Formation of phosphino-substituted isocyanate by reaction of CO2 with group 2 complexes based on the (Me3Si)(i-Pr2P)NH ligand

The group 2 complexes [(Me(3)Si)(i-Pr(2)P)N](2)M(THF)(x) (M = Mg, x = 1; M = Ca/Sr, x = 2) as well as an unusual dimagnesium complex {[(Me(3)Si)(i-Pr(2)P)N](3)Mg}Mg(n-C(4)H(9)) have been prepared and characterized by multinuclear NMR spectroscopy and single crystal X-ray diffraction. Each complex was shown to react with CO(2) under extremely mild conditions (15 min, 1 atm, room temperature) to give the isocyanate (i-Pr)(2)P-N═C═O. The independent syntheses of (i-Pr)(2)P-N═C═O and the carbodiimide dimer [(i-Pr)(2)PNCNP(i-Pr)(2)](2) are also reported.     

Addition of aluminum and gallium species to aromatic and alkyl-substituted 1,4-diaza-1,3-butadiene ligands

In this report, we investigate the interactions of Me(x)MCl(3-x) (x = 0-3, M = Al, Ga) with various aromatic and alkyl-substituted 1,4-diaza-1,3-butadiene (R)DAB ligands (or α-diimine ligands) to give a variety of structures in solution and in the solid state. In combination with other previously reported structures, certain general trends of reactivity of these species can be deduced, although there are still some unexplained modes of reactivity. The methylated Al species react with aromatic-substituted (R)DAB ligands to provide final products that result from C═N insertion into the Al-CH(3) group followed by rearrangement reactions. The addition of methyl groups onto the backbone of the (R)DAB ligand is insufficient to stop the insertion and rearrangement processes from occurring. In the case of MeAlCl(2) with the bulky (DiPP)DAB ligand, the reaction could be followed spectroscopically from the monoadduct through the inserted/rearranged final product. Methylated Ga species, however, are much less predictable in their behavior with aromatic-substituted (R)DAB ligands. Depending on the exact species and ratios used, coordinated adducts can be formed and identified, or inserted/rearranged products similar to the aluminum reactions can be obtained. Quite interestingly, cation/anion pairs can also be formed in which GaCl(3) or MeGaCl(2) act as a chloride acceptors. This behavior was unique and substantially different from the analogous Al reactions which formed either a dicoordinated adduct or an inserted/rearranged complex. When the stronger-donating alkyl-substituted (R)DAB ligands were used with Me(2)GaCl, only cation/anion pairs were obtained. Surprisingly, when the same reactions were performed using Me(2)AlCl as a reagent, irreproducible results were obtained.     

Stochastic integration for set-indexed processes

Diagonalizable derivations of a finite-dimensional algebra usually span an ideal in the Lie algebra of all derivations. This ideal is studied for underlying graded, monomial, and path algebras.     

Theoretical invstigations of the electronic states of porphyrins. I. Basis set development and predicted spectrum of pyrrole

A new minimum basis set was developed for use in computing excitation energies of large molecules. It is particularly suited to calculating ionization potentials and Rydberg transitions. Pyrrole excitation energies and oscillator strengths calculated with this basis set are compared to larger basis set ab initio and semiempirical results. The 6-eV band in the experimental spectrum is predicted to be the result of three Rydberg absorptions, with no underlying (π, π*) absorption. The calculations also provide an explanation for the observed N? H stretch in the 6-eV region.     

On the Role of Mixed Strategies in Elementary Decision Analysis and Related Decision-Support-System Treatments

We first demonstrate that mixed strategies are relevant in decision analysis for a maximin decision-maker quite apart from any game-theory considerations. This rectifies the apparent misconception that results from MS/OR textbooks which discuss mixed strategies only in the game-theory setting. Next we show an example of an implementable mixed strategy, by which we mean a mixed decision strategy which does not require randomization for its implementation. This application is to portfolio construction.     

Teachers Describe Epistemologies of Science Instruction Through Q Methodology

Creating scientifically literate students is a common goal among educational stakeholders. An understanding of nature of science is an important component of scientific literacy in K‐12 science education. Q methodology was used to investigate the opinions of preservice and in‐service teachers on how they intend to teach or currently teach science. Q methodology is a measurement tool designed to capture personal beliefs. Participants included 40 preservice and in‐service elementary and secondary science teachers who sorted 40 self‐referential statements regarding science instruction. The results identified three epistemologies toward teaching science: A Changing World, My Beliefs, and Tried and True. Participants with the A Changing World epistemology believe evidence is reliable, scientific knowledge is generated in multiple ways, and science changes in light of new evidence. The My Beliefs epistemology reflects that scientific knowledge is subject to change due to embedded bias, science is affected by culture and religion, and evolution should not be taught in the classroom. The Tried and True epistemology views a scientific method as an exact method to prove science, believes experiments are crucial for scientific discoveries, absolute truth exists in scientific knowledge, and society and cultural factors can be eliminated from investigations. Implications for preservice teacher education programs and in‐service teacher professional development are addressed.     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.