Ball State Hosted Journals
http://cardinalscholar.bsu.edu/handle/123456789/202202
2020-09-18T11:32:36ZAn invariant of metric spaces under bornologous equivalences
http://cardinalscholar.bsu.edu/handle/123456789/202367
An invariant of metric spaces under bornologous equivalences
Miller, Brittany; Stibich, Laura; Moore, Julie
We define bornologous equivalence between metric spaces, which is a morerestrictive equivalence than coarse equivalence. It requires spaces to have thesame cardinality. We define an invariant of metric spaces under bornologousequivalences. The invariant is essentially the number of ways that sequencescan go to infinity in a space. This invariant is only for a certain class of spacesthat we call sigma stable.
Article published in Mathematics Exchange, 7(1), 2010.
2010-01-01T00:00:00ZTurning Tables, Slicing Pizza, and the Brouwer Fixed-Point Theorem
http://cardinalscholar.bsu.edu/handle/123456789/202366
Turning Tables, Slicing Pizza, and the Brouwer Fixed-Point Theorem
Cai, Jei
Mathematics is everywhere in life. Even within the short dinner time, it helps me solve two big problems.
Scene 1: I have confidence in saying that the four legs of my kitchen table have the same length, since it cost me a lot of money. Unfortunately, it wobbles because of my old floor, which I cannot afford to fix right now. Fortunately, the Dyson-Livesay Theorem gives me a cheaper solution. It tells me that I can fix this by just rotating the table by some angle.
Connect the four feet of our rectangular table diagonally with two line segments. Then these two segments intersect at some angle α and form two diameters of some sphere S2. (See Figure 1(a), 1(b).) Imagine lifting the table, along with the sphere, high above the ground and let f(x) denote the vertical distance from a point x on that sphere to the floor. This function is clearly continuous on our sphere. The Dyson-Livesay Theorem states that we can find two points p and q on the sphere S2 such that f(p) = f(−p) = f(q) = f(−q) and (p, q) = α. That means, if we rotated the table in space so that the four table feet fit into the locations p,−p,q and −q and lowered it to the floor it would rest firmly. Therefore, the same result can be accomplished by simply turning the table on the ground, while keeping the intersection of the diagonals on the same vertical line.
Article published in Mathematics Exchange, 7(1), 2010.
2010-01-01T00:00:00ZApplication of Cox Proportional Hazard Model to the Stock Exchange Market
http://cardinalscholar.bsu.edu/handle/123456789/202342
Application of Cox Proportional Hazard Model to the Stock Exchange Market
Ni, Jiayi
Survival analysis is widely used in mechanical research, engineering and many other ﬁelds. This paper introduces the properties and modeling methods for survival data, then ﬁts a Cox Proportional Hazards Model for stock data in the Shanghai Security Market.
Article published in Mathematics Exchange, 6(1), 2009.
2009-01-01T00:00:00ZA Word from the Editor
http://cardinalscholar.bsu.edu/handle/123456789/202341
A Word from the Editor
Mohammed, Ahmed
As part of an ongoing eﬀort to make the Mathematics Exchange a forum of mathematical ideas among an ever expanding undergraduate student readership we have enlarged the editorial board to include faculty from other colleges and universities that have strong commitment to undergraduate mathematics education. It is hoped this would enable us to bring to the reader a wide range of high quality articles on diverse mathematical topics. The articles in this issue of the Exchange are reﬂections of this change.
Article published in Mathematics Exchange, 6(1), 2009.
2009-01-01T00:00:00Z