A New Hydrindanone Synthesis

The Kanematsu transformation was employed for the preparation of tetrahydroisobenzofuran‐4‐carboxylic acid ( 12 ), α‐methylation, subsequent conversion into the diazoethanone 14 , and, finally, treatment with dirhodium tetraacetate of which furnished the hydrindanone 1 of the steroid C‐D ring structure.     

Lowest-order and hyper-netted-chain calculations of nuclear matter

Employing two model central interactions the binding energy of nuclear matter is calculated within the framework of the Jastrow variational approach using different types of constrains and including all the contributions from hypernetted-chain diagrams.     

The method of interpolating integral equations for quantum fluids.—I

Summary Approximate integral equations, derived by interpolating between HNC and PY approaches, have been used to calculate the pair distribution function for quantum Bose and Fermi fluids. The equations contain a free parameter wich is determined in such a way that a consistency condition is satisfied. The results obtained for liquid⁴He and³He improve upon the PY and HNC equations and are in good agreement with the Monte Carlo results.

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Riassunto La funzione di distribuzione a due corpi per fluidi bosonici e fermionici è stata calcolata risolvendo delle equazioni integrali approssimate, ottenute da una conveniente interpolazione tra le tecniche HNC e PY. Le equazioni contengono un parametro libero che è fissato soddisfacendo una condizione di consistenza. I risultati ottenuti per⁴He e³He liquidi migliorano quelli di HNC e PY e risultano in buon accordo con i risultati ricavati con tecniche di Montecarlo.

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Резюме Приближенные интегральные уравнения, выведенные с помощью интерполяции между HNC и PY подходами, используются для вычисления функции распределения пар для квантовых Бозе—и Ферми-жидкостей. Уравнения содержат свободный параметр, который определяется таким образом, что выполняется условие совместимости. Результаты, полученные для жидких⁴He и³He улучшают результаты вычислений на основе PY и HNC уравнений и согласуются с результатами по методу Монте-Карло.

     

Yield of excited CO molecules from dissociative recombination of HCO+ and HOC+ ions with electrons

The authors have investigated CO band emissions arising from the dissociative recombination of HCO(+) and HOC(+) ions with thermal electrons in a flowing afterglow plasma. The quantitative analysis of the band intensities showed that HCO(+) recombination forms the long-lived CO(a (3)Pi) state with a yield of 0.23+/-0.12, while HOC(+) recombination favors formation of CO(a' (3)Sigma(+)) and CO(d (3)Delta) with a combined yield of greater than 0.4. The observed vibrational distribution for the CO(a) state reproduces theoretical predictions quite well. The vibrational distributions for CO(a') and CO(d) are, in part, inverted, presumably as a consequence of a change in CO equilibrium bond length during recombination. The observations are compatible with current knowledge of the potential surfaces of states of HCO and HCO(+).     

Speed of particles and a relativity of locality in κ-Minkowski quantum spacetime

The last decade of research on κ-Minkowski noncommutative spacetime has been strongly characterized by a controversy concerning the speed of propagation of massless particles. Most arguments suggested that this speed should depend on the momentum of the particle strongly enough to be of interest for some ongoing experimental studies. But the only explicit derivations of worldlines in κ-Minkowski predicted no momentum dependence for the speed of massless particles. We return to this controversy equipped with the recent understanding that in some quantum spacetimes coincidences of events assessed by an observer who is distant from the events can be artifactual. We therefore set up our investigation in such a way that we never rely on the assessment of coincidences of events by distant observers. This allows us to verify explicitly that in κ-Minkowski simultaneously-emitted massless particles of different momentum are detected at different times, and establish a linear dependence of the detection times on momentum.     

On smooth foliations with Morse singularities

Let M be a smooth manifold and let F be a codimension one, C^∞ foliation on M, with isolated singularities of Morse type. The study and classification of pairs (M,F) is a challenging (and difficult) problem. In this setting, a classical result due to Reeb (1946) [11] states that a manifold admitting a foliation with exactly two center-type singularities is a sphere. In particular this is true if the foliation is given by a function. Along these lines a result due to Eells and Kuiper (1962) [4] classifies manifolds having a real-valued function admitting exactly three non-degenerate singular points. In the present paper, we prove a generalization of the above mentioned results. To do this, we first describe the possible arrangements of pairs of singularities and the corresponding codimension one invariant sets, and then we give an elimination procedure for suitable center-saddle and some saddle-saddle configurations (of consecutive indices).In the second part, we investigate if other classical results, such as Haefliger and Novikov (Compact Leaf) theorems, proved for regular foliations, still hold true in presence of singularities. At this purpose, in the singular set, Sing(F) of the foliation F, we consider weakly stable components, that we define as those components admitting a neighborhood where all leaves are compact. If Sing(F) admits only weakly stable components, given by smoothly embedded curves diffeomorphic to S¹, we are able to extend Haefliger?s theorem. Finally, the existence of a closed curve, transverse to the foliation, leads us to state a Novikov-type result.     

Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part II: Computational issues

The implementation of the projected algorithm and of the consistent tangent tensor for general isotropic three-invariant elastoplastic models under plane stress conditions discussed in Part I of this paper [Valoroso, N., Rosati, L., 2008. Consistent derivation of the constitutive algorithm for plane stress isotropic plasticity. Part I: Theoretical formulation. International Journal of Solids and Structures, doi: 10.1016/j.ijsolstr.2008.08.012.] is addressed. The connections between the general three-dimensional case and the plane stress problem are analyzed in detail and an algorithmic treatment taking full advantage of the isotropic properties of the model is presented. In particular, intrinsic (matrix-free) expressions are provided for all steps of the stress computation scheme that allow one to carry out the numerical implementation in a way that is completely independent from the matrix representations. The numerical performances of the present solution scheme are evaluated through representative numerical examples.     

Proprietà topologiche della varietá degli elementi differenziali del secondo ordine dell'S r complesso

Sunto Si considera il modello V, di dimensione complessa 3r-2, della varietà degli elementi differenziali del secondo ordine di uno spazio proiettivo complesso S_r, costruito daG. Gherardelli, E. Bompiani, C. Longo. In questo lavoro tale modello viene considerato come varietà topologica a 2(3r-2) dimensioni reali e, mediante l'uso di un opportuno complesso cellulare, se ne determina il gruppo di omologia intera, assegnando altresì un semplice significato geometrico, nello spazio S_r, per i sistemi fondamentali di cicli delle varie dimensioni. Ne consegue, in particolare, che il gruppo di omologia di V è isomorfo a quello del prodotto di un S_r-1 per la varietà degli elementi di primo ordine di un S_r, in accordo con un risultato diF. Gherardelli ottenuto per altra via; ma si stabilisce d' altra parte che V non è, almeno in generale, omeomorfa a tale prodotto. Si prova, per inciso, che anche la varietá degli elementi di primo ordine di S_r, non è prodotto di un S_r-1 per un S_r, quantunque le due varietà abbiano anch'esse gruppi di omologia isomorfi. A Enrico Bompiani in occasione del suo Giubileo scientifico. Lavoro eseguito nell'ambito del gruppo di ricerca n. 37 del C. N. R. per l'anno accademico 1960–61.