Differentiability of Backward Stochastic Differential Equations in Hilbert Spaces with Monotone Generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control.     

Distribuzione di mantisse e serie di potenze non prolungabili

Sunto Si prende in esame un criterio sufficiente diJ. Gergen eD. V. Widder, atto a garantire la non-prolungabilità di una serie di potenze fuori della circonferenza di convergenza, e se ne fornisce una generalizzazione, stabilendo due nuovi criteri sufficienti: ci si vale di un teorema diH. Weyl sulla distribuzione delle mantisse e di un teorema diE. Fabry - G. Pólya sulle serie di potenze non prolungabili.     

Feasibility of low-energy radiative-capture experiments at the LUNA underground accelerator facility

The LUNA (Laboratory Underground for Nuclear Astrophysics) facility has been designed to study nuclear reactions of astrophysical interest. It is located deep underground in the Gran Sasso National Laboratory, Italy. Two electrostatic accelerators, with 50 and 400 kV maximum voltage, in combination with solid and gas target setups allowed to measure the total cross-sections of the radiative-capture reactions ^2H²H(p, )^3He³Heand ^14N¹⁴N(p, )^15O¹⁵Owithin their relevant Gamow peaks. We report on the gamma background in the Gran Sasso laboratory measured by germanium and bismuth germanate detectors, with and without an incident proton beam. A method to localize the sources of beam-induced background using the Doppler shift of emitted gamma rays is presented. The feasibility of radiative-capture studies at energies of astrophysical interest is discussed for several experimental scenarios.     

Ancora sulla permanenza della struttura lacunare nel prolungamento analitico

Annali di Matematica Pura ed Applicata (1923 -) - Si considerano le serie di potenze f(z;0) lacunari pure con la successione di lacune {ph, qh}, (h=1, 2, 3, ...), qh/ph →1 + Λ, (0...     

13C NMR spectra of cassane diterpenoids. The stereochemistry of the caesalpins

Assignments of the ¹³C NMR resonances for some cassane diterpenoids have been made. The data have proved to be a useful tool for the stereochemical examination of the caesalpins.     

On the genus of real projective spaces

We construct a crystallization of the real projective space whose associated contracted complex is minimal with respect to the number of n-simplexes. Then we compute the regular genus of , which is the minimum genus of a closed connected surface into which a crystallization of regularly embeds. Received: 7 February 2007     

New chiral P-N ligands for the regio- and stereoselective Pd-catalyzed dimerization of styrene

Two new chiral, enantiomerically pure, hybrid P-N ligands, namely (2R,5S)-2-phenyl-3-(2-pyridyl)-1,3-diaza-2-phosphanicyclo[3,3,0]octan-4-one (1) and (2R,5S)-2-phenyl-3-(2-pyridyl)-1,3-diaza-2-phosphanicyclo[3,3,0]octane (2), have been synthesized starting from L-proline. The two ligands differ in the presence or not of a carbonyl group in the diazaphosphane ring. Their coordination chemistry towards Pd(II) was studied by reacting them with [Pd(CH?)Cl(cod)]. A different behaviour was observed: ligand 2 shows the expected bidentate chelating behaviour leading to the mononuclear Pd-complex, while ligand 1 acts as a terdentate ligand giving a dinuclear species. The corresponding cationic derivatives were obtained from the palladium neutral complexes, both as mono- and dinuclear derivatives, and tested as precatalysts for styrene dimerization, yielding E-1,3-diphenyl-1-butene regio- and stereoselectively as the sole product. A detailed analysis of the catalytic behaviour is reported.     

Beliefs and beyond: hows and whys in the teaching of proof

In this paper, we report on a study aimed at describing the way secondary school teachers treat proof and at understanding which factors may influence such a treatment. This study is part of a wider project on proof carried out for many years. In our theoretical framework, we combine references from research on proof with those from research on teachers in relation to their beliefs. The study was carried out through interviews with secondary school teachers aimed at learning how they describe their work with proof in the classroom, and to elicit beliefs and other factors that shape this work. Through the interviews we were able to detect reasons behind teachers’ choices in planning their work in the classroom. In the present paper, we concentrate on four cases that, among other factors, offer elements suitable to unravel the problem of inconsistencies using the construct of leading beliefs, i.e., beliefs (whose nature may vary from teacher to teacher) that seem to drive the way each teacher treats proof.     

Bootstrap Algorithms for Risk Models with Auxiliary Variable and Complex Samples

Resampling methods are often invoked in risk modelling when the stability of estimators of model parameters has to be assessed. The accuracy of variance estimates is crucial since the operational risk management affects strategies, decisions and policies. However, auxiliary variables and the complexity of the sampling design are seldom taken into proper account in variance estimation. In this paper bootstrap algorithms for finite population sampling are proposed in presence of an auxiliary variable and of complex samples. Results from a simulation study exploring the empirical performance of some bootstrap algorithms are presented.      

Assembly maps and realization of splitting obstructions

In 1987 Kharshiladze introduced the concept of type for an element in a Wall group, and proved that the elements of first and second type cannot be realized by normal maps of closed manifolds. This approach is sufficiently easy for computing the assembly maps and sometimes very effective. Here we give a geometrical interpretation of this approach by using the Browder–Quinn surgery obstruction groups for filtered manifolds. To understand the obtained relations we give algebraic definitions of the element types which are based on the algebraic surgery theory of Ranicki. Our approach describes a level of indeterminate for the algebraic passing to surgery on a codimension k submanifold of a given Browder–Livesay filtration. Then we study the realization of splitting obstructions by simple homotopy equivalences of closed manifolds, and compute the assembly maps for some classes of groups.