry. Two different types of electrospray ionization source inlets were converted to LSIV sources by equipping the entrance of the atmospheric pressure inlet aperture with a customized cone that is sealed with a removable glass plate holding the matrix/analyte sample. A laser aligned in transmission geometry (at 180° relative to the inlet) ablates the matrix/analyte sample deposited on the vacuum side of the glass slide. Laser ablation from vacuum requires lower inlet temperature relative to laser ablation at atmospheric pressure. However, higher inlet temperature is required for high-mass analytes, for example, α-chymotrypsinogen (25.6 kDa). Labile compounds such as gangliosides and cardiolipins are detected in the negative ion mode directly from mouse brain tissue as intact doubly deprotonated ions. Multiple charging enhances the ion mobility spectrometry separation of ions derived from complex tissue samples.
Redundancy-Free, Accurate Analytical Center Machine for Classification
Institute of Scientific and Technical Information of China (English)
ZHENGFanzi; QIUZhengding; LengYonggang; YueJianhai
2005-01-01
Analytical center machine (ACM) has remarkable generalization performance based on analytical center of version space and outperforms SVM. From the analysis of geometry of machine learning and principle of ACM, it is showed that some training patterns are redundant to the definition of version space. Redundant patterns push ACM classifier away from analytical center of the prime version space so that the generalization performance degrades, at the same time redundant patterns slow down the classifier and reduce the efficiency of storage. Thus, an incremental algorithm is proposed to remove redundant patterns and embed into the frame of ACM that yields a Redundancy free accurate-Analytical center machine (RFA-ACM) for classification. Experiments with Heart, Thyroid, Banana datasets demonstrate the validity of RFA-ACM.
Description of SSG Geometry - phase 1
DEFF Research Database (Denmark)
Margheritini, Lucia; Kofoed, Jens Peter
The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work.......The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work....
Algebra-Geometry of Piecewise Algebraic Varieties
Institute of Scientific and Technical Information of China (English)
Chun Gang ZHU; Ren Hong WANG
2012-01-01
Algebraic variety is the most important subject in classical algebraic geometry.As the zero set of multivariate splines,the piecewise algebraic variety is a kind generalization of the classical algebraic variety.This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.
Two-spinor geometry and gauge freedom
Canarutto, Daniel
2014-01-01
Gauge freedom in quantum particle physics is shown to arise in a natural way from the geometry of two-spinors (Weyl spinors). Various related mathematical notions are reviewed, and a special ansatz of the kind "the system defines the geometry" is discussed in connection with the stated results.
Poisson Geometry from a Dirac perspective
Meinrenken, Eckhard
2016-01-01
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop "Quantum Groups and Gravity" at the University of Waterloo, April 2016.
Geometry of all supersymmetric type I backgrounds
Gran, Ulf; Papadopoulos, George; Sloane, Peter; Roest, Diederik
2007-01-01
We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9, 1), while th
Information Geometry and Evolutionary Game Theory
Harper, Marc
2009-01-01
The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary game theory are realized information-theoretically. Results are extended to the Lotka-Volterra equation and to multiple population systems.
Recent Advances in Computational Conformal Geometry
Gu, Xianfeng David; Luo, Feng; Yau, Shing-Tung
2009-01-01
Computational conformal geometry focuses on developing the computational methodologies on discrete surfaces to discover conformal geometric invariants. In this work, we briefly summarize the recent developments for methods and related applications in computational conformal geometry. There are two major approaches, holomorphic differentials and curvature flow. Holomorphic differential method is a linear method, which is more efficient and robust to triangulations with lower qua...
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…
Computing Bisectors in a Dynamic Geometry Environment
Botana, Francisco
2013-01-01
In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…
Geometry behind chordal Loewner chains
Contreras, Manuel D; Gumenyuk, Pavel
2010-01-01
Loewner Theory is a deep technique in Complex Analysis affording a basis for many further important developments such as the proof of famous Bieberbach's conjecture and well-celebrated Schramm's Stochastic Loewner Evolution (SLE). It provides analytic description of expanding domains dynamics in the plane. Two cases have been developed in the classical theory, namely the {\\it radial} and the {\\it chordal} Loewner evolutions, referring to the associated families of holomorphic self-mappings being normalized at an internal or boundary point of the reference domain, respectively. Recently there has been introduced a new approach [arXiv:0807.1594v1, arXiv:0807.1715v1, arXiv:0902.3116v1] bringing together, and containing as quite special cases, radial and chordal variants of Loewner Theory. In the framework of this approach we address the question what kind of systems of simply connected domains can be described by means of Loewner chains of chordal type. As an answer to this question we establish a necessary and ...
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.
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 ...
Transformations of units and world's geometry
Quirós, I
2000-01-01
The issue of the transformations of units is treated, mainly, in a geometrical context. Spacetime singularities are shown to be a consequence of a wrong choice of the geometrical formulation of the laws of gravitation. This result is discussed, in particular, for Friedmann-Robertson-Walker cosmology. It is also shown that Weyl geometry is a consistent framework for the formulation of the gravitational laws since the basic laws on which this geometry rests are invariant under the one-parameter Abelian group of units transformations studied in the paper. Riemann geometry does not fulfill this requirement. Arguments are given that point at Weyl geometry as a geometry implicitly containing the quantum effects of matter. The notion of geometrical relativity is presented. This notion may represent a natural extension of general relativity to include invariance under the group of units transformations.
Geometry of Cauchy-Riemann submanifolds
Shahid, Mohammad; Al-Solamy, Falleh
2016-01-01
This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.
Discrete quantum geometries and their effective dimension
Thürigen, Johannes
2015-01-01
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 ef...
Analytics for Customer Engagement
Bijmolt, Tammo H. A.; Leeflang, Peter S. H.; Block, Frank; Eisenbeiss, Maik; Hardie, Bruce G. S.; Lemmens, Aurelie; Saffert, Peter
2010-01-01
In this article, we discuss the state of the art of models for customer engagement and the problems that are inherent to calibrating and implementing these models. The authors first provide an overview of the data available for customer analytics and discuss recent developments. Next, the authors di
Energy Technology Data Exchange (ETDEWEB)
Turcotte, Melissa [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Moore, Juston Shane [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-02-28
User Behaviour Analytics is the tracking, collecting and assessing of user data and activities. The goal is to detect misuse of user credentials by developing models for the normal behaviour of user credentials within a computer network and detect outliers with respect to their baseline.
Analytical Chemistry Laboratory
Anderson, Mark
2013-01-01
The Analytical Chemistry and Material Development Group maintains a capability in chemical analysis, materials R&D failure analysis and contamination control. The uniquely qualified staff and facility support the needs of flight projects, science instrument development and various technical tasks, as well as Cal Tech.
Matsumoto, Kohji
2002-01-01
The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function Audience Researchers and graduate students interested in recent development of number theory
Buckingham Shum, Simon; Ferguson, Rebecca
2012-01-01
We propose that the design and implementation of effective "Social Learning Analytics (SLA)" present significant challenges and opportunities for both research and enterprise, in three important respects. The first is that the learning landscape is extraordinarily turbulent at present, in no small part due to technological drivers.…
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…
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…
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
Developments and retrospectives in Lie theory geometric and analytic methods
Penkov, Ivan; Wolf, Joseph
2014-01-01
This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics. Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current re...
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.
Experimental and Analytical Research on Fracture Processes in ROck
Energy Technology Data Exchange (ETDEWEB)
Herbert H.. Einstein; Jay Miller; Bruno Silva
2009-02-27
Experimental studies on fracture propagation and coalescence were conducted which together with previous tests by this group on gypsum and marble, provide information on fracturing. Specifically, different fracture geometries wsere tested, which together with the different material properties will provide the basis for analytical/numerical modeling. INitial steps on the models were made as were initial investigations on the effect of pressurized water on fracture coalescence.
Fault geometry and earthquake mechanics
Directory of Open Access Journals (Sweden)
D. J. Andrews
1994-06-01
Full Text Available Earthquake mechanics may be determined by the geometry of a fault system. Slip on a fractal branching fault surface can explain: 1 regeneration of stress irregularities in an earthquake; 2 the concentration of stress drop in an earthquake into asperities; 3 starting and stopping of earthquake slip at fault junctions, and 4 self-similar scaling of earthquakes. Slip at fault junctions provides a natural realization of barrier and asperity models without appealing to variations of fault strength. Fault systems are observed to have a branching fractal structure, and slip may occur at many fault junctions in an earthquake. Consider the mechanics of slip at one fault junction. In order to avoid a stress singularity of order 1/r, an intersection of faults must be a triple junction and the Burgers vectors on the three fault segments at the junction must sum to zero. In other words, to lowest order the deformation consists of rigid block displacement, which ensures that the local stress due to the dislocations is zero. The elastic dislocation solution, however, ignores the fact that the configuration of the blocks changes at the scale of the displacement. A volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The volume change is proportional to the product of the slip increment and the total slip since the formation of the junction. Energy absorbed at the junction, equal to confining pressure times the volume change, is not large enongh to prevent slip at a new junction. The ratio of energy absorbed at a new junction to elastic energy released in an earthquake is no larger than P/µ where P is confining pressure and µ is the shear modulus. At a depth of 10 km this dimensionless ratio has th value P/µ= 0.01. As slip accumulates at a fault junction in a number of earthquakes, the fault segments are displaced such that they no longer meet at a single point. For this reason the
Energy Technology Data Exchange (ETDEWEB)
Brune, D.; Forkman, B.; Persson, B.
1984-01-01
This book covers the general theories and techniques of nuclear chemical analysis, directed at applications in analytical chemistry, nuclear medicine, radiophysics, agriculture, environmental sciences, geological exploration, industrial process control, etc. The main principles of nuclear physics and nuclear detection on which the analysis is based are briefly outlined. An attempt is made to emphasise the fundamentals of activation analysis, detection and activation methods, as well as their applications. The book provides guidance in analytical chemistry, agriculture, environmental and biomedical sciences, etc. The contents include: the nuclear periodic system; nuclear decay; nuclear reactions; nuclear radiation sources; interaction of radiation with matter; principles of radiation detectors; nuclear electronics; statistical methods and spectral analysis; methods of radiation detection; neutron activation analysis; charged particle activation analysis; photon activation analysis; sample preparation and chemical separation; nuclear chemical analysis in biological and medical research; the use of nuclear chemical analysis in the field of criminology; nuclear chemical analysis in environmental sciences, geology and mineral exploration; and radiation protection.
Multifunctional nanoparticles: Analytical prospects
Energy Technology Data Exchange (ETDEWEB)
Dios, Alejandro Simon de [University of Oviedo, Department of Physical and Analytical Chemistry, Faculty of Chemistry, Av. Julian Claveria, 8, 33006 Oviedo (Spain); Diaz-Garcia, Marta Elena, E-mail: medg@uniovi.es [University of Oviedo, Department of Physical and Analytical Chemistry, Faculty of Chemistry, Av. Julian Claveria, 8, 33006 Oviedo (Spain)
2010-05-07
Multifunctional nanoparticles are among the most exciting nanomaterials with promising applications in analytical chemistry. These applications include (bio)sensing, (bio)assays, catalysis and separations. Although most of these applications are based on the magnetic, optical and electrochemical properties of multifunctional nanoparticles, other aspects such as the synergistic effect of the functional groups and the amplification effect associated with the nanoscale dimension have also been observed. Considering not only the nature of the raw material but also the shape, there is a huge variety of nanoparticles. In this review only magnetic, quantum dots, gold nanoparticles, carbon and inorganic nanotubes as well as silica, titania and gadolinium oxide nanoparticles are addressed. This review presents a narrative summary on the use of multifuncional nanoparticles for analytical applications, along with a discussion on some critical challenges existing in the field and possible solutions that have been or are being developed to overcome these challenges.
Institute of Scientific and Technical Information of China (English)
MIN Yinghua; LI Zhongcheng
1999-01-01
Delay consideration has been a majorissue in design and test of high performance digital circuits. Theassumption of input signal change occurring only when all internal nodesare stable restricts the increase of clock frequency. It is no longertrue for wave pipelining circuits. However, previous logical delaymodels are based on the assumption. In addition, the stable time of arobust delay test generally depends on the longest sensitizable pathdelay. Thus, a new delay model is desirable. This paper explores thenecessity first. Then, Boolean process to analytically describe thelogical and timing behavior of a digital circuit is reviewed. Theconcept of sensitization is redefined precisely in this paper. Based onthe new concept of sensitization, an analytical delay model isintroduced. As a result, many untestable delay faults under thelogical delay model can be tested if the output waveforms can be sampledat more time points. The longest sensitizable path length is computedfor circuit design and delay test.
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.
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
On Discrete Differential Geometry in Twistor Space
2011-01-01
In this paper we introduce a discrete integrable system generalizing the discrete (real) cross-ratio system in $S^4$ to complex values of a generalized cross-ratio by considering $S^4$ as a real section of the complex Pl\\"ucker quadric, realized as the space of two-spheres in $S^4.$ We develop the geometry of the Pl\\"ucker quadric by examining the novel contact properties of two-spheres in $S^4,$ generalizing classical Lie geometry in $S^3.$ Discrete differential geometry aims to develop disc...
A proposal of foundation of spacetime geometry
Tresguerres, Romualdo
2014-01-01
A common approach to metric-affine, local Poincar\\'e, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to alternative concepts of spacetime. In particular, the construction of the Minkowski metric, and its required invariance, allows either to reorganize the original affine bundle as a metric-affine geometry with explicit Lorentz symmetry, or to restrict it to a Poincar\\'e geometry, both of them constituting the background of a wide class of gauge theories of gravity.
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.
Analytical and physical electrochemistry
Girault, Hubert H
2004-01-01
The study of electrochemistry is pertinent to a wide variety of fields, including bioenergetics, environmental sciences, and engineering sciences. In addition, electrochemistry plays a fundamental role in specific applications as diverse as the conversion and storage of energy and the sequencing of DNA.Intended both as a basic course for undergraduate students and as a reference work for graduates and researchers, Analytical and Physical Electrochemistry covers two fundamental aspects of electrochemistry: electrochemistry in solution and interfacial electrochemistry. By bringing these two subj
DEFF Research Database (Denmark)
Hussain, Abid; Vatrapu, Ravi
2014-01-01
This paper presents the design, development and demonstrative case studies of the Social Data Analytics Tool, SODATO. Adopting Action Design Framework [1], the objective of SODATO [2] is to collect, store, analyze, and report big social data emanating from the social media engagement of and social...... media conversations about organizations. We report and discuss results from two demonstrative case studies that were conducted using SODATO and conclude with implications and future work....
Inorganic Analytical Chemistry
DEFF Research Database (Denmark)
Berg, Rolf W.
The book is a treatise on inorganic analytical reactions in aqueous solution. It covers about half of the elements in the periodic table, i.e. the most important ones : H, Li, B, C, N, O, Na, Mg, Al, P, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Br, Sr, Mo, Ag, Cd, Sn, Sb, I, Ba, W,...
Analytical strategies for phosphoproteomics
DEFF Research Database (Denmark)
Thingholm, Tine E; Jensen, Ole N; Larsen, Martin R
2009-01-01
sensitive and specific strategies. Today, most phosphoproteomic studies are conducted by mass spectrometric strategies in combination with phospho-specific enrichment methods. This review presents an overview of different analytical strategies for the characterization of phosphoproteins. Emphasis...... will be on the affinity methods utilized specifically for phosphoprotein and phosphopeptide enrichment prior to MS analysis, and on recent applications of these methods in cell biological applications....
Encrypting Analytical Web Applications
Fuhry, Benny; Tighzert, Walter; Kerschbaum. Florian
2016-01-01
The software-as-a-service (SaaS) market is growing very fast, but still many clients are concerned about the confidentiality of their data in the cloud. Motivated hackers or malicious insiders could try to steal the clients’ data. Encryption is a potential solution, but supporting the necessary functionality also in existing applications is difficult. In this paper, we examine encrypting analytical web applications that perform extensive number processing operations in the database. Existing ...
Communication Theoretic Data Analytics
Chen, Kwang-Cheng; Huang, Shao-Lun; Zheng, Lizhong; Poor, H. Vincent
2015-01-01
Widespread use of the Internet and social networks invokes the generation of big data, which is proving to be useful in a number of applications. To deal with explosively growing amounts of data, data analytics has emerged as a critical technology related to computing, signal processing, and information networking. In this paper, a formalism is considered in which data is modeled as a generalized social network and communication theory and information theory are thereby extended to data analy...
Analytic Modeling of Insurgencies
2014-08-01
point of view ; small changes in the balance of forces could lead to quick government demise. The other steady- state containment scenario involves...influenced by interests and utilities. 4.1 Carrots and Sticks An analytic model that captures the aforementioned utilitarian aspect is presented in... carrots ” x. A dynamic utility-based model is developed in [26] in which the state variables are the fractions of contrarians (supporters of the
Dollarization: Analytical Issues
Roberto Chang; Andres Velasco
2002-01-01
This paper discusses major analytical aspects of dollarization and their practical implications. We develop a simple model to stress that dollarization implies the loss of independent monetary policy and of seigniorage, yet the significance of such losses can only be evaluated in conjunction with assumptions about the policymaking process. If the government is benevolent and has no credibility problems, dollarization causes a fall in welfare, which can be measured by the implied seigniorage l...
Asst. Prof. Shubhada Talegaon
2014-01-01
Big Data analytics has started to impact all types of organizations, as it carries the potential power to extract embedded knowledge from big amounts of data and react according to it in real time. The current technology enables us to efficiently store and query large datasets, the focus is now on techniques that make use of the complete data set, instead of sampling. This has tremendous implications in areas like machine learning, pattern recognition and classification, senti...
Path Toward a Unifid Geometry for Radiation Transport
Lee, Kerry; Barzilla, Janet; Davis, Andrew; Zachmann
2014-01-01
The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex computer-aided design (CAD) models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN [high charge and energy transport code developed by NASA Langley Research Center (LaRC)], are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their
Path Toward a Unified Geometry for Radiation Transport
Lee, Kerry
The Direct Accelerated Geometry for Radiation Analysis and Design (DAGRAD) element of the RadWorks Project under Advanced Exploration Systems (AES) within the Space Technology Mission Directorate (STMD) of NASA will enable new designs and concepts of operation for radiation risk assessment, mitigation and protection. This element is designed to produce a solution that will allow NASA to calculate the transport of space radiation through complex CAD models using the state-of-the-art analytic and Monte Carlo radiation transport codes. Due to the inherent hazard of astronaut and spacecraft exposure to ionizing radiation in low-Earth orbit (LEO) or in deep space, risk analyses must be performed for all crew vehicles and habitats. Incorporating these analyses into the design process can minimize the mass needed solely for radiation protection. Transport of the radiation fields as they pass through shielding and body materials can be simulated using Monte Carlo techniques or described by the Boltzmann equation, which is obtained by balancing changes in particle fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear collisions. Deterministic codes that solve the Boltzmann transport equation, such as HZETRN (high charge and energy transport code developed by NASA LaRC), are generally computationally faster than Monte Carlo codes such as FLUKA, GEANT4, MCNP(X) or PHITS; however, they are currently limited to transport in one dimension, which poorly represents the secondary light ion and neutron radiation fields. NASA currently uses HZETRN space radiation transport software, both because it is computationally efficient and because proven methods have been developed for using this software to analyze complex geometries. Although Monte Carlo codes describe the relevant physics in a fully three-dimensional manner, their computational costs have thus far prevented their widespread use for analysis of complex CAD models, leading
Supramolecular analytical chemistry.
Anslyn, Eric V
2007-02-02
A large fraction of the field of supramolecular chemistry has focused in previous decades upon the study and use of synthetic receptors as a means of mimicking natural receptors. Recently, the demand for synthetic receptors is rapidly increasing within the analytical sciences. These classes of receptors are finding uses in simple indicator chemistry, cellular imaging, and enantiomeric excess analysis, while also being involved in various truly practical assays of bodily fluids. Moreover, one of the most promising areas for the use of synthetic receptors is in the arena of differential sensing. Although many synthetic receptors have been shown to yield exquisite selectivities, in general, this class of receptor suffers from cross-reactivities. Yet, cross-reactivity is an attribute that is crucial to the success of differential sensing schemes. Therefore, both selective and nonselective synthetic receptors are finding uses in analytical applications. Hence, a field of chemistry that herein is entitled "Supramolecular Analytical Chemistry" is emerging, and is predicted to undergo increasingly rapid growth in the near future.
APPROXIMATE ANALYTICAL SOLUTION FOR THE ISOTHERMAL LANE EMDEN EQUATION IN A SPHERICAL GEOMETRY
Directory of Open Access Journals (Sweden)
Moustafa Aly Soliman
2015-01-01
Full Text Available Este trabajo obtiene una soluci ́on anal ́ıtica aproximada p ara la ecuaci ́on isoterma de Lane-Emden que modela una esfera isot ́ermica au togravitante. La soluci ́on aproximada se obtiene en t ́erminos de par ́ametro s de distancias peque ̃nos y grandes por el m ́etodo de perturbaciones. La soluci ́on apr oximada se compara con la soluci ́on n ́umerica. La soluci ́on aproximada obteni da es v ́alida para todos los valores del par ́ametro de distancia.
2015-04-01
elastostatics [89]. Incompressible constitutive models , by definition, cannot address residual elastic dilatation and hence are not physically realistic in...rather than traditional continuum elasticity. Nonlocal , strain gradient, and/or gauge theories [53, 58] of continua may also enable a physically...the nonlinear thermoelastic response of pressurized cubic crystals. Unlike W̃ , potential Ŵ can be applied to anisotropic solids [66,90]. This model
Modeling of cavities using the analytic modal method and an open geometry formalism
DEFF Research Database (Denmark)
de Lasson, Jakob Rosenkrantz; Christensen, Thomas; Mørk, Jesper;
2012-01-01
-sized simulation domains, this avoids the issue of parasitic reflections from artificial boundaries. We compute the Purcell factor in a two-dimensional micropillar and explore two discretization techniques for the continuous radiation modes. Specifically, an equidistant and a nonequidistant discretization...... are employed, and while both converge, only the nonequidistant discretization exhibits uniform convergence. These results demonstrate that the method leads to more accurate results than existing simulation techniques and constitutes a promising basis for further work....
Melton, Roger
This study guide is part of an interdisciplinary course entitled the Science and Engineering Technician (SET) Curriculum. The course integrates elements from the disciplines of chemistry, physics, mathematics, mechanical technology, and electronic technology, with the objective of training technicians in the use of electronic instruments and their…
Institute of Scientific and Technical Information of China (English)
Song Falun; Cao Jinxiang; Wang Ge
2005-01-01
The purpose of the present work is to present a full-wave analysis of scattering from the weakly ionized plasma in the plane geometry. We have yielded an approximate solution in an analytic form to the electromagnetic wave scattering from the weakly ionizsd plasma. In the normal and oblique incidence, the analytic solution works well, as compared with the exact solution and the solution based on the Wenzell-Kramers-Brillouin-Jeffreys (WKBJ) approximation to the uniform density profile.
Properties of squeezing functions and geometry of bounded domains
Deng, Fusheng; Zhang, Liyou
2012-01-01
In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and metrics on bounded domains in terms of squeezing functions. To study the boundary behavior of squeezing functions, we introduce the notions of (intrinsic) ball pinching radius, and give boundary estimate of squeezing functions in terms of these datum. Finally, we use these results to study geometric and analytic properties of some interesting domains, including planar domains, Cartan-Hartogs domains, and a strongly pseudoconvex Reinhardt domain which is not convex. As a corollary, all Cartan-Hartogs domains are homogenous regular, i.e., their squeezing functions admit positive lower bounds.
Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence
Lehner, L; Gómez, R; Szilágyi, B; Winicour, J; Lehner, Luis; Bishop, Nigel T.; Gómez, Roberto; Winicour, Jeffrey
1999-01-01
We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as an important bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time.
Geometry-induced rigidity in nonspherical pressurized elastic shells.
Lazarus, A; Florijn, H C B; Reis, P M
2012-10-01
We present results from an experimental investigation of the indentation of nonspherical pressurized elastic shells with a positive Gauss curvature. A predictive framework is proposed that rationalizes the dependence of the local rigidity of an indented shell on the curvature in the neighborhood of the locus of indentation, the in-out pressure differential, and the material properties. In our approach, we combine classic theory for spherical shells with recent analytical developments for the pressurized case, and proceed, for the most part, by analogy, guided by our own experiments. By way of example, our results elucidate why an eggshell is significantly stiffer when compressed along its major axis, as compared to doing so along its minor axis. The prominence of geometry in this class of problems points to the relevance and applicability of our findings over a wide range of length scales.
Interplay between geometry and temperature for inclined Casimir plates
Weber, Alexej
2009-01-01
We provide further evidence for the nontrivial interplay between geometry and temperature in the Casimir effect. We investigate the temperature dependence of the Casimir force between an inclined semi-infinite plate above an infinite plate in D dimensions using the worldline formalism. Whereas the high-temperature behavior is always found to be linear in T in accordance with dimensional-reduction arguments, different power-law behaviors at small temperatures emerge. Unlike the case of infinite parallel plates, which shows the well-known T^D behavior of the force, we find a T^{D-1} behavior for inclined plates, and a ~T^{D-0.3} behavior for the edge effect in the limit where the plates become parallel. The strongest temperature dependence ~T^{D-2} occurs for the Casimir torque of inclined plates. Numerical as well as analytical worldline results are presented.
Casimir Force on Real Materials - the Slab and Cavity Geometry
Ellingsen, S A; Brevik, Iver; Ellingsen, Simen A.
2006-01-01
We analyse the potential of the geometry of a slab in a planar cavity for the purpose of Casimir force experiments. The force and its dependence on temperature, material properties and finite slab thickness are investigated both analytically and numerically for slab and walls made of aluminium and teflon FEP respectively. We conclude that such a setup is ideal for measurements of the temperature dependence of the Casimir force. By numerical calculation it is shown that temperature effects are dramatically larger for dielectrics, suggesting that a dielectric such as teflon FEP whose properties vary little within a moderate temperature range, should be considered for experimental purposes. We finally discuss the subtle but fundamental matter of the various Green's two-point function approaches present in the literature and show how they are different formulations describing the same phenomenon.
Business analytics a practitioner's guide
Saxena, Rahul
2013-01-01
This book provides a guide to businesses on how to use analytics to help drive from ideas to execution. Analytics used in this way provides "full lifecycle support" for business and helps during all stages of management decision-making and execution.The framework presented in the book enables the effective interplay of business, analytics, and information technology (business intelligence) both to leverage analytics for competitive advantage and to embed the use of business analytics into the business culture. It lays out an approach for analytics, describes the processes used, and provides gu
Spherical, hyperbolic and other projective geometries: convexity, duality, transitions
Fillastre, François; Seppi, Andrea
2016-01-01
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen as a "limit" of both geometries. Then all the geometries that can be obtained in this way. Some of these geometries had a rich development, most remarkably hyperbolic geometry and the Lorentzian geometries of Minkowski, de Sitter and anti-de Sitter spaces, ...
Attitudes of High School Students towards Geometry
Directory of Open Access Journals (Sweden)
Esat Avcı
2014-12-01
Full Text Available In this research, attitudes of high school students towards geometry were investigated in terms of gender, grade, types of the field and school. Population of research includes students who were studying at high school in five distincs of Mersin in 2013-2014 academical year. Sample of research includes 935 students from twelve high schools. Attitude scale which was developed by Su-Özenir (2008 was used for data collection. For data analysis, mean, standart deviation, t test and ANOVA were used. A meaningful difference between students’ attitudes towards geometry and variance of gender and grade level wasn’t observed, on the other hand a meaningful difference according to field and school type is observed.Key Words: Attitudes towards geometry, high school geometry lesson, attitude scale
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...