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Articles 23821 - 23850 of 27413

Full-Text Articles in Physical Sciences and Mathematics

A Generalized Univariate Change-Of-Variable Transformation Technique, Andrew G. Glen, Lawrence Leemis, John H. Drew Aug 1997

A Generalized Univariate Change-Of-Variable Transformation Technique, Andrew G. Glen, Lawrence Leemis, John H. Drew

Arts & Sciences Articles

We present a generalized version of the univariate change-of-variable technique for transforming continuous random variables. Extending a theorem from Casella and Berger [1990. Statistical Inference, Wadsworth and Brooks/Cole, Inc., Pacific Grove, CA] for many-to-1 transformations, we consider more general univariate transformations. Specifically, the transformation can range from 1-to-1 to many-to-1 on various subsets of the support of the random variable of interest. We also present an implementation of the theorem in a computer algebra system that automates the technique. Some examples demonstrate the theorem's application.

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Lyapunov Exponents, Singularities, And A Riddling Bifurcation, Lora Billings, James H. Curry, Eric Phipps Aug 1997

Lyapunov Exponents, Singularities, And A Riddling Bifurcation, Lora Billings, James H. Curry, Eric Phipps

Department of Mathematics Facuty Scholarship and Creative Works

There are few examples in dynamical systems theory which lend themselves to exact computations of macroscopic variables of interest. One such variable is the Lyapunov exponent which measures the average attraction of an invariant set. This article presents .a family of noninvertible transformations of the plane for which such computations are possible. This model sheds additional insight into the notion of what it can mean for an attracting invariant set to have a riddled basin of attraction.

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Using The Quantum Computer To Break Elliptic Curve Cryptosystems, Jodie Eicher, Yaw Opoku Jul 1997

Using The Quantum Computer To Break Elliptic Curve Cryptosystems, Jodie Eicher, Yaw Opoku

Department of Math & Statistics Technical Report Series

This article gives an introduction to Elliptic Curve Cryptography and Quantum Computing. It includes an analysis of Peter Shor’s algorithm for the quantum computer breakdown of Discrete Log Cryptosystems and an analog to Shor’s algorithm for Elliptic Curve Cryptosystems. An extended example is included which illustrates how this modified Shor’s algorithm will work.

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Magneto-Optic Trapping Of Β-Decaying 38km, 37k From An On-Line Isotope Separator, J. A. Behr, A. Gorelov, T. Swanson, O. Hausser, K. P. Jackson, M. Trinczek, U. Giesen, J. M. D'Auria, R. Hardy, T. Wilson, P. Choboter, F, Leblond, L. Buchmann, M. Dombsky, C. D.P. Levy, G. Roy, B. A. Brown, J. Dilling Jul 1997

Magneto-Optic Trapping Of Β-Decaying 38km, 37k From An On-Line Isotope Separator, J. A. Behr, A. Gorelov, T. Swanson, O. Hausser, K. P. Jackson, M. Trinczek, U. Giesen, J. M. D'Auria, R. Hardy, T. Wilson, P. Choboter, F, Leblond, L. Buchmann, M. Dombsky, C. D.P. Levy, G. Roy, B. A. Brown, J. Dilling

Mathematics

A magneto-optic trap (MOT) can provide a well-polarized, backing-free, localized source of radioactive atoms for β-decay experiments. We have trapped approximately 6000 atoms of 38Km ( t1/2 = 0.925s) and 2000 atoms of 37K (1.226 s) produced at the TRIUMF on-line separator TISOL in a vapor-cell MOT. We have measured optical isotope shifts and deduced the nuclear charge radii, which show an unusual lack of change at the neutron number N = 20 shell closure. Plans include a search for scalar contributions to the β+- ν correlation in the 0+→0+ decay …

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Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab Jul 1997

Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

A Hadamard difference set (HDS) has the parameters (4N2, 2N2 − N, N2 − N). In the abelian case it is equivalent to a perfect binary array, which is a multidimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. We show that if a group of the form H × Z2pr contains a (hp2r, √hpr(2√hpr − 1), √hpr(√hpr − 1)) HDS (HDS), p a prime not dividing |H| …

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What Kind Of Thing Is A Number?: A Talk With Reuben Hersh, Reuben Hersh Jul 1997

What Kind Of Thing Is A Number?: A Talk With Reuben Hersh, Reuben Hersh

Humanistic Mathematics Network Journal

No abstract provided.

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Math Lingo Vs. Plain English: Multiple Entendre, Stephen I. Brown Jul 1997

Math Lingo Vs. Plain English: Multiple Entendre, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

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Abe Shenitzer At 75, Hardy Grant Jul 1997

Abe Shenitzer At 75, Hardy Grant

Humanistic Mathematics Network Journal

No abstract provided.

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A Brief Tribute To Π, J. D. Phillips Jul 1997

A Brief Tribute To Π, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

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Reminiscences Of Paul Erdös (1913-1996), Melvin Henriksen Jul 1997

Reminiscences Of Paul Erdös (1913-1996), Melvin Henriksen

Humanistic Mathematics Network Journal

No abstract provided.

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Sand Songs: The Formal Languages Of Warlpiri Iconography, James V. Rauff Jul 1997

Sand Songs: The Formal Languages Of Warlpiri Iconography, James V. Rauff

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: The Crest Of The Peacock: Non-European Roots Of Mathematics,By George Gheverghese Joseph, Bernadette Anne Berken Jul 1997

Book Review: The Crest Of The Peacock: Non-European Roots Of Mathematics,By George Gheverghese Joseph, Bernadette Anne Berken

Humanistic Mathematics Network Journal

No abstract provided.

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Illumination And Geometry In Islamic Art, Salma Marani Jul 1997

Illumination And Geometry In Islamic Art, Salma Marani

Humanistic Mathematics Network Journal

No abstract provided.

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Al-Khawarizmi's Algebra: The First Paradigm In Algebra, Murad Jurdak Jul 1997

Al-Khawarizmi's Algebra: The First Paradigm In Algebra, Murad Jurdak

Humanistic Mathematics Network Journal

No abstract provided.

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See-Duction: How Scientists And Artists Are Creating A Third Way Of Knowing, Howard Levine Jul 1997

See-Duction: How Scientists And Artists Are Creating A Third Way Of Knowing, Howard Levine

Humanistic Mathematics Network Journal

No abstract provided.

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Curriculum Development Via Literary And Musical Forms, Joel K. Haack Jul 1997

Curriculum Development Via Literary And Musical Forms, Joel K. Haack

Humanistic Mathematics Network Journal

No abstract provided.

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Algebra Anyone?, Leslie Jones, Ted Panitz, Walter Burlage Jul 1997

Algebra Anyone?, Leslie Jones, Ted Panitz, Walter Burlage

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematical Rebuses, Arthur V. Johnson Ii Jul 1997

Mathematical Rebuses, Arthur V. Johnson Ii

Humanistic Mathematics Network Journal

No abstract provided.

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The First Cams Project: A Humanistic Endeavor, Barbara A. Wainwright, Homer W. Austin Jul 1997

The First Cams Project: A Humanistic Endeavor, Barbara A. Wainwright, Homer W. Austin

Humanistic Mathematics Network Journal

No abstract provided.

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Book Reviews: Uncommon Sense, By Alan Cromer, And The Physics Of Immortality, By Frank J. Tipler, Harald M. Ness Jul 1997

Book Reviews: Uncommon Sense, By Alan Cromer, And The Physics Of Immortality, By Frank J. Tipler, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

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Auslander Systems, K. N. Haddad, Aimee S. A. Johnson Jul 1997

Auslander Systems, K. N. Haddad, Aimee S. A. Johnson

Mathematics & Statistics Faculty Works

The authors generalize the dynamical system constructed by J. Auslander in 1959, resulting in perhaps the simplest family of examples of minimal but not strictly ergodic systems. A characterization of unique ergodicity and mean-L-stability is given. The new systems are also shown to have zero topological entropy and fail to be weakly rigid. Some results on the set of idempotents in the enveloping semigroup are also achieved.

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Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal Jul 1997

Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal

Department of Math & Statistics Faculty Publications

Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.

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High-Order Finite-Difference Schemes And Their Application To Computational Acoustics, Joe Leo Manthey Jul 1997

High-Order Finite-Difference Schemes And Their Application To Computational Acoustics, Joe Leo Manthey

Mathematics & Statistics Theses & Dissertations

The primary focus of this study is upon the numerical stability of high-order finite-difference schemes and their application to duct acoustics. Since acoustic waves are known to be non-dissipative and non-dispersive, high-order schemes are favored for their low dissipation and low dispersion relative to the low-order schemes. The primary obstacle to the the development of explicit high-order finite-difference schemes is the construction of boundary closures which simultaneously maintain the formal order of accuracy and the numerical stability of the overall scheme. In this thesis a hybrid seven-point, fourth-order stencil for computing spatial derivatives is presented and the time stability is …

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Reverse Engineering Of Aircraft Wing Data Using A Partial Differential Equation Surface Model, Jacalyn M. Huband Jul 1997

Reverse Engineering Of Aircraft Wing Data Using A Partial Differential Equation Surface Model, Jacalyn M. Huband

Mathematics & Statistics Theses & Dissertations

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of …

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Transformations Of Index Set For Skorokhod Integral With Respect To Gaussian Processes, Leszek Gawarecki Jun 1997

Transformations Of Index Set For Skorokhod Integral With Respect To Gaussian Processes, Leszek Gawarecki

Mathematics Publications

We consider a Gaussian process {Xt,t∈T} with an arbitrary index set T and study consequences of transformations of the index set on the Skorokhod integral and Skorokhod derivative with respect to X. The results applied to Skorokhod SDEs of diffusion type provide uniqueness of the solution for the time-reversed equation and, to Ogawa line integral, give an analogue of the fundamental theorem of calculus.

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Discrete Tomography: Determination Of Finite Sets By X-Rays, Richard J. Gardner, Peter Gritzmann Jun 1997

Discrete Tomography: Determination Of Finite Sets By X-Rays, Richard J. Gardner, Peter Gritzmann

Mathematics Faculty Publications

We study the determination of finite subsets of the integer lattice Zn, n ≥ 2, by X-rays. In this context, an X-ray of a set in a direction u gives the number of points in the set on each line parallel to u. For practical reasons, only X-rays in lattice directions, that is, directions parallel to a nonzero vector in the lattice, are permitted. By combining methods from algebraic number theory and convexity, we prove that there are Sour prescribed lattice directions such that convex subsets of Zn (i.e., finite subsets F with F = Z …

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Positive Braids With A Half Twist Are Prime, Michael C. Sullivan Jun 1997

Positive Braids With A Half Twist Are Prime, Michael C. Sullivan

Articles and Preprints

We shall prove that a knot which can be represented by a positive braid with a half twist is prime. This is done by associating to each such braid a smooth branched 2-manifold with boundary and studying its intersection with a would-be cutting sphere.

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The Role Of Mathematics In Culture, W. James Bradley May 1997

The Role Of Mathematics In Culture, W. James Bradley

ACMS Conference Proceedings 1997

This paper examines theories of the role of mathematics in culture and seeks to understand how a Christian should view the role of mathematics.

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Solomon's Sea And The Biblical Π, Andrew Simoson May 1997

Solomon's Sea And The Biblical Π, Andrew Simoson

ACMS Conference Proceedings 1997

From I Kings 7:23, the apparent diameter and circumference of a circular ring are given as 10 and 30 cubits which suggests that the Biblical value of π is 3 rather a number closer to π. However we recount seven different somewhat whimsical explanations as to why this conclusion is overly-hasty.

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Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch May 1997

Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch

ACMS Conference Proceedings 1997

The philosophy of mathematics has provided insight on questions of foundations and mathematical truth; however, it has not been very fruitful in guiding the practice of mathematics. This paper attempts to find points of contact between a Christian worldview and the choice of mathematical projects and methods. Three areas are considered: (i) dubitability in current research, (ii) the intrinsic value of contemporary mathematics to contemporary society, and (iii) the affirmation of human value in the use of mathematics. Finally, a framework for valuing mathematics is proposed as an encouragement to think more deeply about how a Christian might choose a …

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