My Account
Digital Library
Bookstore
News
Archives
Contact
Donate
Become A Member
Society for Industrial and Applied Mathematics
Become a Member
Login
Get Involved
Society for Industrial and Applied Mathematics
Home
Publications
Journals
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal (MMS)
SIAM Journal on Applied Algebra and Geometry (SIAGA)
SIAM Journal on Applied Dynamical Systems (SIADS)
SIAM Journal on Applied Mathematics (SIAP)
SIAM Journal on Computing (SICOMP)
SIAM Journal on Control and Optimization (SICON)
SIAM Journal on Discrete Mathematics (SIDMA)
SIAM Journal on Financial Mathematics (SIFIN)
SIAM Journal on Imaging Sciences (SIIMS)
SIAM Journal on Mathematical Analysis (SIMA)
SIAM Journal on Mathematics of Data Science (SIMODS)
SIAM Journal on Matrix Analysis and Applications (SIMAX)
SIAM Journal on Numerical Analysis (SINUM)
SIAM Journal on Optimization (SIOPT)
SIAM Journal on Scientific Computing (SISC)
SIAM / ASA Journal on Uncertainty Quantification (JUQ)
SIAM Review (SIREV)
Theory of Probability and Its Applications (TVP)
Related
Recent Articles
Information for Authors
Subscriptions and Ordering Information
Journal Policies
Open Access
Books
Book Series
For Authors
For Booksellers
For Librarians
For Educators
SIAM News
SIURO
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 7
Volume 6
Volume 5
Volume 4
Volume 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
Related
Editorial Information
Instructions for Undergraduate Authors
Reports
Digital Library
SIAM Unwrapped
Proceedings
Research Areas
Analysis and Partial Differential Equations
Applied Geometry
Applied Mathematics Education
Classical Applied Mathematics
Computational Science & Numerical Analysis
Control and Systems Theory
Data Science
Discrete Mathematics and Theoretical Computing
Dynamical Systems, Nonlinear Waves
Financial Mathematics and Engineering
Geosciences and Mathematics of Planet Earth
Imaging Science
Life Sciences
Linear Algebra
Mathematical Aspects of Materials Science
Optimization
Uncertainty Quantification
Conferences
Calendar
SIAM Conferences
Cooperating Conferences
Archives
Travel Support
SIAM Student Travel Awards
SIAM Early Career Travel Awards
About SIAM Conferences
Conference Guidelines
Navigating a SIAM Conference
Featured Lectures & Videos
Ways to Sponsor
Exhibitors and Sponsors
Propose a Conference or Workshop
FAQ
Proceedings
Careers
Job Board
Internships
Fellowships
Research Opportunities
Resources
Companies and Industries
Careers in the Math Sciences
What is Applied Mathematics and Computational Science?
Students & Education
Programs & Initiatives
BIG Math Network
Gene Golub SIAM Summer School
Mathematics and Statistics Awareness Month
MathWorks Math Modeling (M3) Challenge
SIAM Science Policy Fellowship Program
SIAM Visiting Lecturer Program
Thinking of a Career in Applied Mathematics?
Resources
For Graduate Students
For Undergraduate Students
For K-12 Students
For Educators
Student Chapters
Start a Chapter
Student Chapter Directory
Chapter Resources
Membership
Join SIAM
Individual Members
Institutional Members
Activity Groups
Algebraic Geometry SI(AG)2
Analysis of Partial Differential Equations
Applied and Computational Discrete Algorithms
Applied Mathematics Education
Computational Science and Engineering
Control and Systems Theory
Data Mining and Analytics
Discrete Mathematics
Dynamical Systems
Financial Mathematics and Engineering
Geometric Design
Geosciences
Imaging Science
Life Sciences
Linear Algebra
Mathematics of Planet Earth
Mathematical Aspects of Materials Science
Nonlinear Waves and Coherent Structures
Optimization
Orthogonal Polynomials and Special Functions
Supercomputing
Uncertainty Quantification
Related
Start an Activity Group
Information for Activity Group Officers
Sections
SIAM Central States Section
Great Lakes Section of SIAM
Mexico Section of SIAM
SIAM Northern States Section
SIAM Pacific Northwest Section
SIAM Southeastern Atlantic Section
SIAM Southern California Section
SIAM Texas-Louisiana Section
SIAM Washington-Baltimore Section
Argentina Section of SIAM
Bulgaria Section of SIAM
Colombia Section of SIAM
East Asia Section of SIAM
United Kingdom and Republic of Ireland of SIAM
Related
Start a Section
Information for Section Officers
Prizes & Recognition
Deadline Calendar
Major Prizes & Lectures
AWM-SIAM Sonia Kovalevsky Lecture
George Pólya Prize for Mathematical Exposition
George Pólya Prize in Applied Combinatorics
George Pólya Prize in Mathematics
Germund Dahlquist Prize
I.E. Block Community Lecture
James H. Wilkinson Prize for Numerical Software
James H. Wilkinson Prize in Numerical Analysis and Scientific Computing
John von Neumann Lecture
Julian Cole Lectureship
Ralph E. Kleinman Prize
Richard C. DiPrima Prize
SIAM Oustanding Paper Prizes
SIAM Prize for Distinguished Service to the Profession
SIAM/ACM Prize in Computational Science and Engineering
Theodore von Kármán Prize
W.T. and Idalia Reid Prize
Activity Group Prizes
Dénes König Prize
Gábor Szegö Prize
J.D. Crawford Prize
Jürgen Moser Lecture
Martin Kruskal Lecture
Red Sock Award
SIAM Activity Group on Algebraic Geometry Early Career Prize
SIAM Activity Group on Analysis of Partial Differential Equations Prize
SIAM Activity Group on Computational Science and Engineering Best Paper Prize
SIAM Activity Group on Computational Science and Engineering Early Career Prize
SIAM Activity Group on Control and Systems Theory Best SICON Paper Prize
SIAM Activity Group on Control and Systems Theory Prize
SIAM Activity Group on Financial Mathematics and Engineering Conference Paper Prize
SIAM Activity Group on Financial Mathematics and Engineering Early Career Prize
SIAM Activity Group on Geometric Design Early Career Prize
SIAM Activity Group on Geosciences Career Prize
SIAM Activity Group on Geosciences Early Career Prize
SIAM Activity Group on Imaging Science Best Paper Prize
SIAM Activity Group on Imaging Science Early Career Prize
SIAM Activity Group on Life Sciences Early Career Prize
SIAM Activity Group on Linear Algebra Best Paper Prize
SIAM Activity Group on Linear Algebra Early Career Prize
SIAM Activity Group on Optimization Best Paper Prize
SIAM Activity Group on Optimization Early Career Prize
SIAM Activity Group on Supercomputing Best Paper Prize
SIAM Activity Group on Supercomputing Career Prize
SIAM Activity Group on Supercomputing Early Career Prize
SIAM Activity Group on Uncertainty Quantification Early Career Prize
T. Brooke Benjamin Prize in Nonlinear Waves
Student Prizes
Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student
SIAM Award in the Mathematical Contest in Modeling
SIAM Student Paper Prize
SIAM Student Travel Awards
SIAM Early Career Travel Awards
Joint Prizes
George B. Dantzig Prize
George David Birkhoff Prize
Gerald and Judith Porter Public Lecture
JPBM Communications Award
Lagrange Prize in Continuous Optimization
Norbert Wiener Prize
Peter Henrici Prize
Pioneer Prize
Fellows Program
Nomination Procedures
Selection Criteria
Eligibility
All SIAM Fellows
FAQ
Policies & Guidelines
SIAM Prize Policy
Prizes & Recognition FAQ
For Selection Committees
For Prize Winners
For Nominators
Publications
SIURO
Volume 1, Issue 1
Text/HTML
SIAM Undergraduate Research Online
Volume 1, Issue 1
Visualizer
A Simple Expression for Multivariate Lagrange Interpolation
Published electronically July 2, 2008
DOI:
10.1137/08S010025
Author:
Kamron Saniee (New Providence High School, New Providence, NJ)
Sponsor:
Richard Glahn (New Providence High School, New Providence, NJ)
Abstract:
We derive a simple formula for constructing the degree
n
multinomial function which interpolates a set of
{n+m \choose n} points in R
^{m+1}
, when the function is unique. The formula coincides with the standard Lagrange interpolation formula if the points are given in R
^{2}
. We also provide examples to show how the formula is used in practice.
Testing for the Benford Property
Published electronically July 2, 2008
DOI:
10.1137/08S010098
Author:
Daniel P. Pike (School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York)
Sponsor:
David L. Farnsworth (School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York)
Abstract:
Benford's Law says that many naturally occurring sets of observations follow a certain logarithmic law. Relative frequencies of the first significant digits k are log(1 + 1/k) for k = 1, 2, ..., 9, where the base of the logarithm is ten. Financial and other auditors routinely check data sets against this law in order to investigate for fraud. We present the principal underlying mechanism that produces sets of numbers with the Benford property. Examples in which each observation consists of a product of variables are given. Two standard statistical tests that are useful for testing compliance with Benford's Law are outlined. A new Minitab macro, which implements both statistical tests and produces a graphical output, is presented.
The Potential of Tidal Power from the Bay of Fundy
Published electronically July 11, 2008
DOI:
10.1137/08S010062
Author:
Justine M. McMillan and Megan J. Lickley (Department of Mathematics & Statistics, Acadia University, Wolfville, NS, Canada)
Sponsor:
Richard Karsten and Ronald Haynes
Abstract:
Large tidal currents exist in the Minas Passage, which connects the Minas Basin to the Bay of Fundy off the north-western coast of Nova Scotia. The strong currents through this deep, narrow channel make it a promising location for the generation of electrical power using in-stream turbines. Using a finite-volume numerical model, the high tidal amplitudes throughout the Bay of Fundy are simulated within a root mean square difference of 8 cm in amplitude and 3.1
^{o}
in phase. The bottom friction in the Minas Passage is then increased to simulate the presence of turbines and an estimate of the extractable power is made. The simulations suggest that up to 6.9 GW of power can be extracted; however, as a result, the system is pushed closer to resonance which causes an increase in tidal amplitude of over 15% along the coast of Maine and Massachusetts. The tides in the Minas Basin will also experience a decrease of 30% in amplitude if the maximum power is extracted. Such large changes can have harmful environmental impacts; however, the simulations also indicate that up to 2.5 GW of power can be extracted with less than a 6% change in the tides throughout the region. According to Nova Scotia Energy, 2.5 GW can power over 800,000 homes.
Expository: Moving Forward by Traveling in Circles
Published electronically August 22, 2008
DOI:
10.1137/08S010050
Author:
Stuart Boersma (Central Washington University)
Abstract:
The purpose of this paper is to introduce the reader to the mathematical construct known as
holonomy
. Holonomy is a measurement of the change in a certain angle as one travels along a curve. For this paper, we will consider two physical situations which involve "traveling in a circle" and comparing an initial and final measurement of an angle. In the first case we will see how this angular displacement can be used to prove that the Earth rotates! In the second example we explore the workings of a nineteenth century cartographic instrument. In both cases, traveling in circles yields interesting mathematical information.