Practitioner's Research: A Study in Changing Preservice Teachers’ Conceptions About Mathematics and Mathematics Teaching and Learning

Educators involved in the current reform movement in mathematics education recommend that students be actively involved in constructing their own knowledge and developing powerful mathematical concepts. This study suggests how ideas based on constructivist learning theory can be put into practice in a preservice mathematics education class.     

Chromatographic separation of cannabinoids and their monooxygenated derivatives.

delta1-Tetrahydrocannabinol, delta6-tetrahydrocannabinol, cannabinol, cannabidiol and several of their monooxygenated derivatives have been separated from each other by a combination of liquid, thin-layer and gas chromatography. Retention volumes (on Sephadex LH-20), Rf values and retention times can be recorded, and may provide guidance in the separation and identification of these known cannabinoids.     

Hölder continuity of solutions of elliptic systems

The purpose of this note is to observe that a variant of the method of Morrey, as exposed in [4] and [5], can be used to show that weak solutions of a certain class of elliptic systems of quasilinear equations of arbitrary order of the form $$\mathop {\sum\limits_{\left| \alpha \right| \leqslant m} {( - 1)^{\left| \alpha \right|} D^\alpha F_{\alpha ,v} (x,u,Du, \ldots ,D^m u) = 0,v = 1,2 \ldots ,N} }\limits_{u = (u_1 ,u_2 , \ldots ,u_{N)} } $$ are Hölder continuous, thus partially extending results of Lady?enskaja-Ural'ceva [3] and Serrin [8] to higher order equations. A full extension is not possible. With suitable assumptions the Hölder continuity holds out to the boundary.     

The Green function for uniformly elliptic equations

The authors discuss a generalization of the usual Green function to equations with only measurable and bounded coefficients. The existence and uniqueness as well as several other important properties are shown. Such a Green function proves useful in connection with quasilinear elliptic systems of diagonal type.