A Notion of Nonlocal Curvature

We consider a nonlocal (or fractional) curvature and we investigate similarities and differences with respect to the classical local case. In particular, we show that the nonlocal mean curvature can be seen as an average of suitable nonlocal directional curvatures and there is a natural asymptotic convergence to the classical case. Nevertheless, different from the classical cases, minimal and maximal nonlocal directional curvatures are not in general attained at perpendicular directions and, in fact, one can arbitrarily prescribe the set of extremal directions for nonlocal directional curvatures. Also the classical directional curvatures naturally enjoy some linear properties that are lost in the nonlocal framework. In this sense, nonlocal directional curvatures are somewhat intrinsically nonlinear.     

On unitals in PG(2,q^2) stabilized by a homology group

The linear collineation group of a classical unital of $\mathrm{PG}(2,q^2)$ contains a group of homologies of order $q+1$ . In this paper we prove that if $\mathcal{U }$ is a unital of PG $(2,q^2)$ stabilized by a homology group of order $q+1$ and $q$ is a prime number, then $\mathcal{U }$ is classical.     

3-Nets realizing a group in a projective plane

In a projective plane $\mathit{PG}(2,\mathbb{K})$ defined over an algebraically closed field $\mathbb{K}$ of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky (Compos. Math. 140:1614–1624, 2004), arises from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky (Adv. Math. 219:672–688, 2008), comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzúa’s 3-nets (Adv. Geom. 10:287–310, 2010) realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds in characteristic p>0 apart from three possible exceptions $\rm{Alt}_{4}$ , $\rm{Sym}_{4}$ , and $\rm{Alt}_{5}$ . Motivation for the study of finite 3-nets in the complex plane comes from the study of complex line arrangements and from resonance theory; see (Falk and Yuzvinsky in Compos. Math. 143:1069–1088, 2007; Miguel and Buzunáriz in Graphs Comb. 25:469–488, 2009; Pereira and Yuzvinsky in Adv. Math. 219:672–688, 2008; Yuzvinsky in Compos. Math. 140:1614–1624, 2004; Yuzvinsky in Proc. Am. Math. Soc. 137:1641–1648, 2009).     

Highly reduced iron-doped lithium niobate for optoelectronic tweezers

We investigate the applicability of highly reduced lithium niobate samples doped with iron for the use as optoelectronic tweezers. Increasing the reduction degree of Fe-doped lithium niobate is well known to increase the photoconductivity and reduce the writing time of internal space-charge fields. Based on our measurements of the photorefractive properties, we determine the optimal conditions for dielectrophoretic trapping and present the application of Fe-doped lithium niobate as optoelectronic tweezers. For higher reduction degrees, an unexpected decrease in the photovoltaic current density and the saturation space-charge field is reported.     

Solid–liquid equilibria for the dimethyl ether + carbon dioxide binary system

A recently built experimental setup was employed for the estimation of the solid–liquid equilibria of alternative refrigerants systems. The behavior of dimethyl ether (DME) + carbon dioxide was measured down to temperatures of 131.6 K. To confirm the reliability of the apparatus, the triple point of the DME was measured. The triple point data measured revealed a good consistency with the literature. The results obtained for the mixtures were corrected by the Rossini method and interpreted by means of the Schröder equation.     

Negishi cross-coupling of organotellurium compounds: synthesis of biaryls, aryl-, and diaryl acetylenes

A functional group tolerant palladium-catalyzed Negishi coupling of diaryl tellurides with organozinc has been developed. This methodology permits efficient preparation of biaryls, aryl acetylenes and diaryl acetylenes in moderate to good yields. A preliminary study to gain further insight into the reaction was performed using in situ ReactIR technology.     

Stimulus‐responsive polymers based on 2‐hydroxypropyl acrylate prepared by RAFT polymerization

Homopolymerization and diblock copolymerization of 2‐hydroxypropyl acrylate (HPA) has been conducted using reversible addition fragmentation chain transfer (RAFT) chemistry in tert‐butanol at 80 °C. PHPA homopolymers were obtained with high conversions and narrow molecular weight distributions over a wide range of target degrees of polymerization. Like its poly(2‐hydroxyethyl methacrylate) isomer, PHPA homopolymer exhibits inverse temperature solubility in dilute aqueous solution, with cloud points increasing systematically on lowering the mean chain length. The nature of the end groups is shown to significantly affect the cloud point, whereas no effect of concentration was observed over the PHPA concentration range investigated. Various thermoresponsive PHPA‐based diblock copolymers were prepared via one‐pot syntheses in which the second block was either permanently hydrophilic or pH‐responsive. Preliminary studies confirmed that poly(ethylene oxide)‐poly(2‐hydroxypropyl acrylate) (PEO₄₅‐PHPA₄₈) and poly(2‐hydroxypropyl acrylate)‐ poly(2‐hydroxyethyl acrylate) (PHPA₄₉‐PHEA₆₈)diblock copolymers formed well‐defined PHPA‐core micelles in 10 mM sodium nitrate solution at 40 °C and 70 °C with mean hydrodynamic diameters of 20 nm and 35 nm, respectively. In contrast, most other PHPA‐based diblock copolymers investigated formed larger colloidal aggregates in 10 mM NaNO₃ solution at elevated temperatures. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2032–2043, 2010     

Hair analysis and the early detection of imbalances in trace elements for members of expeditions in Antarctica

In the framework of the Human Biology and Medicine Project of the National Program for Research in Antarctica (Programma Nazionale di Ricerche in Antartide, PNRA) a study was undertaken to explore the suitability of trace element determination in human hair as a tool for the early detection of the impact of extreme environmental conditions on the health of members of the Italian and French expeditions. This study included three campaigns, namely, the 1995–1996 expedition to the Italian base of Terra Nova Bay, as well as the 1997–1998 and 1998–1999 expeditions to both the Italian base of Terra Nova Bay and the Italian–French base of Dome C. Sampling of hair of participants in the expeditions was carried out both prior to departure and at the end of the period spent at the bases. As regards storage, pre-treatment and analysis of hair samples they were performed in accordance with previously established procedures. Acid-assisted microwave digestion was adopted as the best approach for preparing solutions for subsequent analysis by inductively coupled plasma atomic emission spectrometry and inductively coupled plasma mass spectrometry. In the first part of this study, only the elements Ca, Cu, Fe, Mg and Zn were selected, while at a later stage it was decided to also include Co, Cr, Mn, Mo and Ni. Experimental results were subjected to basic statistical analysis to detect possible significant differences in element concentrations that occurred during the sojourn at the bases, with a view to identify possible remedial action to minimize adverse consequences.