Scalar quantum electrodynamics on lattice correlation inequalities and infinite volume limit

We consider Wilson's lattice approximation to scalar Quantum Electrodynamics. We establish correlation inequalities of Griffiths-Kelly-Sherman type and a rigorous transfer matrix formalism, from which existence and non triviality of the infinite volume limit follow.     

Extensions of combinatorial geometries by the addition of a unique line

All extensions of a combinatorial geometry G are determined which can be obtained adjoining a unique line. The result is achieved investigating Dilworth structures and modular cuts of Dilworth truncation of G.     

Intense shake-up satellites in the XPS spectra of planar and sterically hindered N-piperidyl-nitrobenzenes and -nitrothiophens

The shake-up satellites present in the O_1s and N_1s energy regions of the XPS spectra of the planar 4-N-piperidyl-nitrobenzene (1) and 2-N-piperidyl-5-nitrothiophen (3), and of the sterically hindered 2-N-piperidyl-nitrobenzene (2), 2-N-piperidyl-3-nitrothiophen (4) and 3-N-piperidyl-2-nitrothiophen (5) and, for comparison, of 2-bromo-3-nitrothiophen (6) have been analyzed with the help of CNDO/S CI calculations. The spectra of the planar derivatives closely resemble these of the related compounds previously analysed, the main satellites deriving from the transition between the highest occupied molecular orbital (HOMO, localized at the donor-ring moiety) towards the lowest unoccupied one (LUMO, localized at the nitro group). Calculations indicate that in the ortho derivatives new relaxation processes are allowed upon N_1s/NO₂ ionization. In 2, where the angle of rotation θ is closer to 90° than 60°, the NR ₂ lone-pair orbital relaxes through space towards the core-ionized N/NO₂ atom. In 4 and 5, where 45° ? θ ? 60°, both through-ring and through-space relaxations are present. The assignment of the main N_1s/NO₂ line in 1 is discussed.     

Permanganate oxidation of 3-methyl-4-nitro-5-styrilisoxazole: a correction

In contrast with a previous report, permanganate oxidation of the title compound $\text{3}$ gives the nitroisoxazolone $\text{8}$ and not 3-methyl-4- nitroisoxazole-5-carboxylic acid $\text{2}$; a reaction pathway, involving the spirocyclisation of the carboxylate $\text{10}$, is suggested.     

Sul minimo di funzionali definiti sullo spazio delle funzioni di variazione limitata inn dimensioni

Summary Given a proper normal integrand we define a functional on the space of functions of bounded variations inR ⁿ; sufficient conditions which assure the existence of the minimum of this functional are given.

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Entrata in Redazione il 27 aprile 1977.

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Lavoro eseguito nell'ambito dell'attività del Laboratorio per la Matematica Applicata.     

Spectroscopic diagnostics of R.F. discharges at moderate pressure and chemical applications—I. Pure nitrogen

A vibro-rotational analysis has been performed of the second positive system (SPS) of N₂ and of the first negative system (FNS) of N⁺₂ emitted by 35 MHz discharges in flowing nitrogen operated at pressures of 5–50 torr and power densities of the order of 1–10 W-cm^-3. The distributions of the vibrational and of the rotational levels follow Boltzmann's law in both the SPS and the FNS with T_v = 4000°K and T_R = 2800°K for the N₂(C³Π_u) state and T_v = 5100°K and T_R = 5800°K for the N⁺₂(B²Σ⁺_g) state and independent of pressure. Kinetic gas temperatures are between 1200 and 2000°K and increase with pressure; electron temperatures are in the range 15,000–9,500°K. The reversal of line intensities of the SPS and of the FNS observed with increasing pressure has been tentatively interpreted. Possible chemical implications of these results have been examined.