 On the Bass Note of a Schottky Group [PDF]  Peter G. Doyle
Using a classical method from physics called Rayleigh's cutting method, Doyle proves the conjecture of Phillips and Sarnak that there is a universal lower bound L2 > 0 for the lowest eigenvalue of the quotient manifold of a classical Schottky group,
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 On the Evolution of Islands  Doyle, Mallows, Orlitsky, Shepp
On islands and seas: an island is a maximal set of adjacent marked cells in a ring or row; a sea is a maximal set of adjacent unmarked cells. An inductive proof and a countingargument proof. A paper that appeared in the Israel Journal of Mathematics.
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 On the Puzzles with polyhedra and numbers  Jorge Rezende
Several articles in PDF format, with related links: one on a set of didactic puzzles published by the Portuguese Mathematical Society (SPM); "Jogos com poliedros e permutações", an article in Portuguese describing puzzles with polyhedra
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 Open Directory  Science: Math  Netscape
A comprehensive directory of math sites on the Web, listing links of mathematical interest by general topics, math topic, and site name.
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 Open Directory  Science:Math:Statistics  Netscape
A comprehensive directory of statistics sites on the Web, listing links of statistical interest by general topics, statistics topic, and site name.
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 Open Discrete Dynamic Programming Template (OpenDDPT)  Centi Riccardo
OpenDiscreteDynamicProgrammingTemplate : founds optimal constrainted parameters of a discrete controls with second order optimization template replacing Hessian with directional derivatives and backpropagation for digital filter (as neural network).
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 OpenFVM CFD solver
OpenFVM is a general CFD solver released under the GPL license. It was
developed to simulate the flow in complex 3D geometries. Therefore, the
mesh can be unstructured and contain control volumes with arbritrary shape.
The code uses the finite volume
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 OpenMath
A language for communicating mathematical data between computer programs. Its purpose is to enhance different programs capable of handling mathematical data, such as symbolic algebra packages, typesetters, Web browsers, and the like, by providing a basis
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 OpenMath  The OpenMath Society
An extensible standard for representing mathematical objects with their semantics, allowing them to be exchanged between computer programs, stored in databases, or published on the web. Intended for those working with mathematics on computers, for those
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 Open Problem Garden  Matt DeVos and Robert Šámal
A collection of unsolved problems  mainly, graph theory, combinatorics, and number theory. A wiki for each open problem includes relevant bibliographical citations, importance rating, and recommendation for undergraduates. Navigate by math subject,
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 Open Problems in Dynamical Systems & Ergodic Theory  Sergiy Kolyada
This collection of problems originated in the Katsiveli2000 Open Problems Session (Chairman  Benjamin Weiss). New problems are being added. Copies of the page are also at http://iml.univmrs.fr:80/~kolyada/opds/ and http://www.math.iupui.edu/~mmisiure/open/.
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 Open Problems  Jeff Erickson
Open problems, mostly in geometry, including folding, combinatorial, and algorithmic problems. Contents include: Existence Problems: Does Object X exist?
Combinatorial Problems: How complex is Object X? Algorithmic Problems: How fast can Problem X be
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 Open Problems (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on open problems in geometry: antipodes; bounded degree triangulation; centers of maximum matchings; chromatic number of the plane; combinatorial complexity of spheres; covering points by rectangles; cube
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 Open Source Mathematics  David Joyner
An index of open source math software, texts, and papers.
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 OpenStat4 (OS4)  Bill Miller
A statistics package offering descriptive statistics such as central tendency and variability indexes, xy plots, and frequency distributions; Pearson productmoment correlations and partial correlations; analyses of variance including 1, 2 and 3way
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 Operational Research Society
Operational Research (OR) or Operations Research or Management Science (OR/MS) looks at an organisation's operations and uses mathematical or computer models, or other analytical approaches, to find better ways of doing them. The OR Society, with members
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 The Operational Research Society  the Operational Research Society
The Operational Research Society, with members in many countries, provides training, conferences, publications and information to those working in Operational Research. Shop for books, training courses, conferences and one day events; learn about OR (publicity
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 Operations Research Society of the Philippines
Activities, officers and members, the ORSPCorps, and links to related OR sites.
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 Operator Algebra Resources  N. Christopher Phillips
Lists of some resources useful to mathematicians working in the subject of operator algebras. General operator algebra sites and publications, information on regular series of conferences, and some important general mathematical resources.
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 OpsResearch  DRA Systems
A collection of Java classes for developing operations research programs and other mathematical applications. The site includes documentation and tutorials, and software download is free. Also features a bookstore and related links.
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 Optimization Links  Tom Cavalier; Industrial and Manufacturing Engineering, Penn State Univ.
Links to online information on various aspects of optimization; interactive guides/case studies; optimization software/test problems; and other sites. Also general operations research sites; OR/Optimization people. Location/Routing/ Conference Information;
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 Optimization Technology Center  Argonne National Laboratory and Northwestern University
A research center dedicated to optimization problems. The "optimization tree," with descriptions of the different subfields of numerical optimization; interactive demonstrations and case studies, including the diet problem and minimum surface area; linear
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 Optimizer for Anyshape  SAMTEC
A professional profile nesting software package designed to maximize the use of material by generating most optimized nested layouts. It is a powerful true profile nesting software for gas/plasma/oxyfuel/laser cutting that will automatically optimize
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 Optimizer Suite  SAMTEC
A professional rectangular nesting software package designed to maximize the use of material by generating most optimized nested layouts. It is based on a highly advanced cutting algorithm, specially designed to optimize the cutting layouts in shearing,
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 OptNet  Michael Jünger; SIGOPT, Deutsche Mathematiker Vereinigung (DMV)
An electronic forum for the optimization community organized by SIGOPT under the auspices of the Deutsche Mathematiker Vereinigung (DMV). The basic services are a weekly digest containing a moderated list of contributions, a unique email address and
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 Order  Kluwer Online
A journal on the theory of ordered sets and its applications. Order occurs throughout mathematics and especially in algebra, combinatorics, geometry, model theory, set theory and topology.
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 Ordinary Differential Equations Project  Blanchard, Devaney, Hall; Boston University
This project included the development of a textbook (publisher Brooks/Cole Publishing Co.) as well as various workshops on teaching differential equations. Instructors manuals and selected articles are available from this site: "Teaching Differential
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 The Organic Mathematics Project  Centre for Experimental and Constructive Mathematics (CECM)
A collaborative research project involving a number of researchers at the Centre for Experimental and Constructive Mathematics (CECM). Involves in part the development of WWWbased and Mapleassisted tools for document annotation and math activation.
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 Organic Mathematics Workshop: The Proceedings  Borwein, Borwein, Corless, Jörgenson, Sinclair, eds.
Proceedings of a 1996 workshop held at Simon Fraser University, Vancouver, Canada. Speakers (top experimental and computational mathematicians); their articles, with equations, code, photos, videos, and annotations; and related resources and links. Invited
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 Organisation des nombres premiers  Mustapha Chouar
Une répartition des nombres premiers qui utilse la fonction 1+4+2 avec une représentation graphique de l'addition des carrés et une spirale.
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 Origami (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on the Japanese art of paper folding, obviously geometrical in nature. Some origami masters have looked at constructing geometric figures such as regular polyhedra from paper. In the other
direction, some
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 ORLibrary  J. E. Beasley; Imperial College of Science, Medicine and Technology
A collection of test data sets for a variety of Operations Research (OR) problems, available via emailing to o.rlibrary@ic.ac.uk a message containing the name of the required file, or via FTP/WWW using the links provided. Also at http://mscmga.ms.ic.ac.uk/info.html.
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 OR/MS Today
Online version of the magazine for members of the Institute for Operations Research and the Management Sciences (INFORMS). Current and previous issues, with full text of many articles; subscription information; software surveys; classified ads and list
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 ORNotes  J. E. Beasley
Introductory originally used in an introductory OR course at Imperial College. Topics: Introductory (basic concepts); Deterministic (data envelopment analysis, facility layout and location, graph theory, integer programming, inventory control, justintime,
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 Orthogonal Polynomials, Integral Transforms and Solutions for Dynamics of Multilevel Systems  Vadim Zelenkov; International Sakharov Environmental University
Papers and preprints by a small group (Savva, Mazurenko, Zelenkov) that studies multiphoton excitation of molecules by infrared laser radiation in an attempt to find analytic solutions of the dynamic equations using miscellaneous orthogonal polynomials
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 Other Maths  Jon Perry
Notes, applets, and proofs on a variety of open problems and conjectures: roots of x^p, highest power of 2 that divides ab + bc + ca, a prime product paradox, consecutive integers, (n + 1)!, Collatz, nsecting a line, the first lower digit, Fibonacci,
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 The Oughtred Society  Oughtred
An organization dedicated to the history and collection of slide rules. Meet William Oughtred, inventor of the modern slide rule; learn about the history and background of the Oughtred Society and its principles; join or renew membership; browse tables
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 An Outline of the Proof of Gödel's Incompleteness Theorem  Michal Wojcik
On this page we give an outline of the proof of Goedel's Incompleteness Theorem. We construct a statement in set theory such that it is not a theorem and its negation is not a theorem. What we show on this page is not a presentation of the proof that
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 outofprintmath  Klaus Schmid
A blog for consumers of math books to "vote" for the outofprint publications they would like to see come back into print.
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 Overview of "Mathematician's Secret Room"  Hisanori Mishima
Challenges to unsolved problems in Number Theory, some translated into English from the Japanese.
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 Pacific Institute for the Mathematical Sciences (PIMS)
A networked institute based in Alberta and British Columbia, Canada. Primarily dedicated to the support and advancement of mathematical science in Western Canada and the Pacific Rim, it maintains physical offices at the Universities of Alberta, British
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 Palisade
Software for Excel, including @RISK, using Monte Carlo simulation, and PrecisionTree, for risk analysis, decision analysis, optimization, and forecasting.
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 PAM Electronic Discussion List (PAMnet)  Parker Ladwig and Thurston Miller (list owners)
An electronic discussion forum for the discussion of library and information resource issues relevant to the fields of physics, astronomy and mathematics, maintained by the PhysicsAstronomyMathematics (PAM) Division of the Special Libraries Association.
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 Panagiotis Stefanides
Geometry presented at national conferences in Greece. Contents include: Quantization of Circle Duality; Logos Pyr Chronos; 'Buena Fortuna' (artwork); Geometric Mean Ratio (T) by Ruler and Compass; Quadrature Master Theorem; Corollary (Circle Circumference
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 Papers  Chaim GoodmanStrauss, Dept. of Mathematics, Univ. of Arkansas
On Composite Twisted Unknots; Matching Rules and Substitution Tilings; Aperiodic Hierarchical Tilings; Bounding the Results of Arithmetic Operations on Random Variables with Unknown Dependency; A Small Set of Planar Aperiodic Tiles; A Pair of Aperiodic
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 Papers Online: Advanced Chaos  The Chaos Group, Univ. of Maryland at College Park
An online collection of published articles and preprints on advanced chaos theory, covering the topics of: Control and Targeting, Dimensions, Fractal Basin Boundaries, General Chaos, Quantum Chaos, Riddled Basins, and Shadowing.
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 Parallel Applications in Statistics and Economics (PASE)
Announcements of meetings, previous PASE workshops and where conference proceedings are published. Subjects: parallel algorithms and artificial neural networks; dynamical chaotic systems and fuzzy logic; stochastic optimization concepts; genetic algorithms
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 Pascal's Triangle from Top to Bottom  Matthew Hubbard and Tom Roby
A comprehensive resource for the study of Pascal's Triangle. The section "Applications" addresses questions such as "What types of questions are answered by the binomial coefficients?" and "What number greater than 1 shows up most often in Pascal's Triangle?"
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 A Passion for Pi  Ivars Peterson (MathLand)
Some of you may be familiar with the sentence: How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics! The number of letters in each word represents successive digits of pi: 3.14159265358979. How Simon Plouffe memorized
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 Past Lectures  Gresham College
Dozens of video lectures by Robin Wilson, Gresham Professor of Geometry and former Visiting Professor in the History of Mathematics: "The Great Mathematicians," "Early Mathematics Day," "Lewis Carroll in Numberland," "Topics in the History of Financial
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