Expanding Students' Conceptions of the Arithmetic Mean

The arithmetic mean is the most commonly used measure of central tendancy; nevertheless, many students who can add all the elements of a data set and then divide that sum by the number of elements do not truly understand the concept of mean. This article presents four activities designed to help elementary and middle school students develop a concept of mean. To bring about a desirable level of understanding, all computational formulae and algorithms in mathematics should be preceded by experience emphasizing conceptual understanding. Since that is not the normal instructional sequence for the arithmetic mean, the activities presented in the article assume previous exposure to the computational algorithm for the arithmetic mean.     

The gas analysis modeling system (GAMS)

This paper gives an overview of a large integrated model of the natural gas industry in the United States. The system described has been used to evaluate the impacts of natural gas legislation before the U.S. Congress. Many common operations research tools such as linear programming, dynamic programming and network flow theory are used at various stages in the model.     

Ferroelectric properties of mixtures of a liquid crystalline polymer and its side-group mesogen

We present the results of our studies of the ferroelectric properties of mixtures of a high polarization, ferroelectric liquid crystalline copolymer and its side-group antecedent, a high polarization, low molecular weight, ferroelectric mesogen. These two materials are found to be completely miscible in all proportions. Spontaneous polarization values and electro-optical response times are found to be monotonic functions of the weight percentage of the mesogen in the mixture, while optical tilt angles do not exhibit such a monotonic dependence.     

Studies of the hyperfine interaction of111Cd in gaseous InCl and InCl3 systems

Using the perturbed γ-γ angular correlation at excited¹¹¹Cd-ions from the decay of¹¹¹In, the time-integral attenuation coefficientG ₂₂(∞) was measured in gaseous InCl and InCl₃ surroundings. The perturbation depends as well on the character and the density of the surrounding gas, as on the angular momentum of the electronic shell of the Cd-ion.G ₂₂(∞) varied between 0.012 and 0.828, while the molecule densities varied between 2×10¹⁴ and 2×10²⁰ molecules/cm³. For high densities it is to be noted, that the perturbation vanishes much faster for the InCl systems. Using a stochastic model, it is possible to calculate the mean hyperfine frequency Ω₀, and to estimate cross-sections for molecule-ion collisions at thermal energies.     

Eine Klassifikation der Laguerre-Ebenen nachℒ-Streckungen undℒ-Translationen

Ohne Zusammenfassung     

Transition operators of diffusions reduce zero-crossing

If is a solution of a one-dimensional, parabolic, second-order, linear partial differential equation (PDE), then it is known that, under suitable conditions, the number of zero-crossings of the function decreases (that is, does not increase) as time increases. Such theorems have applications to the study of blow-up of solutions of semilinear PDE, time dependent Sturm Liouville theory, curve shrinking problems and control theory. We generalise the PDE results by showing that the transition operator of a (possibly time-inhomogenous) one-dimensional diffusion reduces the number of zero-crossings of a function or even, suitably interpreted, a signed measure. Our proof is completely probabilistic and depends in a transparent manner on little more than the sample-path continuity of diffusion processes.

     

Study of the electroosmotic flow as a means to propel the mobile phase in capillary electrochromatography in view of further miniaturization of capillary electrochromatography systems

In this paper, we investigate the phenomenon of electroosmosis as a means to propel a mobile phase, in particular in view of an application in microfluidic systems, which are characterized by significantly smaller volumes of the reservoirs and the separation channels compared to conventional instrumentation. In the microfluidic chip, pH changes due to water electrolysis quickly showed an effect on the electroosmotic flow (EOF), which could be counteracted by either regularly exchanging or buffering the mobile phase. Surface treatment was of no effect in regard to EOF stabilization in empty channels but may have an influence in channels filled with a charged monolith. In fused-silica capillaries the EOF was generally found to decrease from 'naked' to surface-treated to monolith-filled capillaries. The EOF tended to be higher when an organic solvent (acetonitrile) was added to the mobile phase and could be further increased by substituting the water with equal amounts of methanol. In addition, the hydrostatic pressure exerted by the EOF was investigated. In a microfluidic chip with empty (cross-)channels such an effect could be responsible for a redirection of the flow. In capillaries partially filled with a noncharged (non-EOF-generating) monolith, a linear relationship could be established between the EOF created in the empty section of the capillary (apparent mobility) and the length of the monolith (backpressure). In capillaries partially filled with a charged (EOF-producing) monolith, flow inhomogeneities must be expected as a consequence of a superimposition of hydrodynamic pressure and EOF as mobile phase driving force.