Physical Sciences and Mathematics Commons^™

A Homotopy Theory Of Orbispaces, Weimin Chen Chen

Weimin Chen

An orbifold is a singular space which is locally modeled on the quotient of a smooth manifold by a smooth action of a finite group. It appears naturally in geometry and topology when group actions on manifolds are involved and the stabilizer of each fixed point is finite. The concept of an orbifold was first introduced by Satake under the name “V -manifold” in a paper where he also extended the basic differential geometry to his newly defined singular spaces (cf. [32]). The local structure of an orbifold – being the quotient of a smooth manifold by a finite group …

Geometric Realization And K-Theoretic Decomposition Of C*-Algebras, Claude Schochet

Mathematics Faculty Research Publications

Suppose that A is a separable C*-algebra and that G∗ is a (graded) subgroup of the ℤ/2-graded group K∗(A). Then there is a natural short exact sequence

0 → G∗ → K∗(A) → K∗(A)/G∗ → 0.

In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. As a result, we KK-theoretically decompose A as

0 → A ⊗ [cursive]K → A_ƒ → SA_t → 0

where K∗(A_t) is the torsion subgroup of …

Towards Regional Assimilation Of Lagrangian Data: The Lagrangian Form Of The Shallow Water Reduced Gravity Model And Its Inverse, J. L. Mead, A. F. Bennett

Mathematics Faculty Publications and Presentations

Variational data assimilation for Lagrangian geophysical fluid dynamics is introduced. Lagrangian coordinates add numerical difficulties into an already difficult subject, but also offer certain distinct advantages over Eulerian coordinates. First, float position and depth are defined by linear measurement functionals. Second, Lagrangian or ‘comoving’ open domains are conveniently expressed in Lagrangian coordinates. The attraction of such open domains is that they lead to well-posed prediction problems [Bennett and Chua (1999)] and hence efficient inversion algorithms. Eulerian and Lagrangian solutions of the inviscid forward problem in a doubly periodic domain, with North Atlantic mesoscales, are compared and found to be in …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

What "Is" Mathematics?: In Memoriam Of Gian-Carlo Rota, Gian-Carlo Rota

Humanistic Mathematics Network Journal

No abstract provided.

Hotel Infinity, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

Poetry, Arnold L. Trindade

Humanistic Mathematics Network Journal

No abstract provided.

Naïve Thoughts On The Paradox Of Gödel, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

A Geometry Course For Prospective Secondary School Teachers, Jeff Connor, Barbara Grover

Humanistic Mathematics Network Journal

No abstract provided.

The Need To Diversify The Ranks Of Teachers Of Mathematics, Frederick L. Uy

Humanistic Mathematics Network Journal

This paper intends to give rationales for the need to diversify the ranks of teachers of mathematics. It also suggests ideas that we can take to alleviate the situation that we currently are confronting.

Announcement: Association For Women In Mathematics Mentor Network

Humanistic Mathematics Network Journal

No abstract provided.

Problems In Which Given Information Is Ignored, Howard Wachtel

Humanistic Mathematics Network Journal

A set of problems is presented and discussed for which there is a tendency for students to ignore part of the given information in the problem and to substitute some extraneous assumptions. Typical student reactions are also discussed.

Educating The Public About School Mathematics, Zalman Usiskin

Humanistic Mathematics Network Journal

No abstract provided.

Zero, Sheila A. Mcneill

Humanistic Mathematics Network Journal

No abstract provided.

Hamilton's Icosian Calculus And His Icosian Game, Katye O. Sowell

Humanistic Mathematics Network Journal

No abstract provided.

Representation, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: The Teaching Gap By James W. Stigler And James Hiebert, Michael L. Brown

Humanistic Mathematics Network Journal

No abstract provided.

Journal Review: Third International Anthology On Paradoxism, Joanne Growney

Humanistic Mathematics Network Journal

No abstract provided.

Students And Their Learning From Reading, Chris Fenwick

Humanistic Mathematics Network Journal

My aim in this article is to summarize work I have done over the last three years, focusing on the issue of helping students learn from whatever mathematics text they read. Although these types of texts generally contain 3 modes of communication, namely technical English, the language of mathematics itself and diagrams, I will focus this article only on the technical English of such texts. The idea, then, that students can develop techniques and strategies for learning from what they read is generally known as “reading to learn.”

Funny Problems, Florentin Smarandache

Humanistic Mathematics Network Journal

No abstract provided.

A Note On The Decimal Numeral System, Shaharir Bin Mohamad Zain

Humanistic Mathematics Network Journal

No abstract provided.

Real Numbers, Math Lives, Arnold L. Trindade

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Constance (A Poem Dedicated To Constance Reid), Arthur T. Benjamin

All HMC Faculty Publications and Research

Mathematical Constance (A Poem Dedicated to Constance Reid)

I think that I shall never see

A constant lovelier than e,

Whose digits are too great too state,

They're 2.71828…

And e has such amazing features

It's loved by all (but mostly teachers).

With all of e's great properties

Most integrals are done with … ease.

Theorems are proved by fools like me

But only Euler could make an e.

I suppose, though, if I had to try

To choose another constant, I

Might offer i or phi or pi.

But none of those would satisfy.

Of all the …

There Really Are No Contradictions: A Response, Calvin Jongsma

Faculty Work Comprehensive List

Response to "There are no Contradictions" by T.G. Ammon in The College Mathematics Journal, Vol. 31, No. 1 (Jan., 2000), pp. 48-49 which was part of the "Fallacies, Flaws, and Flimflam" column edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.

On A New Mathematical Model Of The Molecular Bond, Donald Greenspan

Mathematics Technical Papers

Using a new model of the molecular bond, we produce a set of initial conditions for the ground state H2 molecule which yield, over one complete period, bond length and vibrational frequency which are identical to the experimental results.

Minkowski's Inequality For Convex Curves, Mostafa Ghandehari

Mathematics Technical Papers

Minkowski's inequality is a relation between mixed areas of two curves and their respective areas. The concept of mixed area is defined. A variational technique is used to give a proof of Minkowski's inequality. As a special case the isoperimetric inequality is obtained.

Discrete Spring Solitons, Donald Greenspan

Mathematics Technical Papers

A soliton is a local, traveling wave pulse. It is significant in a variety of unrelated areas, like studies of water waves, acoustic waves, electron transfer, gravity waves, plasmas, optics and condensed matter (Miura [4], Newell [5]). In this paper we will generate and study solitons in a new context, that is, from the point of view of discrete string motion in the XY plane. Our approach enables one to elucidate the complexities of soliton interactions easily using only a scientific personal computer and velocity profiles. Detailed examples are presented and displayed graphically.

A Geometric Inequality For Convex Polygons, Mostafa Ghandehari

Mathematics Technical Papers

Consider a regular polygon with vertices P1, P2, , Pn. Assume P is an interior point. Let [see pdf for notation] denote the Euclidean distance from P to Pi, i = 1, ...., n. Let A denote the area of the polygon. It is shown that [see pdf for notation] special cases of the above inequality are proved for some nonregular convex polygons. An example is given to show that the above inequality is not true for a general convex polygon.

Generalized Minimum Penalized Hellinger Distance Estimation And Generalized Penalized Hellinger Deviance Testing For Generalized Linear Models: The Discrete Case, Huey Yan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, robust and efficient alternatives to quasi-likelihood estimation and likelihood ratio tests are developed for discrete generalized linear models. The estimation method considered is a penalized minimum Hellinger distance procedure that generalizes a procedure developed by Harris and Basu for estimating parameters of a single discrete probability distribution from a random sample. A bootstrap algorithm is proposed to select the weight of the penalty term. Simulations are carried out to compare the new estimators with quasi-likelihood estimation. The robustness of the estimation procedure is demonstrated by simulation work and by Hapel's α-influence curve. Penalized minimum Hellinger deviance tests …

Generalizations Of The Zero-Divisor Graph Of A Ring, Shane Patrick Redmond

Doctoral Dissertations

Let R be a commutative ring with 1, and let Z(R) denote the set of zero­divisors of R. We define an undirected graph Γ(R) with vertices Z(R)* = Z(R) - {0}, where distinct vertices x and y of R are connected if and only if xy = 0. This graph is called the zero-divisor graph of R. We extend the definition of the zero-divisor graph to a noncommutative ring in several ways. Next, given a commutative ring R and ideal Ι of R, we introduce the notion of an …