Regiodivergent and Stereoselective Hydrosilylation of 1,3‐Disubstituted Allenes

Methods for the highly stereoselective and regiodivergent hydrosilylation of 1,3‐disubstituted allenes have been developed. The synthesis of E allylsilanes is accomplished with palladium NHC catalysts, and trisubstituted Z alkenylsilanes are accessed with nickel NHC catalysts. Unsymmetrically substituted allenes are well tolerated with nickel catalysis and afford Z alkenylsilanes. Evidence for a plausible mechanism was obtained through an isotopic double‐labeling crossover study.     

Catalyst‐Switchable Regiocontrol in the Direct Arylation of Remote C?H Groups in Pyrazolo[1,5‐a]pyrimidines

The regiodivergent palladium‐catalyzed C H arylation of pyrazolo[1,5‐a]pyrimidine has been achieved, wherein the switch in regioselectivity between positions C3 and C7 is under complete catalyst control. A phosphine‐containing palladium catalyst promotes the direct arylation at the most acidic position (C7), whereas a phosphine‐free catalyst targets the most electron‐rich position (C3).     

Force field‐dependent solution properties of glycine oligomers

Molecular simulations can be used to study disordered polypeptide systems and to generate hypotheses on the underlying structural and thermodynamic mechanisms that govern their function. As the number of disordered protein systems investigated with simulations increase, it is important to understand how particular force fields affect the structural properties of disordered polypeptides in solution. To this end, we performed a comparative structural analysis of Gly₃ and Gly₁₀ in aqueous solution from all atom, microsecond molecular dynamics (MD) simulations using the CHARMM 27 (C27), CHARMM 36 (C36), and Amber ff12SB force fields. For each force field, Gly₃ and Gly₁₀ were simulated for at least 300 ns and 1 μs, respectively. Simulating oligoglycines of two different lengths allows us to evaluate how force field effects depend on polypeptide length. Using a variety of structural metrics (e.g., end‐to‐end distance, radius of gyration, dihedral angle distributions), we characterize the distribution of oligoglycine conformers for each force field and show that each sample conformation space differently, yielding considerably different structural tendencies of the same oligoglycine model in solution. Notably, we find that C36 samples more extended oligoglycine structures than both C27 and ff12SB. © 2015 Wiley Periodicals, Inc.     

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.     

Electrochemical assessment of water|ionic liquid biphasic systems towards cesium extraction from nuclear waste

A room temperature ionic liquid (IL) composed of a quaternary alkylphosphonium (trihexyltetradecylphosphonium, P₆₆₆₁₄⁺) and tetrakis(pentafluorophenyl)borate anion (TB⁻) was employed within a water|P₆₆₆₁₄TB (w|P₆₆₆₁₄TB or w|IL) biphasic system to evaluate cesium ion extraction in comparison to that with a traditional water|organic solvent (w|o) combination. ¹³⁷Cs is a major contributor to the radioactivity of spent nuclear fuel as it leaves the reactor, and its extraction efficiency is therefore of considerable importance. The extraction was facilitated by the ligand octyl(phenyl)-N,N′-diisobutylcarbamoylphosphine oxide (CMPO) used in TRans-Uranium EXtraction processes and investigated through well established liquid|liquid electrochemistry. This study gave access to the metal ion to ligand (1:n) stoichiometry and overall complexation constant, β, of the interfacial complexation reaction which were determined to be 1:3 and 1.6 × 10¹¹ at the w|P₆₆₆₁₄TB interface while the study at w|o elicited an n equal to 1 with β equal to 86.5. Through a straightforward relationship, these complexation constant values were converted to distribution coefficients, δ_α, with the ligand concentrations studied for comparison to other studies present in the literature; the w|o and w|IL systems gave δ_α of 2 and 8.2 × 10⁷, respectively, indicating a higher overall extraction efficiency for the latter. For the w|o system, the metal ion-ligand stoichiometries were confirmed through isotopic distribution analysis of mass spectra obtained by the direct injection of an emulsified water–organic solvent mixture into an electron spray ionization mass spectrometer.     

On the fluid approximation to a nonlinear Schrödinger equation

We present a heuristic proof that the nonlinear Schrödinger equation (NLS) - in 2 + 1 dimensions has a family of solutions which can be well approximated by a collection of point vortices for a planar incompressible fluid. The novelty of our approach is that we begin with a representation of the NLS as a compressible perturbation of Euler's equations for hydrodynamics.     

A Heuristic for the Prime Number Theorem

Conclusion  Might there be a chance of proving in a simple way thatx/π(x) is asymptotic to an increasing function, thus getting another proof of PNT? This is probably wishful thinking. However, there is a natural candidate for the increasing function. LetL(x) be the upper convex hull of the full graph ofxπ(x) (precise definition to follow). The piecewise linear functionL(x) is increasing becausex/π(x) → ∞ asx → ∞. Moreover, using PNT, we can give a proof thatL(x) is indeed asymptotic tox/π(x). But the point of our work in this article is that for someone who wishes to understand why the growth of primes is governed by natural logarithms, a reasonable approach is to convince oneself via computation that the convex hull just mentioned satisfies the hypothesis of our theorem, and then use the relatively simple proof to show that this hypothesis rigorously implies the prime number theorem.