An infinite sequence of non-realizable weavings

A weaving is a number of lines drawn in the plane so that no three lines intersect at a point, and the intersections are drawn so as to show which of the two lines is above the other. For each integer n4 we construct a weaving of n lines, which is not realizable as a projection of a number of lines in 3-space, all of whose subfigures are realizable as such projections.     

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     

Single and Dual-Domain Models to Evaluate the Effects of Preferential Flow Paths in Alluvial Sediments

Typical features of preferential flow paths were evidenced by numerical tests of convective transport of conservative solutes performed in three blocks of alluvial sediments at the scale of depositional elements. The numerical experiments are analysed with standard single-domain models (SDMs) and with dual-domain models (DDMs): the model parameters are identified by minimisation of the misfit between the ??experimental?? and the modelled cumulative breakthrough curves (BTCs) and between the ??experimental?? and the modelled temporal moments of the BTCs. The results for the SDMs show different behaviours for the three model blocks and for the different flow directions, in good agreement with their hydrostratigraphic characteristics. The results for the DDMs sometimes correspond to cases for which one of the two domains is dominant and its values of diffusivity and average velocity are close to those obtained for the SDM; in some cases the DDM performs much better than the SDM and correctly represents the effects of preferential flow paths. Finally the relevance of the DDM is analysed in the framework of multi-objective optimisation: a proper choice of the objective-functions yields Pareto sets whose geometries are different for single- and dual-domain media.     

Surgery on pairs of closed manifolds

To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group LP* generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the case of an elementary fundamental group. Then we generalize them, and obtain several further results about the realization of elements in the Browder-Quinn surgery obstruction groups by means of normal maps to a closed manifold filtered by closed submanifolds. Partially supported by the RFFI Grant No. 05-01-00993, by the GNSAGA of the National Research Council of Italy, by the MIUR (Ministero della Istruzione, Università e Ricerca) of Italy within the project ‘Proprietà Geometriche delle Varietà Reali e Complesse’, and by a Research Grant of the University of Modena and Reggio Emilia. The second author would like to thank the MPI (Bonn), the ICTP (Trieste), and the University of Modena and Reggio Emilia for their kind hospitality and support in different periods during the year 2007, and the Commission on Development and Exchange of IMU for the travel support.     

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.     

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.      

Oxygen-17 NMR Spectroscopy: Effect of Substituents on Chemical Shifts and Width Line in Ortho Substituted Nitro Benzenes

¹⁷O-NMR spectra, of ortho, meta and para substituted nitrobenzene are reported. The ¹⁷O nucleus of NO₂ group in ortho derivatives absorb at lower field that meta and para compounds. Moreover, width line of ¹⁷O resonance appears to be strongly dependent by substituent position. The ¹⁷O chemical shifts are correlated with U. V. spectra and X-ray diffraction data.     

Study of the interference effects in an optical cavity for organic light-emitting diode applications

The interference effects generated in a bottom-emitting electroluminescent device fabricated on a polymer underlayer introduced with the aim of improving the anode roughness have been studied. The analysis of the interference fringes at different detection angles and the spatial coherence demonstrates that this phenomenon is due to multiple internal reflections that propagate in the polymer layer. This effect can be eliminated by modifying the polymer thickness and the incidence angle of the electromagnetic radiation at the anode-polymer interface. Inkjet etching technology is adopted for microcavities-shaped polymer structuring to destroy the resonator effect of the optical cavity.     

On Four-Dimensional Poincaré Duality Cobordism Groups

This paper continues the study of four-dimensional Poincaré duality cobordism theory from our previous work Cavicchioli et al. (Homol. Homotopy Appl. 18(2):267–281, 2016). Let P be an oriented finite Poincaré duality complex of dimension 4. Then, we calculate the Poincaré duality cobordism group \(\Omega _{4}^{{\text {PD}}}(P)\). The main result states the existence of the exact sequence \(0 \rightarrow L_4 (\pi _1 (P))/A_4 (H_2 (B\pi _1 (P), L_2)) \rightarrow {{\widetilde{\Omega }}}_{4}^{\mathrm{PD}}(P) \rightarrow \mathbb Z_8 \rightarrow 0\), where \({{\widetilde{\Omega }}}_{4}^{\mathrm{PD}}(P)\) is the kernel of the canonical map \({\Omega }_{4}^{\mathrm{PD}}(P) \rightarrow H_4 (P, \mathbb Z) \cong \mathbb Z\) and \(A_4 : H_4 (B\pi _1, \mathbb L) \rightarrow L_4 (\pi _1 (P))\) is the assembly map. It turns out that \({\Omega }_{4}^{\mathrm{PD}}(P)\) depends only on \(\pi _1 (P)\) and the assembly map \(A_4\). This does not hold in higher dimensions. Then, we discuss several examples. The cases in which the canonical map \(\Omega _{4}^{{\text {TOP}}}(P) \rightarrow \Omega _{4}^{{\text {PD}}}(P)\) is not surjective are of particular interest. Its image coincides with the kernel of the total surgery obstruction map. In fact, we establish an exact sequence

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where s is Ranicki’s total surgery obtruction map. In the above cases, there are \({\text {PD}}_4\)-complexes X which cannot be homotopy equivalent to manifolds.