Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented pre-service teachers (Study 1), middle school students (Study 2), and math and sci...

While the scientific visualization community is comfortable with isosurfacing and volume rendering of scalar fields, data from simulations and sensors often have additional constraints or dimensions that are not easily handled by these algorithms. In the first part of this dissertation we consider volume fraction data and the material interface reconstruction problem, for which existing isosurf...

-The paper is concerned with the flow of dispersions of gas bubbles in liquid, with bubble sizes such that the inertia forces on the bubbles are of importance to the dynamics. One-dimensional conservation equations are derived, which govern the flow when the deviations from the uniform state are small. These are used to describe the features of the propagation of void fraction disturbances, and...

A visual method for adding fractions is introduced. The similarities between this and another method are studied. A formal definition is introduced in an intuitive and visual way. The multiplication is discussed as well as analogies between addition and multiplication with union and intersection of two sets. A final discussion on the philosophy of the method and a comparison with another method...

Ninety-three patients with aortic valve disease were evaluated to determine the effect of the preoperative left ventricular ejection fraction (EF) on the results of aortic valve replacement (AVR). Forty-six patients had aortic stenosis (AS), 16 had aortic insufficiency (Al), and 31 had mixed aortic stenosis and insufficiency (MX). Immediate and long-term survival curves in AS and MX, and in AS ...

In a manuscript discovered in 1976 by George E. Andrews, Ramanujan states a formula for a certain continued fraction, without proof. In this paper we establish formulae for the convergents to the continued fraction, from which Ramanujan's result is easily deduced.

Glossary Canonical realization: A state-space realization that has specific properties that makes it unique. Characteristic polynomial: The scalar denominator of a transfer function. Column-reduced: A polynomial matrix with non-singular column leading coefficient matrix. Coprime: See relatively prime. Denominator polynomial: The polynomial appearing in the denominator of a rational transfer fun...