Osservazioni su alcuni operatori ibridi iperbolico-ipoellittici

Riassunto Viene dimostrata l'equivalenza di alcune condizioni sul polinomio a coefficienti costantiP(ζ). La prima (si vedaH?rmander [3]), garantisce l'esistenza di una soluzione fondamentale diP(D) con supporto singolare in un cono convesso; l'ultima esprime il carattere ibrido diP(ζ). Viene infine costruita una soluzione fondamentale ultradistribuzione per un operatore 1/β-iperbolico-1/α-ipoellittico estendendo un precedente risultato [5] dell'autore.

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Summary The equivalence of some conditions on the polynomialP(ζ) with constant coefficients is proved. The first one (seeH?rmander [3]), implies the existence of a fundamental solution forP(D) with singular support contained in a convex cone; the last one shows thatP(ζ) is an hyperbolic-hypoelliptic polynomial. Finally an ultradistribution fundamental solution for a 1/β-hyperbolic-1/α-hypoelliptic operator is constructed, so extending a previous result [5] of the author.

     

Toda flows and real Hessenberg manifolds

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Effect of CO2 Flow Rate on the Extraction of Astaxanthin and Fatty Acids from Haematococcus pluvialis Using Supercritical Fluid Technology

Haematococcus pluvialis is the largest producer of natural astaxanthin in the world. Astaxanthin is a bioactive compound used in food, feed, nutraceutics, and cosmetics. In this study, astaxanthin extraction from H. pluvialis by supercritical fluid extraction was evaluated. The effects of temperature (40 and 50 °C), pressure (40 and 50 MPa), and CO₂ flow rate (2 and 4 L/min) were investigated. The results showed that the highest astaxanthin recovery was obtained at 50 °C/50 MPa and the CO₂ flow rates evaluated had no significant effect. It was possible to achieve astaxanthin recoveries of 95% after 175 min for a CO₂ flow rate of 2 L/min, and 95 min for CO₂ flow rate of 4 L/min. The ω-6/ω-3 ratios obtained were similar in all conditions, reaching 0.87, demonstrating that the extracts from H. pluvialis by SFE are rich in unsaturated fatty acids (UFA) which increases their positive effects when used as a functional ingredient in food.     

Mechanophotonics: Flexible Single-Crystal Organic Waveguides and Circuits

We present the one-dimensional optical-waveguiding crystal dithieno[3,2-a:2′,3′-c]phenazine with a high aspect ratio, high mechanical flexibility, and selective self-absorbance of the blue part of its fluorescence (FL). While macrocrystals exhibit elasticity, microcrystals deposited at a glass surface behave more like plastic crystals due to significant surface adherence, making them suitable for constructing photonic circuits via micromechanical operation with an atomic-force-microscopy cantilever tip. The flexible crystalline waveguides display optical-path-dependent FL signals at the output termini in both straight and bent configurations, making them appropriate for wavelength-division multiplexing technologies. A reconfigurable 2×2-directional coupler fabricated via micromanipulation by combining two arc-shaped crystals splits the optical signal via evanescent coupling and delivers the signals at two output terminals with different splitting ratios. The presented mechanical micromanipulation technique could also be effectively extended to other flexible crystals.     

Phase-space tomography with a programmable Radon-Wigner display

We show the adaptation of a multifunctional optical system consisting of two spatial light modulators for the optimal measurement of the Radon-Wigner transform of one-dimensional signals. The proposed Radon-Wigner display allows reconstructing the Wigner distribution and the phase or the mutual intensity of fully or partially coherent fields, respectively. It is also suitable for the analysis of two-dimensional rotationally symmetric or separable in Cartesian coordinates optical fields. The feasibility of the proposed scheme is experimentally demonstrated in several examples.     

On the geometry of curves and conformal geodesics in the Möbius space

This article deals with the study of some properties of immersed curves in the conformal sphere \({\mathbb{Q}_n}\), viewed as a homogeneous space under the action of the Möbius group. After an overview on general well-known facts, we briefly focus on the links between Euclidean and conformal curvatures, in the spirit of F. Klein’s Erlangen program. The core of this article is the study of conformal geodesics, defined as the critical points of the conformal arclength functional. After writing down their Euler–Lagrange equations for any n, we prove an interesting codimension reduction, namely that every conformal geodesic in \({\mathbb{Q}_n}\) lies, in fact, in a totally umbilical 4-sphere \({\mathbb{Q}_4}\). We then extend and complete the work in Musso (Math Nachr 165:107–131, 1994) by solving the Euler–Lagrange equations for the curvatures and by providing an explicit expression even for those conformal geodesics not included in any conformal 3-sphere.     

Deformation and Flow Driven by Osmotic Processes in Porous Materials: Application to Bituminised Waste Materials

This paper presents a coupled Chemo-Hydro-Mechanical (CHM) analysis of the behaviour of leached Bituminized Waste materials (BW). Under geological disposal conditions the main factor that affects the long-term behaviour of this kind of materials is water uptake. First, the long-term behavior of BW in contact with water has been studied. A formulation has been proposed for the analysis of deformation induced by dissolution of salts in porous media in contact with water. The equations include the effect of coupled transport phenomena and the formulation has been included as an extension in the coupled THM program CODE_BRIGHT. The impact of osmotic forces on the swelling of the material has been investigated by simulating water uptake swelling tests under confined conditions. The numerical analysis has proven to be able to furnish a satisfactory representation of the main observed patterns of the behaviour. A sensitivity analysis has also been carried out to examine the effect of various key parameters.     

Novel Stereocontrolled Preparation of Amino Polyols from 2,3-Aziridine Alcohols

Starting from 2,3-aziridine alcohols, a novel and versatile preparation of optically active amino polyol was achieved using a simple strategy with few purification steps and a good overall yield.     

Targeting proteins to liquid-ordered domains in lipid membranes

We demonstrate the construction of novel protein-lipid assemblies through the design of a lipid-like molecule, DPIDA, endowed with tail-driven affinity for specific lipid membrane phases and head-driven affinity for specific proteins. In studies performed on giant unilamellar vesicles (GUVs) with varying mole fractions of dipalymitoylphosphatidylcholine (DPPC), cholesterol, and diphytanoylphosphatidyl choline (DPhPC), DPIDA selectively partitioned into the more ordered phases, either solid or liquid-ordered (L(o)) depending on membrane composition. Fluorescence imaging established the phase behavior of the resulting quaternary lipid system. Fluorescence correlation spectroscopy confirmed the fluidity of the L(o) phase containing DPIDA. In the presence of CuCl(2), the iminodiacetic acid (IDA) headgroup of DPIDA forms the Cu(II)-IDA complex that exhibits a high affinity for histidine residues. His-tagged proteins were bound specifically to domains enriched in DPIDA, demonstrating the capacity to target protein binding selectively to both solid and L(o) phases. Steric pressure from the crowding of surface-bound proteins transformed the domains into tubules with persistence lengths that depended on the phase state of the lipid domains.