Conclaves of planes in PG (4,2) and certain planes external to the Grassmannian ${\cal G}_{1,4,2} \subset$ PG(9,2)

We show that in $\operatorname{PG}(4,2)$ there exist octets $\mathcal{P} _{8}=\{\pi_{1},\,\ldots\,,\pi_{8}\}$ of planes such that the 28 intersections $\pi_{i}\cap\pi_{j}$ are distinct points. Such conclaves (see [6]) $\mathcal{P}_{8}$ of planes in $\operatorname{PG}(4,2)$ are shown to be in bijective correspondence with those planes $P$ in $\operatorname{PG}(9,2)$ which are external to the Grassmannian $\mathcal{G}_{1,4,2}$ and which belong to the orbit $\operatorname{orb}(2\gamma)$ (see [4]). The fact that, under the action of $\operatorname{GL}(5,2),$ the stabilizer groups $\mathcal{G}_{\mathcal{P}_{8}}$ and $\mathcal{G}_{P}$ both have the structure $2^{3}:(7:3)$ is thus illuminated. Starting out from a regulus-free partial spread $\mathcal{S}_{8}$ in $\operatorname{PG}(4,2)$ we also give a construction of a conclave of planes $P\in\operatorname{orb}(2\gamma)\subset\operatorname{PG}(9,2).$     

Scenario optimization

Uncertainty in the parameters of a mathematical program may present a modeller with considerable difficulties. Most approaches in the stochastic programming literature place an apparent heavy data and computational burden on the user and as such are often intractable. Moreover, the models themselves are difficult to understand. This probably explains why one seldom sees a fundamentally stochastic model being solved using stochastic programming techniques. Instead, it is common practice to solve a deterministic model with different assumed scenarios for the random coefficients. In this paper we present a simple approach to solving a stochastic model, based on a particular method for combining such scenario solutions into a single, feasible policy. The approach is computationally simple and easy to understand. Because of its generality, it can handle multiple competing objectives, complex stochastic constraints and may be applied in contexts other than optimization. To illustrate our model, we consider two distinct, important applications: the optimal management of a hydro-thermal generating system and an application taken from portfolio optimization.     

Helium cosmic ray flux measurements at Mars

The helium energy spectrum in Martian orbit has been observed by the MARIE charged particle spectrometer aboard the 2001 Mars Odyssey spacecraft. The orbital data were taken from March 13, 2002 to October 28, 2003, at which time a very intense Solar Particle Event caused a loss of communication between the instrument and the spacecraft. The silicon detector stack in MARIE is optimized for the detection of protons and helium in the energy range below , which typically includes almost all of the flux during SPEs. This also makes MARIE an efficient detector for GCR helium in the energy range of 50–. We will present the first fully normalized flux results from MARIE, using helium ions in this energy range.     

On Greene-Kleitman's theorem for general digraphs

Linial conjectured that Greene—Kleitman's theorem can be extended to general digraphs. We prove a stronger conjecture of Berge for digraphs having k-optimal path partitions consisting of ‘long’ paths. The same method yields known results for acyclic digraphs, and extensions of various theorems of Greene and Frank to acyclic digraphs.     

Application of the MC SCF method to the π → π* excitation energies of ethylene

The MC SCF method is employed to calculate the N → T and N → V π → π^* vertical excitation energies of ethylene. To obtain accurate excitation energies it is found to be necessary to utilize an expanded valence space containing two π and two π^* orbitals. Relatively small MC SCF calculations, allowing at most one-electron excitations from the sigma space, are found to yield excitation energies and spatial extents of the excited states in excellent agreement with the predictions of large multi-reference or iterative-natural-orbital CI calculations. These results show that within an MC SCF framework σ-σ correlation is unimportant for describing the π → π^* processes. We also conclude that the neglect of the effects of unlinked cluster terms in some of the CI calculations may have introduced small, but important, errors in the excitation energies and predictions of the spatial extent of the V state.     

Structural studies on 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido[1,2-a]pyrimidines by 1H, 13C and 15N NMR spectroscopy

¹H, ¹³C and ¹⁵N NMR studies demonstrated that 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido-[1,2-a] pyrimidlnes exist as an equilibrium mixture of Z-E isomers in the hydrazono–imino tautomeric form having an exocyclic double bond. Proton-catalysed Z-E interconversion is fast. Substituent and solvent effects revealed that the decisive factors controlling the Z:E ratio are internal hydrogen bonding in the Z-isomer, stabilization by solvation and steric interaction.     

Iron plasma: Sensitivity of photoelectric cross sections to different models and general features of the Fermi-Amaldi-Modified model

Photoelectric cross sections in several atomic models are presented as a function of temperature and density. The models discussed are Thomas-Fermi (TF), Fermi-Amaldi-Modified (FAM), and Debye-Hückel-Thomas-Fermi (DHTF). We also present some systematic results for the less known FAM potential model regarding predictions for: electrostatic potentials, bound electron level energies, pressures, and branching ratios of photoelectric cross sections. The pure iron plasma which we explored had a temperature in the range of 0.2–3 keV and a density in the range of 50–1000 g/cm³. Our conclusion is that except near threshold the photoelectric cross sections per fully occupied subshell are less sensitive to changes in density and temperature, at least in the ranges of our investigation, than other factors, such as occupation numbers.     

Motivic orthogonal two-dimensional representations of Gal(ℚ/ℚ)

Given a two-dimensional compatible family of ℓ-adic representations which is motivic and which respects an orthogonal form up to similitudes, we show how to express itsL-function in terms of a Hecke character. We give several examples and in particular we analyze a representation associated to a certainK3 surface which arose in the study of Kloosterman sums.