Polynomials over division rings

LetD be a division ring with a centerC, andD[X ₁, …,X _N] the ring of polynomials inN commutative indeterminates overD. The maximum numberN for which this ring of polynomials is primitive is equal to the maximal transcendence degree overC of the commutative subfields of the matrix ringsM _n(D),n=1, 2, …. The ring of fractions of the Weyl algebras are examples where this numberN is finite. A tool in the proof is a non-commutative version of one of the forms of the “Nullstellensatz”, namely, simpleD[X ₁, …,X _m]-modules are finite-dimensionalD-spaces. This paper was written while the authors were Fellows of the Institute for Advanced Studies, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, Israel.     

Synthesis of silver nanodisks using polystyrene mesospheres as templates

We report the synthesis of Ag nanodisk using polystyrene mesospheres as templates. TEM measurements show that the average disk thickness is 9.0 +/- 1.0 nm and the diameter is 36 +/- 8 nm. The particles exhibit an intense electronic spectrum that differs markedly from that for spheres (purple vs yellow solutions). We present electromagnetic theory calculations which exhibit a qualitative match with the observed spectrum, enabling us to assign several of the plasmon resonance features.     

Sodium-lead alloy in the decomposition of organic samples for the detection of heteroelements

The decomposition of organic samples using open-tube fusion with sodium-lead alloy was demonstrated to be safe, complete, and controlled, in most cases. The detection of heteroelements in the fusion mixture of common organic samples was successful with samples of 10 to 20 mg. Detection of chlorine and nitrogen by classical methods in “difficult” compounds was secured, and the detection of fluorine in the fusion mixture of fluorocompounds extended the use of the alloy into this area. The use of the pyrazolone color reaction in the detection of nitrogen allowed the detection of more minute amounts of nitrogen than was previously detected using Prussian blue formation. The detection limits for heteroelements in organic samples were in the low microgram region. The application of sodium-lead alloy in quantitative work was briefly studied and will be considered in greater detail in the future.     

Electrophilic tetraalkylammonium nitrate nitration. II. Improved anhydrous aromatic and heteroaromatic mononitration with tetramethylammonium nitrate and triflic anhydride,including selected microwave examples

A new one-pot nitration employing tetramethylammonium nitrate and trifluoromethanesulfonic anhydride in dichloromethane to provide a ready source of the nitronium triflate nitrating agent is presented. Rapid and selective nitration with a variety of aromatic and heteroaromatic substrates is achieved resulting in the synthesis of several novel organic compounds. A distinct advantage is the removal of undesired byproducts by aqueous workup. This very mild nitration permits large-scale syntheses and gives high isolated product yields that often require no further purification. This tetramethylammonium nitrate-based nitration also has been applied to microwave-assisted conditions, and the results with several compounds are outlined.