Formulating a State Approach to Professional Development

When viewed from the perspective of an entire state\u27s needs, the challenges of designing professional development to meet the requirements of the federal No Child Left Behind legislation of 2001 are daunting. In Oklahoma, the concerns about delivering to rural and urban populations which contain a variety of underserved populations are further complicated by the differences in the way science and mathematics are structured as disciplines. We describe two model programs, one in science and one in mathematics, which take much different approaches. However, the programs have three common elements that make them highly successful. Each program engages teachers strongly, seeks to change learning by altering both teachers\u27 behavior and content knowledge, and is continuously reflective

A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi

Non-invasive investigations of a wall painting using optical coherence tomography and hyperspectral imaging

Multispectral and hyperspectral imaging are efficient methods of measuring spectral reflectance at high spatial resolution. This non-invasive technique has been applied to the imaging of paintings over the last 20 years. PRISMS (Portable Remote Imaging System for Multispectral Scanning) was designed specifically for imaging wall paintings. Optical Coherence Tomography (OCT) is a low coherence interferometric technique capable of fast non-invasive imaging of subsurface microstructure. This paper shows the first application of in situ OCT imaging of a wall painting. The combination of PRISMS and OCT gives information on the varnish and paint layer structure, pigment identification, the state of degradation of the paint and varnish layers and informing curators on the painting schemes and techniques

Generalizations of the St\"ormer Problem for Dust Grain Orbits

We consider the generalized St\"ormer Problem that includes the electromagnetic and gravitational forces on a charged dust grain near a planet. For dust grains a typical charge to mass ratio is such that neither force can be neglected. Including the gravitational force gives rise to stable circular orbits that encircle that plane entirely above/below the equatorial plane. The effects of the different forces are discussed in detail. A modified 3rd Kepler's law is found and analyzed for dust grains.Comment: 21 pages LaTeX, 12 figure

A control system formulation of the mechanism that controls the secretions of serum group hormone in humans during sleep

Plasma growth hormone concentrations during sleep were determined experimentally. An elevated level of plasma growth hormone was observed during the initial phase of sleep and remained elevated for approximately 3 hr before returning to the steady-state level. Moreover, subsequent to a prolonged interruption of sleep, of the order of 2-3 hr, an elevated level of plasma growth hormone was again observed during the initial phase of resumed sleep. A control system formulation of the mechanism that controls the secretions of serum growth hormone in humans was used to account for the growth hormone responses observed

New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities

With the Delsarte-MacWilliams inequalities as a starting point, an upper bound is obtained on the rate of a binary code as a function of its minimum distance. This upper bound is asymptotically less than Levenshtein's bound, and so also Elias's

Loose mechanochemical coupling of molecular motors

In living cells, molecular motors convert chemical energy into mechanical work. Its thermodynamic energy efficiency, i.e. the ratio of output mechanical work to input chemical energy, is usually high. However, using two-state models, we found the motion of molecular motors is loosely coupled to the chemical cycle. Only part of the input energy can be converted into mechanical work. Others is dissipated into environment during substeps without contributions to the macro scale unidirectional movement