Bottom Schur functions

We give a basis for the space V spanned by the lowest degree part \hat{s}_\lambda of the expansion of the Schur symmetric functions s_\lambda in terms of power sums, where we define the degree of the power sum p_i to be 1. In particular, the dimension of the subspace V_n spanned by those \hat{s}_\lambda for which \lambda is a partition of n is equal to the number of partitions of n whose parts differ by at least 2. We also show that a symmetric function closely related to \hat{s}_\lambda has the same coefficients when expanded in terms of power sums or augmented monomial symmetric functions. Proofs are based on the theory of minimal border strip decompositions of Young diagrams.Comment: 16 pages, 13 figures To appear in the Electronic Journal of Combinatoric

Effects of electron transfer on the stability of hydrogen bonds.

The measurement of the dimerization constants of hydrogen-bonded ruthenium complexes (12, 22, 32) linked by a self-complementary pair of 4-pyridylcarboxylic acid ligands in different redox states is reported. Using a combination of FTIR and UV/vis/NIR spectroscopies, the dimerization constants (KD) of the isovalent, neutral states, 12, 22, 32, were found to range from 75 to 130 M-1 (ΔG0 = -2.56 to -2.88 kcal mol-1), while the dimerization constants (K2-) of the isovalent, doubly-reduced states, (12)2-, (22)2-, (32)2-, were found to range from 2000 to 2500 M-1 (ΔG0 = -4.5 to -4.63 kcal mol-1). From the aforementioned values and the comproportionation constant for the mixed-valent dimers, the dimerization constants (KMV) of the mixed-valent, hydrogen-bonded dimers, (12)-, (22)-, (32)-, were found to range from 0.5 × 106 to 1.2 × 106 M-1 (ΔG0 = -7.78 to -8.31 kcal mol-1). On average, the hydrogen-bonded, mixed-valent states are stabilized by -5.27 (0.04) kcal mol-1 relative to the isovalent, neutral, hydrogen-bonded dimers and -3.47 (0.06) kcal mol-1 relative to the isovalent, dianionic hydrogen bonded dimers. Electron exchange in the mixed valence states imparts significant stability to hydrogen bonding. This is the first quantitative measurement of the strength of hydrogen bonds in the presence and absence of electronic exchange

On positivity and roots in operator algebras

In earlier papers the second author and Charles Read have introduced and studied a new notion of positivity for operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. The present paper consists of complements to some facts in the just mentioned papers, concerning this notion of positivity. For example we prove a result on the numerical range of products of the roots of commuting operators with numerical range in a sector.Comment: 11 pages, to appear Integral Equations Operator Theor

Steric and electronic control of an ultrafast isomerization.

Synthetic control of the influence of steric and electronic factors on the ultrafast (picosecond) isomerization of penta-coordinate ruthenium dithietene complexes (Ru((CF3)2C2S2)(CO)(L)2, where L = a monodentate phosphine ligand) is reported. Seven new ruthenium dithietene complexes were prepared and characterized by single crystal X-ray diffraction. The complexes are all square pyramidal and differ only in the axial vs. equatorial coordination of the carbonyl ligand. Fourier Transform Infrared (FTIR) spectroscopy was used to study the ν(CO) bandshapes of the complexes in solution, and these reveal rapid exchange between two or three isomers of each complex. Isomerization is proposed to follow a Berry psuedorotation-like mechanism where a metastable, trigonal bipyramidal (TBP) intermediate is observed spectroscopically. Electronic tuning of the phosphine ligands L = PPh3, P((p-Me)Ph)3, ((p-Cl)Ph)3, at constant cone angle is found to have little effect on the kinetics or thermodynamic stabilities of the axial, equatorial and TBP isomers of the differently substituted complexes. Steric tuning of the phosphine ligands over a range of phosphine cone angles (135 < θ < 165°) has a profound impact on the isomerization process, and in the limit of greatest steric bulk, the axial isomer is not observable. Temperature dependence of the FTIR spectra was used to obtain the relative thermodynamic stabilities of the different isomers of each of the seven ruthenium dithietene complexes. This study details how ligand steric effects can be used to direct the solution state dynamics on the picosecond time scale of discrete isomers energetically separated by <2.2 kcal mol-1. This work provides the most detailed description to date of ultrafast isomerization in the ground states of transition metal complexes

Chemical approaches to carbon dioxide utilization for manned Mars missions

Use of resources available in situ is a critical enabling technology for a permanent human presence in space. A permanent presence on Mars, e.g., requires a large infrastructure to sustain life under hostile conditions. As a resource on Mars, atmospheric CO2 is as follows: abundant; available at all points on the surface; of known presence; chemically simple; and can be obtained by simple compression. Many studies focus on obtaining O2 and the various uses for O2 including life support and fuel; discussion of CO, the coproduct from CO2 fixation revolves around its uses as a fuel, being oxidized back to CO2. Several new proposals are studied for CO2 fixation through chemical, photochemical, and photoelectrochemical means. For example, the reduction of CO2 to hydrocarbons such as acetylene (C2H2) can be accomplished with H2. C2H2 has a theoretical vacuum specific impulse of approx. 375 secs. Potential uses were also studied of CO2, as obtained or further reduced to carbon, as a reducing agent in metal oxide processing to form metals or metal carbides for use as structural or power materials; the CO2 can be recycled to generate O2 and CO