World Library  



Topology


Topology (from the Greek t?p??, “place”, and ?????, “study”) is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example, deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation.

 
  • Cover Image

Topological Characteristics of the Magnetic Field of the Earth Mag...

By: Marine Chkhitunidze
Read More
  • Cover Image

Plos One : Topological Strata of Weighted Complex Networks, Volume 8

By: Renaud Lambiotte

Description : The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and –more recently– correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body propert...

Read More
  • Cover Image

Plos One : Long-term Effects of Attentional Performance on Functio...

By: Yong He

Description : Individuals differ in their cognitive resilience. Less resilient people demonstrate a greater tendency to vigilance decrements within sustained attention tasks. We hypothesized that a period of sustained attention is followed by prolonged changes in the organization of ‘‘resting state’’ brain networks and that individual differences in cognitive resilience are related to differences in post-task network reorganization. We compared the topological and spatia...

Read More
  • Cover Image

Algebraic Topology : A Computational Approach

By: T. Kaczynski

Mathematics document containing theorems and formulas.

Excerpt: Basic Notions From Topology Differetiable Functions to Problems In Algebra.

Read More
  • Cover Image

Topology of Polyhedra Asd Reiated Questioks

Mathematics document containing theorems and formulas.

Excerpt: After some further preliminary properties the results of (VII) will first be applied to the homology theories associated with polyhedra. From the topological standpoint a polyhedron may as well be replaced by a simplicial partition. Unless otherwise stated therefore all polyhedral complexes under consideration will be simplicial, i.e., they will be Euclidean complexes. In addition to the general type we shall also discuss geometric manifolds and their special in...

Read More
  • Cover Image

Combinatorial Differential Topology and Geometry

By: Robin Forman

Mathematics document containing theorems and formulas.

Excerpt: A variety of questions in combinatorics lead one to the task of analyzing the topology of a simplicial complex, or a more general cell complex. However, there are few general techniques to aid in this investigation. On the other hand, the subjects of differential topology and geometry are devoted to precisely this sort of problem, except that the topological spaces in question are smooth manifolds. In this paper we show how two standard techniques from the study...

Read More
  • Cover Image

An Algebraic Representation for the Topology of Multi-Component Phase

By: Don J. Orser

Technical Reference Publication

Abstract: A new non-graphical method for representing the topology of phase diagrams is presented. The method exploits the fact that the topological relations between the variously dimensioned equilibria making up the structure of a phase diagram may be treated as a special type of algebraic structure, called an incidence lattice. Corresponding to each topologically distinct phase diagram there is a finite incidence lattice whose elements correspond to the invariant (ver...

Read More
  • Cover Image

Undergraduate Lecture Notes in Topological Quantum Field Theory

By: Vladimir G. Ivancevic

Description: These third–year lecture notes are designed for a 1–semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second–year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism.

Read More
  • Cover Image

Constrained minimization under vector-valued criteria in linear to...

By: Da Cunha, N. O. ; Polak, E

Supplemental catalog subcollection information: NASA Publication Collection; Astrophysics and Technical Documents; Constrained minimization under vector valued criteria in linear topological spaces

Read More
  • Cover Image

Introduction to Algebraic Topology and Algebraic Geometry

By: Genova

Description: This note provides an introduction to algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory. Covered topics are: Algebraic Topology, Singular homology theory, Introduction to sheaves and their cohomology, Introduction to algebraic geometry, Complex manifolds...

Read More
  • Cover Image

Landscape (Topology version) : Full score: Full score

By: Robert Davidson (b. 17 December 1965)

Description: Landscape (Topology version) (Davidson, Robert); Robert Davidson was a Australian composer during the Modern period; Piecestyle: Modern; Instrumentation: soprano saxophone, violin, viola, double bass, piano; Quintet; Number of Movements: 1; Pieces|For saxophone, violin, viola, double bass, piano|Scores featuring the saxophone|Scores featuring the violin|Scores featuring the viola|Scores featuring the double bass|Scores featuring the piano|For 5 players.

Read More
  • Cover Image

Landscape (Topology version) : Double Bass part: Double Bass part

By: Robert Davidson (b. 17 December 1965)

Description: Landscape (Topology version) (Davidson, Robert); Robert Davidson was a Australian composer during the Modern period; Piecestyle: Modern; Instrumentation: soprano saxophone, violin, viola, double bass, piano; Quintet; Number of Movements: 1; Pieces|For saxophone, violin, viola, double bass, piano|Scores featuring the saxophone|Scores featuring the violin|Scores featuring the viola|Scores featuring the double bass|Scores featuring the piano|For 5 players.

Read More
  • Cover Image

Landscape (Topology version) : Piano part: Piano part

By: Robert Davidson (b. 17 December 1965)

Description: Landscape (Topology version) (Davidson, Robert); Robert Davidson was a Australian composer during the Modern period; Piecestyle: Modern; Instrumentation: soprano saxophone, violin, viola, double bass, piano; Quintet; Number of Movements: 1; Pieces|For saxophone, violin, viola, double bass, piano|Scores featuring the saxophone|Scores featuring the violin|Scores featuring the viola|Scores featuring the double bass|Scores featuring the piano|For 5 players.

Read More
  • Cover Image

Landscape (Topology version) : Saxophone part: Saxophone part

By: Robert Davidson (b. 17 December 1965)

Description: Landscape (Topology version) (Davidson, Robert); Robert Davidson was a Australian composer during the Modern period; Piecestyle: Modern; Instrumentation: soprano saxophone, violin, viola, double bass, piano; Quintet; Number of Movements: 1; Pieces|For saxophone, violin, viola, double bass, piano|Scores featuring the saxophone|Scores featuring the violin|Scores featuring the viola|Scores featuring the double bass|Scores featuring the piano|For 5 players.

Read More
  • Cover Image

Landscape (Topology version) : Viola part: Viola part

By: Robert Davidson (b. 17 December 1965)

Description: Landscape (Topology version) (Davidson, Robert); Robert Davidson was a Australian composer during the Modern period; Piecestyle: Modern; Instrumentation: soprano saxophone, violin, viola, double bass, piano; Quintet; Number of Movements: 1; Pieces|For saxophone, violin, viola, double bass, piano|Scores featuring the saxophone|Scores featuring the violin|Scores featuring the viola|Scores featuring the double bass|Scores featuring the piano|For 5 players.

Read More
  • Cover Image

Landscape (Topology version) : Violin part: Violin part

By: Robert Davidson (b. 17 December 1965)

Description: Landscape (Topology version) (Davidson, Robert); Robert Davidson was a Australian composer during the Modern period; Piecestyle: Modern; Instrumentation: soprano saxophone, violin, viola, double bass, piano; Quintet; Number of Movements: 1; Pieces|For saxophone, violin, viola, double bass, piano|Scores featuring the saxophone|Scores featuring the violin|Scores featuring the viola|Scores featuring the double bass|Scores featuring the piano|For 5 players.

Read More
  • Cover Image

Plos Biology : Topology and Dynamics of the Zebrafish Segmentation...

By: Denise Montell

Description : During vertebrate embryogenesis, the rhythmic and sequential segmentation of the body axis is regulated by an oscillating genetic network termed the segmentation clock. We describe a new dynamic model for the core pace-making circuit of the zebrafish segmentation clock based on a systematic biochemical investigation of the network’s topology and precise measurements of somitogenesis dynamics in novel genetic mutants. We show that the core pace-making circui...

Read More
  • Cover Image

Introduction to General Topology

Mathematics document containing theorems and formulas.

Excerpt: The scope of the chapter is sufficiently clear from its title. Particular attention has been paid to compactness and there is also a thoroughgoing treab ment of inverse mapping systems which come strongly to the fore in (11), and also in (VI, VII) in connection with the homology theory of topological spaces. General references: The standard treatises and in addition: AlesandroffUrysohn [a], Cech [g], Steenrod [a], Tukey [TI, Wallace [a], Wallman [a].

Read More
  • Cover Image

Introduction to Differential Topology

By: Matthew G. Brin

Mathematics document containing theorems and formulas.

Excerpt: This is a quick of motes on basic differential topology. It gets sketchier as it goes on.

Read More
  • Cover Image

Plos Biology : Topology and Robustness in the Drosophila Segment P...

By: Arthur Lander

Description : A complex hierarchy of genetic interactions converts a single-celled Drosophila melanogaster egg into a multicellular embryo with 14 segments. Previously, von Dassow et al. reported that a mathematical model of the genetic interactions that defined the polarity of segments (the segment polarity network) was robust (von Dassow et al. 2000). As quantitative information about the system was unavailable, parameters were sampled randomly. A surprisingly large fr...

Read More
 
3
|
4
|
5
|
6
|
7
Records: 81 - 100 of 1,216 - Pages: 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library on the Kindle are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.