## 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

## The Mineral Nutrition of Single Plants in Soil

*Peter B. Tinker and Peter Nye*

### in Solute Movement in the Rhizosphere

- Published in print:
- 2000
- Published Online:
- November 2020
- ISBN:
- 9780195124927
- eISBN:
- 9780197561324
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195124927.003.0014
- Subject:
- Earth Sciences and Geography, Soil Science

Earlier chapters in this book have dealt with the various components of the soil –root system. In this chapter we aim to synthesize them into a unified treatment of a ... 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.

## Danebury Revisited: A English Iron Age Hillfort in a Digital Landscape

*Gary R. Lock and Trevor M. Harris*

### in Anthropology, Space, and Geographic Information Systems

- Published in print:
- 1996
- Published Online:
- November 2020
- ISBN:
- 9780195085754
- eISBN:
- 9780197560495
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195085754.003.0016
- Subject:
- Archaeology, Archaeological Methodology and Techniques

The doyen of British field archaeology, O. G. S. Crawford, noted that “The surface of England is a palimpsest, a document that has been written on and erased over and ... More

## The Use of GIS to Measure Spatial Patterns of Ethnic Firms in the Los Angeles Garment Industry

*Christopher G. Arnold and Richard P. Appelbaum*

### in Anthropology, Space, and Geographic Information Systems

- Published in print:
- 1996
- Published Online:
- November 2020
- ISBN:
- 9780195085754
- eISBN:
- 9780197560495
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195085754.003.0006
- Subject:
- Archaeology, Archaeological Methodology and Techniques

The purpose of this chapter is to describe the methodology and present some initial results in our efforts to understand the role of spatial organization in ethnic ... More

## 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

## Statistics

*Patrick Magee and Mark Tooley*

### in The Physics, Clinical Measurement and Equipment of Anaesthetic Practice for the FRCA

- Published in print:
- 2011
- Published Online:
- November 2020
- ISBN:
- 9780199595150
- eISBN:
- 9780191918032
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199595150.003.0006
- Subject:
- Clinical Medicine and Allied Health, Anesthesiology

This chapter will provide background to enable the reader to understand basic statistics and be able then to follow more complex statistical ideas. Although statistics ... 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

## Pinwheels and Quarter Turns

*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/9780691181387.003.0015
- Subject:
- Mathematics, Educational Mathematics

This chapter is the first of three that will prove a generalization of the Graph Master Picture Theorem which works for any convex polygon P without parallel sides. The final result is Theorem 16.9, ... More

## Existence of Infinite Orbits

*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/9780691181387.003.0022
- Subject:
- Mathematics, Educational Mathematics

This chapter begins Part 5 of the book. This part is devoted mostly to the study of the distribution of the plaid polygons: their size and number depending on the parameter. Section 21.2 gives a ... More

## Existence of Many Large Orbits

*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/9780691181387.003.0023
- Subject:
- Mathematics, Educational Mathematics

A plaid polygon is called N-fat if it is not contained in any strip of width N. As a related notion, a plaid polygon is called N-long if it has diameter at least N. This chapter will prove Theorem ... 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