Vertex Algebras, Lie Algebras, and Superstrings

We construct Lie algebras from vertex superalgebras and study their structure. They are sometimes generalized Kac–Moody algebras. In some special cases we can calculate the multiplicities of the roots.     

Metal-acetylide addition to tetracyanoethylene

Two push-pull chromophores that have shown utility in the field of molecular electronics and non-linear optics are DDMEBT (1, 2-(4-dimethylamino)phenyl)-3-((4-(dimethylamino)phenyl)ethynyl)buta-1,3-diene-1,1,4,4-tetracarbonitrile) and TDMEE (2, 4-(4-dimethylamino)phenyl)but-1-en-3-yne-1,1,2-tricarbonitrile). Unfortunately, the methods reported for their synthesis give variable yields, use toxic solvents, and only provide small amounts of material. We report improved synthetic protocols, providing access to larger quantities of material. By investigating multiple metal-acetylides of 4-ethynyl-N,N-dimethylaniline and their subsequent addition to TCNE, we obtained various products depending on the identity of the metal ion. This led to the simple synthesis of push-pull chromophoric compounds.     

Synthesis of Stable Diarylpalladium(II) Complexes: Detailed Study of the Aryl–Aryl Bond‐Forming Reductive Elimination

The synthesis of diarylpalladium(II) complexes by twofold aryl C?H bond activation was developed. These intermediates of oxidative cyclization reactions are stabilized by chelation with acetyl groups while still maintaining sufficient reactivity to study their reductive elimination. Four distinct triggers were found for the reductive elimination of these complexes to dibenzofurans and carbazoles. Thermal elimination occurs at very high temperatures, whereas ligand‐promoted and oxidatively induced reductive eliminations proceed readily at room temperature. Under these conditions, no isomerization occurs. In contrast, weak Brønsted acids, such as acetic acid, lead to a sequence of proto‐demetalation, isomerization to a κ³‐diarylpalladium(II) complex, and reductive elimination to non‐symmetrical cyclization products.     

Bis(trimethylsilyl)diimine: Preparation,Structure, and Reactivity

The highly reactive compound bis(trimethylsilyl)diimine (BSD), which was first prepared by oxidation of lithium tris(trimethylsilyl)hydrazide, is light blue, sensitive to thermolysis and hydrolysis, and ignites spontaneously in air. On the basis of electron transfer, acid-base, or free-radical reactions, it acts in particular as a (preparatively useful) redox system and as an agent for the introduction of azo groups. Redox reactions lead by oxidation or reduction of the other reactant through two oxidation stages to hydrazine derivatives or molecular nitrogen, and in the case of electrochemical reduction, to BSD radical-anions. Azo-group transfers, on the other hand, yield new inorganic azo compounds with no change in the oxidation state of the diimine group.     

Boltwoodite [K(UO2)(SiO3OH)(H2O)1.5] and compreignacite K2[(UO2)3O2(OH)3]2.7H2O characterized by laser fluorescence spectroscopy

Synthetically prepared boltwoodite and compreignacite were characterized with time-resolved laser-induced fluorescence spectroscopy (TRLFS). The obtained TRLFS emission spectra of both synthesized uranium minerals differ from each other in their positions of the vibronic peak maxima and in their fluorescence lifetimes. Also, the shapes of the spectra and their respective intensities are different. The TRLFS-spectrum of boltwoodite showed well-resolved sharp vibronic peaks at 485.1, 501.5, 521.2, 543.0, 567.4, and 591.4nm with deep notches between them and compreignacite is characterized by two broad peaks with various shoulders. Here five emission bands were identified at 500.7, 516.1, 532.4, 554.3, and 579.6nm. The shape of the TRLFS spectra of compreignacite is typical for uranium in a hydroxide coordination environment. For both minerals two fluorescence lifetimes were extracted. The two species of boltwoodite and compreignacite, respectively, showed the same positions of the peak maxima showing that the coordination environments are similar, but differ in the chemistry and number of possible quenchers, e.g. water molecules and hydroxide groups. For boltwoodite fluorescence lifetimes of 382 and 2130ns, and for compreignacite shorter ones of 202 and 914ns, respectively, were determined. The spectroscopic signatures of the two uranyl minerals reported here could be useful for identifying uranyl(VI) mineral species as colloids, as thin coatings on minerals, as minor component in soils, or as alteration products of nuclear waste.     

Multiple single-peaked solutions of a class of semilinear Neumann problems via the category of the domain boundary

For a smooth domain with compact boundary we investigate the problem with Neumann boundary conditions, where f has superlinear but subcritical growth. Provided that is sufficiently small we show the existence of at least positive solutions with single maximum points that lie on . We replace the standard variational setting used in the case of homogeneous f by considering the restriction of the free functional to a suitable submanifold of the Sobolev Space . Received May 25, 1997 / Accepted October 3, 1997     

Constant-cutoff approach to radiative decays of hyperons: E2/M1 transition ratios

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study the radiative decays ofJ ^π=3/2⁺ baryons using the constant-cutoff approach to theSU(3) collective treatment of the Skyrme model for hyperons. Thus we evaluate the widths and E2/M1 ratios, showing that there is a general qualitative agreement with the results obtained using the complete Skyrme model, as well as the nonrelativistic quark model and quenched lattice model, for the total widths.