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» Vol. 5, Issue 1, 2004 «



Title: An Array of Disjoint Maximal Constant Weight Codes
Author: Christine Berkesch, Butler University Author Bio    
Abstract: We show that when gcd(n,w) = 1, the set of binary words of length n and weight w can be partitioned to give n maximal w-weight codes. It follows that under the same hypothesis, the least cardinal of a maximal constant weight code is at most 1/n times n choose w.
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Title: Finding a Matrix of Given Sign Pattern and Line Sums
Author: Edward Kung, University of Illinois Author Bio    
Abstract: In this paper we propose an algorithm that constructs a matrix with a specified sign pattern and row sums and column sums. We also investigate propoerties of such matrices, such as the uniqueness of solutions and integer-only solutions.
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Title: Sequentially Decreasing Subsets of Metric Spaces
Author: Josh Isralowitz, New Jersey Inst of Technology Author Bio    
Abstract: We introduce and discuss various properties of sequences of subsets {On} of metric spaces with the property that the limit of delta(On} ) is 0 where delta denotes the diameter of a set, which we call sequentially decreasing subsets. As applications of the theory developed, we give a short proof of a well known necessary condition for a metric space to be connected, give sufficient conditions for subsets of a connected metric space to be totally disconnected, and discuss a specific outer measure on metric spaces.
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Title: Generalized Cantor Expansions
Author: Joseph Galante, University of Rochester Author Bio    
Abstract: There are many ways to represent a number, commonly known as base expansions. The most frequently used base is ten, which is the basis for our decimal number system. However a more uncommon way to represent a number is the so called Cantor expansion of the number. This system uses factorials rather than numbers to powers as the basis for the system, and it can be shown that this produces a unique expansion for every natural number. However, if you view factorials as products, then it becomes natural to ask what happens if you use other types of products as bases. This paper explores that question and shows there are an uncountably infinite number of bases which can be used to represent the natural, and real numbers uniquely. By using these new and interesting types of bases, it becomes possible to formulate bases in which all rational numbers have a terminating expansion.
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Title: Neonatal Jaundice-Its Mathematical Model and Treatments
Authors: Tram Hoang, California State University, Fullerton
Sazia Khan, California State University, Fullerton
Lorena Ortiz, California State University, Fullerton
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Abstract: Neonatal jaundice (icterus neonatorium) is caused by the excessive accumulation of bilirubin, a byproduct of the red blood cells decomposition. Shortly after birth, newborn babies carry a very high level of red blood cells and thus a high concentration of bilirubin. If a baby’s liver is premature, it cannot process the bilirubin as quickly as its body produces. The excessive bilirubin then flows out of the bloodstream and permeates to the body surface causing yellow-colored skin and sclera of the eye and inside lining of the mouth. If jaundice is left untreated, the infant can develop Kernicterus, a form of permanent brain damage. In this paper, we derive a mathematical model for the mass transport of the bilirubin concentration in the human body using the Mass Balance Law. We also incorporate into the model three types of treatments: blood transfusion, phototherapy, and medication. Our goal is, by observing the bilirubin concentration in the blood, to find the optimal treatment(s) to bring the concentration of bilirubin down to a normal level. We will also develop a program that automatically chooses the treatments based on the severity of the bilirubin level.
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