38,544 research outputs found
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 Conceptual Framework for Studying the Sources of Variation in Program Effects
Evaluations of public programs in many fields reveal that (1) different types of programs (or different versions of the same program) vary in their effectiveness, (2) a program that is effective for one group of people might not be effective for other groups of people, and (3) a program that is effective in one set of circumstances may not be effective in other circumstances. This paper presents a conceptual framework for research on such variation in program effects and the sources of this variation. The framework is intended to help researchers -- both those who focus mainly on studying program implementation and those who focus mainly on estimating program effects -- see how their respective pieces fit together in a way that helps to identify factors that explain variation in program effects and thereby support more systematic data collection on these factors. The ultimate goal of the framework is to enable researchers to offer better guidance to policymakers and program operators on the conditions and practices that are associated with larger and more positive effects
On the size of approximately convex sets in normed spaces
Let X be a normed space. A subset A of X is approximately convex if
for all and where is
the distance of to . Let \Co(A) be the convex hull and \diam(A) the
diameter of . We prove that every -dimensional normed space contains
approximately convex sets with \mathcal{H}(A,\Co(A))\ge \log_2n-1 and
\diam(A) \le C\sqrt n(\ln n)^2, where denotes the Hausdorff
distance. These estimates are reasonably sharp. For every , we construct
worst possible approximately convex sets in such that
\mathcal{H}(A,\Co(A))=\diam(A)=D. Several results pertaining to the
Hyers-Ulam stability theorem are also proved.Comment: 32 pages. See also http://www.math.sc.edu/~howard
Extremal Approximately Convex Functions and Estimating the Size of Convex Hulls
A real valued function defined on a convex is anemconvex function iff
it satisfies A thorough study of
approximately convex functions is made. The principal results are a sharp
universal upper bound for lower semi-continuous approximately convex functions
that vanish on the vertices of a simplex and an explicit description of the
unique largest bounded approximately convex function~ vanishing on the
vertices of a simplex.
A set in a normed space is an approximately convex set iff for all
the distance of the midpoint to is . The bounds
on approximately convex functions are used to show that in with the
Euclidean norm, for any approximately convex set , any point of the
convex hull of is at a distance of at most
from . Examples are given to show
this is the sharp bound. Bounds for general norms on are also given.Comment: 39 pages. See also http://www.math.sc.edu/~howard
Pattern formation of microtubules and motors: inelastic interaction of polar rods
We derive a model describing spatio-temporal organization of an array of
microtubules interacting via molecular motors. Starting from a stochastic model
of inelastic polar rods with a generic anisotropic interaction kernel we obtain
a set of equations for the local rods concentration and orientation. At large
enough mean density of rods and concentration of motors, the model describes
orientational instability. We demonstrate that the orientational instability
leads to the formation of vortices and (for large density and/or kernel
anisotropy) asters seen in recent experiments.Comment: 4 pages, 5 figures, to appear in Phys. Rev. E, Rapid Communication
Markov Process of Muscle Motors
We study a Markov random process describing a muscle molecular motor
behavior. Every motor is either bound up with a thin filament or unbound. In
the bound state the motor creates a force proportional to its displacement from
the neutral position. In both states the motor spend an exponential time
depending on the state. The thin filament moves at its velocity proportional to
average of all displacements of all motors. We assume that the time which a
motor stays at the bound state does not depend on its displacement. Then one
can find an exact solution of a non-linear equation appearing in the limit of
infinite number of the motors.Comment: 10 page
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