The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions

The immaculate basis of the non-commutative symmetric functions was recently introduced by the first and third authors to lift certain structures in the symmetric functions to the dual Hopf algebras of the non-commutative and quasi-symmetric functions. It was shown that immaculate basis satisfies a positive, multiplicity free right Pieri rule. It was conjectured that the left Pieri rule may contain signs but that it would be multiplicity free. Similarly, it was also conjectured that the dual quasi-symmetric basis would also satisfy a signed multiplicity free Pieri rule. We prove these two conjectures here.     

Zero electron kinetic energy spectroscopy of the para-fluorotoluene cation

Zero electron kinetic energy (ZEKE) spectroscopy is employed to gain information on the vibrational energy levels of the para-fluorotoluene (pFT) cation. Vibrationally resolved spectra are obtained following excitation through a range of intermediate vibrational energy levels in the S1 state. These spectra allow the observation of different cationic vibrational modes, whose assignment is achieved both from a knowledge of the S1 vibrational states and also by comparison with density functional calculations. In one notable case, clean ZEKE spectra were obtained from two overlapped S1 features. From the authors' data, the adiabatic ionization energy of pFT was derived as 70,946+/-4 cm(-1). The information on the cationic energy levels obtained will be useful in untangling the intramolecular vibrational redistribution dynamics of pFT in the S1 state.     

Inequalities between Littlewood-Richardson coefficients

We prove that a conjecture of Fomin, Fulton, Li, and Poon, associated to ordered pairs of partitions, holds for many infinite families of such pairs. We also show that the bounded height case can be reduced to checking that the conjecture holds for a finite number of pairs, for any given height. Moreover, we propose a natural generalization of the conjecture to the case of skew shapes.     

A quantum-mechanical investigation of a collinear model for collision-induced dissociation

Quantum-mechanical wavepacket results are reported for a collinear A + BC → A + B + C dissociation model previously investigated semi-classically by Rusinek and Roberts. The quantum-mechanical and semi-classical probabilities are found to be in very good agreement.     

N,N′‐Di­methyl‐1,4‐dithiine‐1,2:4,5‐tetracarbox­imide and N,N′‐di­methyl‐1,4‐diselenine‐1,2:4,5‐tetracarbox­imide

The title compounds of sulfur, C₁₀H₆N₂O₄S₂, (I), and selenium, C₁₀H₆N₂O₄Se₂, (II), are isomorphous. The crystallographically centrosymmetric mol­ecules are planar. The bond distances and angles, except for those involving the S and Se atoms, are comparable. The mol­ecules are disposed in layers parallel to the bc plane. The molecular axes differ by 75° for (I) and by 80° for (II) from one layer to the next.     

Dilute sulfuric acid hydrolysis of biomass for ethanol production

A series of pilot plant experiments have been conducted to compare the performance of a system utilizing two percolation reactors in series to a single reactor system. Although theoretically capable of producing higher glucose yields or concentrations, the two-reactor system concentrations were approximately the same and the yields were considerably lower than those from the single reactor study. An associated kinetics study found the glucose degradation kinetics to be accelerated by chromium ions, but this effect was greatly reduced in the presence of wood. The presence of metal surfaces also increased the rate of degradation even without large ion concentrations. The poor performance of the reactor system is proposed to be caused by intraparticle glucose diffusion effects and the catalytic effect on glucose degradation reactions of chromium ions from the corrosion of stainless steel by the acid. Strategies for reducing the effects of these phenomena on PBR performance are presented.

     

Modified one-body memory function for classical fluids

A microscopic theory applicable to simple classical fluids, particularly in the hydrodynamic regime, is presented. A simple isomorphic transformation of the space of one-body additive phase-space functions is considered whose distinguishing feature is that the total energy density is contained in the new space. A projection operator formalism for this subspace has certain desirable properties for the study of the hydrodynamic regime. It is shown that, for a broad class of approximations, one obtains a prediction for the VanHove structure factorS(k, ω) that has the correct hydrodynamic structure and in which the only quantities that are approximated are the dissipative transport coefficients; all thermodynamic quantities appearing in the expression are rendered exactly. In particular, a weak coupling approximation is made on the memory function, and results are compared with the analogous theory of Forster and Martin. Agreement is found for the dissipative transport coefficients to lowest nontrivial order in the coupling. On the other hand, thermodynamic quantities are accurately predicted only to second order by Forster and Martin, whereas in the present theory they are exact.