## Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

*Juan Luis Vázquez*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.001.0001
- Subject:
- Mathematics, Applied Mathematics

This book is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as ... More

## Annuity demand theory

*Edmund Cannon and Ian Tonks*

### in Annuity Markets

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199216994
- eISBN:
- 9780191711978
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199216994.003.0007
- Subject:
- Business and Management, Pensions and Pension Management

This chapter discusses Yaari's (19665) annuitization result, which states that a risk-averse individual concerned about longevity risk (uncertain length of life) will always purchase actuarially-fair ... More

## Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

*Ludwig Fahrmeir and Thomas Kneib*

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.001.0001
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) ... More

## Smoothness and Asymptotic Smoothness

*Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav*

### in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153551
- eISBN:
- 9781400842698
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153551.003.0008
- Subject:
- Mathematics, Analysis

This chapter describes the modulus of smoothness of a function in the direction of a family of subspaces and the much simpler notion of upper Fréchet differentiability. It also considers the notion ... More

## Between Scylla and Charybdis: Improving the Cost Effectiveness of Public Pension Retirement Plans

*M. Barton Waring*

### in The Future of Public Employee Retirement Systems

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573349
- eISBN:
- 9780191721946
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573349.003.0004
- Subject:
- Business and Management, Public Management, Pensions and Pension Management

Unless defined benefit pension plans are managed much better and more cost-effectively, they will be replaced by defined contribution plans. Benefit and contribution policies need to be carefully ... More

## Searching for Structure in Point Data

*Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray*

### in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691151687
- eISBN:
- 9781400848911
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691151687.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Inferring the probability density function (pdf) from a sample of data is known as density estimation. The same methodology is often called data smoothing. Density estimation in the one-dimensional ... More

## Spatial variation in risk

*Dirk U. Pfeiffer, Timothy P. Robinson, Mark Stevenson, Kim B. Stevens, David J. Rogers, and Archie C. A. Clements*

### in Spatial Analysis in Epidemiology

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198509882
- eISBN:
- 9780191709128
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509882.003.0006
- Subject:
- Biology, Disease Ecology / Epidemiology

This chapter discusses spatial variation in risk. Epidemiological disease investigations should include an assessment of the spatial variation of disease risk, as this may provide important clues ... More

## Absent Hair

*Susan Niditch*

### in "My Brother Esau Is a Hairy Man": Hair and Identity in Ancient Israel

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780195181142
- eISBN:
- 9780199869671
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195181142.003.0005
- Subject:
- Religion, Judaism

This chapter explores a set of biblical texts dealing with the loss or absence of hair: the tale of David's envoys in 2 Samuel 10:4–5; related texts concerning conquest and images of shaving; ... More

## The Pharmacology of Vascular Smooth Muscle

*C. J. Garland and J. A. Angus (eds)*

- Published in print:
- 1996
- Published Online:
- March 2012
- ISBN:
- 9780192623874
- eISBN:
- 9780191724671
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780192623874.001.0001
- Subject:
- Neuroscience, Sensory and Motor Systems

This book provides an understanding of how events at the cellular level impact on the cardiovascular system as a whole. Advances in knowledge are highlighted and all the themes are presented from the ... More

## DIFFUSION EQUATION

*George Em Karniadakis and Spencer J. Sherwin*

### in Spectral/hp Element Methods for Computational Fluid Dynamics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198528692
- eISBN:
- 9780191713491
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528692.003.0005
- Subject:
- Mathematics, Numerical Analysis

This chapter considers the diffusion equation: an implicit in time discretization leads to the Helmholtz equation. Both the temporal discretization and eigenspectra of second-order operators that ... More

## INTRODUCTION

*Terry Lyons and Zhongmin Qian*

### in System Control and Rough Paths

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198506485
- eISBN:
- 9780191709395
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506485.003.0001
- Subject:
- Mathematics, Probability / Statistics

The concept of a differential equation controlled by a rough path can be motivated by quite simple examples. One such example is a linear system driven by two-dimensional noise. This example is ... More

## Numerical Simulation Of Microflows And Nanoflows

*Narayan R. Aluru and George Em Karniadakis*

### in Micro/Nano Technology Systems for Biomedical Applications: Microfluidics, Optics, and Surface Chemistry

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199219698
- eISBN:
- 9780191594229
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219698.003.0003
- Subject:
- Mathematics, Mathematical Biology

In this chapter we review recent advances in numerical simulation of micro and nanoflows. For coarse-grained simulation of microfuidics, we present an overview of Lattice Boltzmann, Brownian ... More

## Working with roots

*Christopher G. Small and Jinfang Wang*

### in Numerical Methods for Nonlinear Estimating Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506881
- eISBN:
- 9780191709258
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506881.003.0004
- Subject:
- Mathematics, Probability / Statistics

This chapter studies the broad class of models which have difficult problems of nonlinearity and multiple roots. These models include the mixture models, a model for bivariate normal paired data with ... More

## Superfast FDE

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0010
- Subject:
- Mathematics, Applied Mathematics

This chapter addresses the question of extending the theory and estimates of the FDE to cover the singular range m ≤ 0, that has only been partially considered in previous chapters. This completes ... More

## Evolution equations of the p-Laplacian type

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0012
- Subject:
- Mathematics, Applied Mathematics

This chapter presents the application of the foregoing ideas to the p-Laplacian evolution equation and the doubly nonlinear evolution equation. Topics covered include the doubly linear diffusion ... More

## Introduction

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0001
- Subject:
- Mathematics, Applied Mathematics

This introductory chapter opens with an explanation of the purpose of the book, which is to obtain basic estimates for some particular nonlinear parabolic equations and to derive consequences about ... More

## Smoothing effect and time decay. Data in L 1 (R n ) or M (R n )

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0003
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses the smoothing and decay effects for the porous medium equation, using as a model case the famous Barenblatt solutions that have explicit formulas. Topics covered include ... More

## Smoothing effect and time decay from L p or M p

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter addresses the question of boundedness for the same equation when the initial data are chosen in the Lebesgue space Lp, p Ɛ (1, ∞). It is assumed that m > mc . The ... More

## Subcritical range of the FDE. Critical line. Extinction. Backward effect

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0006
- Subject:
- Mathematics, Applied Mathematics

This chapter studies the smoothing effect and decay rates for the FDE in the subcritical range m < mc , and also for the critical exponent mc = (n - 2)/n. ... More

## Logarithmic diffusion in 2D and intermediate 1D range

*Juan Luis Vázquez*

### in Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199202973
- eISBN:
- 9780191707919
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199202973.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter studies two transition situations where non-uniqueness plays an important role. The first deals with the range -1 < m ≤ 0 in n = 1, which looks like supercritical but contains the ... More