The topology of two-dimensional real algebraic varieties

Sunto È noto che ogni spazio analitico reale è localmente omeomorfo al cono su un poliedro con caratteristica di Eulero-Poincaré pari. Si dimostra che questa condizione è anche sufficiente affinchè un poliedro (compatto) di dimensione due P sia omeomorfo ad una varietà algebrica reale affine P. Segue inoltre dalla costruzione che la P ottenuta ha, in un certo senso, un insieme di singolarità algebriche minimale, compatibilmente con la topologia di P.

---

---

The authors are members of the G.N.S.A.G.A.     

Model-based clustering of probability density functions

Complex data such as those where each statistical unit under study is described not by a single observation (or vector variable), but by a unit-specific sample of several or even many observations, are becoming more and more popular. Reducing these sample data by summary statistics, like the average or the median, implies that most inherent information (about variability, skewness or multi-modality) gets lost. Full information is preserved only if each unit is described by a whole distribution. This new kind of data, a.k.a. “distribution-valued data”, require the development of adequate statistical methods. This paper presents a method to group a set of probability density functions (pdfs) into homogeneous clusters, provided that the pdfs have to be estimated nonparametrically from the unit-specific data. Since elements belonging to the same cluster are naturally thought of as samples from the same probability model, the idea is to tackle the clustering problem by defining and estimating a proper mixture model on the space of pdfs. The issue of model building is challenging here because of the infinite-dimensionality and the non-Euclidean geometry of the domain space. By adopting a wavelet-based representation for the elements in the space, the task is accomplished by using mixture models for hyper-spherical data. The proposed solution is illustrated through a simulation experiment and on two real data sets.     

Catalytic properties of iron-based mixed oxides in the oxidation of methanol and olefins

The selective oxidation of alcohols and olefins is carried out commercially on complex systems based on Fe and Mo or Sb mixed oxides. The role of active phases and of the dopant in the catalysts has been elucidated using several characterization techniques and catalytic data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muonium radicals in molecular plastic crystals Norbornene and bicyclooctene

Muonium adduct radicals have been studied in Norbornene and Bicyclooctene as a function of temperature from the liquid phase down to the plastic phase and through the low temperature transition to a typical solid (brittle phase). The features of the radical hyperfine spectra are discussed. The temperature coefficient for the hyperfine constants is 0.1 MHz/K for the NBE exo isomer, 0.09 MHz/K for the BCOE radical and 0 for the NBE endo isomer. Regarding the dinamical features of the plastic phase, the present data suggest the onset of anisotropy of the molecular reorientations prior to the transition to the brittle phase.     

Electromagnetic decay of the 6+ isomer of102Rh

Conversion electrons, and X rays from¹⁰²Rh^m (6⁺,T _1/2=1057 d) have been studied. An electromagnetic branch (2.3±0.3) ·10^–3 feeding the¹⁰²Rh first excited state has been observed in the 6⁺ isomeric decay. The excitation energy of the 6⁺ isomer turns out to be 140.7 keV above the 2^– ground state.We wish to thank P. Del Carmine, M. Ottanelli, and A. Pecchioli for their skillful collaboration during the measurements and the Technical Staffs of LNS and LNL for operation of the Tandem Accelerators.     

Structure and reactivity of vanadium-phosphorus oxides

The contribution of thermal methods of analysis to the study of the structure and reactivity of vanadium-phosphorus oxides is examined. In particular, data are reported on the solid-state reaction VOHPO₄·1/2H₂O(VO)₂P₂O₇+2 H₂O for VOHPO₄·1/2H₂O prepared in different ways, on the redox properties of oxidation and reduction of vanadium for catalysts prepared with different PV atomic ratios in the range 0.9–1.3, and on the surface properties determined by TPD of catalysts with different PV ratios. The relationship between these properties and the catalytic properties in the selective oxidation ofn-butane and but-1-ene is discussed.

---

Zusammenfassung Der Beitrag thermischer Analysenmethoden zur Untersuchung der Struktur und Reaktivität von Vanadin-Phosphor-Oxiden wird erörtert. Insbesondere werden sich auf die Festkörperreaktion 2VOHPO₄.1/2H₂O(VO)₂P₂O₇+2H₂O für auf verschiedene Weise dargestelltes VOHPO₄.1/2H₂O, auf die Redox-Eigenschaften von Vanadin in Katalysatoren mit P/V-Atomverhältnissen im Bereich 0.9–1.3 und auf durch TPD bestimmte Oberflächeneigenschaften von Katalysatoren mit unterschiedlichen P/V-Verhältnissen beziehende Angaben gemacht. Zusammenhänge zwischen diesen Eigenschaften und den katalytischen Eigenschaften bei der selektiven Oxydation von n-Butan und N-Buten werden diskutiert.

---

- . , VOHPO₄ · 1/2H₂O, VOHPO₄ · 1/2H₂O(VO)₂P₂O₇ + 2H₂O, - PV 0,91,3. - 1-.

     

The (N=1) Supersymmetric Sine-Gordon model in two dimensions. I

In this paper and its companion (II) we prove that the SupersymmetricN=1 massless Sine-Gordon field theory, at finite (space) volume, exists and is analytic in the coupling constant . Moreover at finite (space) volume is Witten index is=1.