On lightlike geometry: isometric actions,and rigidity aspects

Degenerate Riemannian metrics exist naturally in various contexts. Unfortunately, their study stops to the ‘admission of failure’ that they are too poor, for instance, to generate a coherent intrinsic or extrinsic differential geometry, e.g. a kind of Levi-Civita connection. In this first text, we start the investigation of rigidity aspects of these structures, from the point of view of isometric actions of ‘big’ (e.g. semi-simple) Lie groups. To cite this article: E. Bekkara et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Rectangular arrays

In this paper we studied m×n arrays with row sums $\text{nr}\text{(n,m)}$ and column sums $\text{mr}\text{(n,m)}$ where (n,m) denotes the greatest common divisor of m and n. We were able to show that the function H_m,n(r), which enumerates m×n arrays with row sums and column sums $\text{nr}\text{(m,n)}$ and $\text{mr}\text{(n,m)}$ respectively, is a polynomial in r of degree (m?1)(n?1). We found simple formulas to evaluate these polynomials for negative values, ?r, and we show that certain small negative integers are roots of these polynomials. When we considered the generating function G_m,n(y) = Σ_r?0H_m,n(r)y^r, it was found to be rational of degree less than zero. The denominator of G_m,n(y) is of the form (1?y)^(m?1)(n?1)+3, and the coefficients of the numerator are non-negative integers which enjoy a certain symmetric relation.     

Hyperon and multi-kaon production in K+p interactions at 4.3 GeV/c incident momentum

We present results of a study of hyperon and multikaon production in K⁺p. The data were obtained from a 7.37±0.18 event/μb exposure of the 30″ MURA-ANL hydrogen bubble chamber to a 4.27 GeV/c separated K⁺ beam. Cross-section results for 3, 4, 5, and 6-body hyperon and multi-kaon final states are presented. We observe production of φ(1019), K¹(892), and Y¹(1385), but find no evidence for a Y = 2, B = 0 exotic resonance in the KK invariant mass distributions. A study of the inclusive reaction K⁺p→Λ+ anything is also reported.     

Prompt γ-rays emitted in the thermal-neutron induced fission of 233U and 239Pu

The average number and average energy of γ-rays emitted within ≈ 5 nsec after fission have been determined as functions of fragment mass and as functions of total kinetic energy. They were obtained from a four-parameter experiment that recorded, event-by-event, correlated of γ-rays and of fission-fragment pairs and the time, relative to fission, at which a γ-ray was detected. For ²³³U(n_th, f) the average total number and energy emitted per fission were found to be 6.31 ± 0.3 and 6.69 ± 0.3 MeV, respectively, giving an average photon energy of 1.06 ± 0.07 MeV. The results for ²³⁹Pu(n_th, f) given in the same order, are 6.88 ± 0.35,6.73 ± 0.35 MeV, and 0.98 ± 0.07 MeV.     

Influence of Ti addition on boehmite-derived aluminum silicate aerogels: structure and properties

Aluminosilicate aerogels offer potential for extremely low thermal conductivities at temperatures greater than 900?°C, beyond where silica aerogels reach their upper temperature use limits. Aerogels have been synthesized at two Al:Si ratios, a 3Al:1Si mullite composition, and an 8Al:1Si alumina rich composition. Boehmite (AlOOH) is used as the Al source, and tetraethoxysilane as the Si precursor. The influence of Ti as a ternary constituent, introduced through the addition of titanium isopropoxide in the sol?Cgel synthesis, on aerogel morphology and thermal properties is evaluated. Four different boehmite precursor powders are evaluated. Morphology, surface area and pore size, and thermal transformation vary with the crystallite size of the starting boehmite powder, as does incorporation of titanium and evolution of Ti-containing crystalline phases. The addition of Ti influences sol viscosity, gelation time, surface area and pore size distribution, as well as phase formation on heat treatment.     

Structure and electrochemical properties for complexes of nitrocompounds with inorganic ions: A theoretical approach

Reduction and oxidation (redox) reactions are widely used for removal of nitrocompounds from contaminated soil and water. Structures and redox properties for complexes of nitrocompounds, such as 2,4,6‐trinitrotoluene (TNT), 2,4‐dinitrotoluene (DNT), 2,4‐dinitroanisole (DNAN), and 5‐nitro‐2,4‐dihydro‐3H?1,2,4‐triazol‐3‐one (NTO), with common inorganic ions (Na⁺, Cl^?, ) were investigated at the SMD(Pauling)/PCM(Pauling)/MPWB1K/TZVP level of theory. Atoms in molecules (AIM) theory was applied to analyze the topological properties of the bond critical points involved in the interactions between the nitrocompounds and the ions. Topological analyses show that intermolecular interactions of the types O(N)…Na⁺, C‐H…Cl^?( ), and C…Cl^?( ) may be discussed as noncovalent closed‐shell interactions, while N‐H···Cl^?( ) hydrogen bonds are partially covalent in nature. Complexation causes significant decrease of redox activity of the nitrocompounds. Analysis of the reduction potentials of the complexes obtained through application of the Pourbaix diagram of an iron/water system revealed that sodium complexes of NTO might be reduced by metallic iron. © 2016 Wiley Periodicals, Inc.