## The Income Concept

*Fred Campano and Dominick Salvatore*

### in Income Distribution: Includes CD

- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780195300918
- eISBN:
- 9780199783441
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195300912.003.0002
- Subject:
- Economics and Finance, Development, Growth, and Environmental

The definition of income in developed and developing countries is introduced. The use of household sample surveys to gather information on income distribution is discussed as well as the derived ... More

## Quadratic Forms of Type F4

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0009
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents various results about quadratic forms of type F₄. The Moufang quadrangles of type F₄ were discovered in the course of carrying out the classification of Moufang polygons and ... More

## Residues

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0010
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter deals with the residues of a Bruhat-Tits building whose building at infinity is an exceptional quadrangle. It begins with the remark that if Λ is an arbitrary quadratic space of type Eℓ ... More

## Unramified Quadrangles of Type E6, E7 and E8

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0011
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter deals with the case that the building at infinity of the Bruhat-Tits building Ξ is a Moufang quadrangle of type E⁶, E₇, and E₈. It begins with a hypothesis that takes into account a ... More

## Quadrangles of Type E6, E7 and E8: Summary

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0014
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter summarizes the different cases about Moufang quadrangles of type E⁶, E₇ and E₈. The first case is that the building at infinity of the Bruhat-Tits building Ξ is an unramified ... More

## Distributions of data—four plots

*Steve Selvin*

### in The Joy of Statistics: A Treasury of Elementary Statistical Tools and their Applications

- Published in print:
- 2019
- Published Online:
- May 2019
- ISBN:
- 9780198833444
- eISBN:
- 9780191872280
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198833444.003.0002
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics

An introduction to four graphic statistical descriptions, namely histograms, stem-leaf plots, frequency polygons, and frequency distributions.

## Convex lattice vesicles and directed animals

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0006
- Subject:
- Mathematics, Mathematical Physics

Chapter 6 covers partition and stack polygons and their scaling. Solutions of the staircase vesicle and convex polygons are reviewed, as well as the solutions of bargraph and column convex vesicles. ... More

## Self-avoiding walks and polygons

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0007
- Subject:
- Mathematics, Mathematical Physics

Chapter 7 provides an overview of self-avoiding walks, polygons and half-space walks. The Hammersley-Welsh construction is discussed, as well as the bridge decomposition of half-space walks. Loops, ... More

## Areas, Angles, and Polyhedra

*Glen Van Brummelen*

### in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175997
- eISBN:
- 9781400844807
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175997.003.0007
- Subject:
- Mathematics, History of Mathematics

This chapter explains how to find the area of an angle or polyhedron. It begins with a discussion of how to determine the area of a spherical triangle or polygon. The formula for the area of a ... More

## Buildings

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter assembles a few standard definitions, fixes some notation, and reviews a few of the results about buildings and Moufang polygons. It also summarizes the basic facts about Coxeter groups ... More

## Moufang Polygons

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0003
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces some basic facts about Moufang polygons and root group sequences. For each root group sequence Ω, there is a unique Moufang polygon Δ such that Ω is isomorphic to a root ... More

## Movement patterns and telemetry

*Bruce A. Kingsbury and Nathan J. Robinson*

### in Reptile Ecology and Conservation: A Handbook of Techniques

- Published in print:
- 2016
- Published Online:
- June 2016
- ISBN:
- 9780198726135
- eISBN:
- 9780191825934
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198726135.003.0009
- Subject:
- Biology, Biodiversity / Conservation Biology, Animal Biology

This chapter offers a methodological ‘road-map’ to assist researchers contemplating telemetry projects. Telemetry devices are often used in these studies to track the animals’ movements and this ... More

## Lattice Models of Linear and Ring Polymers

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0001
- Subject:
- Mathematics, Mathematical Physics

In Chapter 1 the self-avoiding walk connective constant, growth constant and subadditivity are introduced. Concatenation and the supermultiplicativity of lattice polygons are discussed. Scaling, ... More

## Directed lattice paths

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0005
- Subject:
- Mathematics, Mathematical Physics

Chapter 5 is an overview of Dyck, Motzkin and partially directed path models of polymer entropy. Adsorbing paths, the Temperley method and factorisation methods are discussed, including the Bethe ... More

## Spatially balanced sampling

*David G. Hankin, Michael S. Mohr, and Ken B. Newman*

### in Sampling Theory: For the Ecological and Natural Resource Sciences

- Published in print:
- 2019
- Published Online:
- December 2019
- ISBN:
- 9780198815792
- eISBN:
- 9780191853463
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198815792.003.0012
- Subject:
- Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Ecology

In many ecological and natural resource settings, there may be a high degree of spatial structure or pattern to the distribution of target variable values across the landscape. For example, the ... More

## Advanced statistical techniques: spatial patterns, life tables, modelling, and population viability analysis

*David J. Gibson*

### in Methods in Comparative Plant Population Ecology, Second Edition

- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780199671465
- eISBN:
- 9780191792496
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199671465.003.0008
- Subject:
- Biology, Plant Sciences and Forestry

This chapter moves forward from Chapter 7 (planning, choosing, and using statistics) and introduces some more advanced statistical methods that are of particular importance to plant population ... More

## Definition of the Plaid Model

*Richard Evan Schwartz*

### in The Plaid Model: (AMS-198)

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691181387
- eISBN:
- 9780691188997
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181387.003.0002
- Subject:
- Mathematics, Educational Mathematics

This chapter defines the plaid model. The input to the plaid model is a rational A = p/q ɛ (0, 1) with pq even. The output is the union PLA of plaid polygons. The chapter is organized as follows. ... More

## Using the Model

*Richard Evan Schwartz*

### in The Plaid Model: (AMS-198)

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691181387
- eISBN:
- 9780691188997
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181387.003.0004
- Subject:
- Mathematics, Educational Mathematics

This chapter explores some consequences of the results in Chapter 2, especially Theorem 2.3. It suggests that Theorem 2.3 gives a way to extract information from the geometry of the low capacity ... More

## Three-Dimensional Interpretation

*Richard Evan Schwartz*

### in The Plaid Model: (AMS-198)

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691181387
- eISBN:
- 9780691188997
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181387.003.0006
- Subject:
- Mathematics, Educational Mathematics

This chapter explains the 3-dimensional interpretation of the plaid model. Section 5.2 stacks the blocks on top of each other in such a way that remotely adjacent blocks appear actually adjacent to ... More

## The Plaid Master Picture Theorem

*Richard Evan Schwartz*

### in The Plaid Model: (AMS-198)

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691181387
- eISBN:
- 9780691188997
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691181387.003.0009
- Subject:
- Mathematics, Educational Mathematics

This chapter aims to prove Theorem 1.4 and Theorem 0.3, the Plaid Master Picture Theorem. Both of these results are deduced from Theorem 8.2, which says that the union PLA of plaid polygons is ... More