Gaussian expansions for polyatomic molecules

A method for obtaining finite series expansions of Slater-type atomic orbitals in terms of an arbitrary number of Gaussian-type functions is described. The method is based on numerical quadrature procedures applied to the Laplace transform of the exponential radial dependence of the Slater orbital. Accuracy of the expansions is evaluated by examining various overlap and one-electron energy integrals. A further application is made to the evaluation of two-centre Coulomb electron repulsion integrals and it is seen that six-place accuracy is obtainable using sixteen term expansions.     

Rearrangement equations for plutonium

The percents of all oxidation states produced by Pu disproportionation, including unreacted starting material, can be obtained by new equations that are easy to apply. The equations are useful for quantifying the extent and the stoichiometry of disproportionation, the consequences of complexation, and the effects of temperature changes on the composition of the oxidation-state mixture.     

Fostering creativity through instruction rich in mathematical problem solving and problem posing

Although creativity is often viewed as being associated with the notions of “genius” or exceptional ability, it can be productive for mathematics educators to view creativity instead as an orientation or disposition toward mathematical activity that can be fostered broadly in the general school population. In this article, it is argued that inquiry-oriented mathematics instruction which includes problem-solving and problem-posing tasks and activities can assist students to develop more creative approaches to mathematics. Through the use of such tasks and activities, teachers can increase their students’ capacity with respect to the core dimensions of creativity, namely, fluency, flexibility, and novelty. Because the instructional techniques discussed in this article have been used successfully with students all over the world, there is little reason to believe that creativity-enriched mathematics instruction cannot be used with a broad range of students in order to increase their representational and strategic fluency and flexibility, and their appreciation for novel problems, solution methods, or solutions.     

Slope estimations at terminal values of three equidistant data

A new method is presented for estimating derivatives at the end points of three curvilinear data points. For first derivatives, the accuracy of the method is similar to that of the standard method, but it has the advantage that second derivatives are not necessarily all equal and can be more accurate than those predicted by conventional methods.