Hardy spaces and Laguerre expansions on the dual of the Heisenberg group

Sia D il dominio di Siegel e H_n il gruppo di Heisenberg. Si considera il sistema ortogonale ottenuto dai monomi normalizzati delta palla unitaria di ⁿ⁺¹ tramite la trasformata di Cayley. La trasformata di Fourier di tali funzioni ristrette ad H_n viene esplicitamente calcolata. Rispetto alla base di Hermite di L²( ⁿ ), si ottengono operatori di rango uno espressi in termini di funzioni di Laguerre.     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.     

Characterization and Valorization of the Agricultural Waste Obtained from Lavandula Steam Distillation for Its Reuse in the Food and Pharmaceutical Fields

The main focus of the current research was the characterization of the by-products from the steam distillation of Lavandula angustifolia Mill. (LA) and Lavandula x intermedia Emeric ex Loisel (LI) aerial parts, as they are important sources of bioactive compounds suitable for several applications in the food, cosmetic, and pharmaceutical industries. The oil-exhausted biomasses were extracted and the total polyphenol and flavonoid contents were, respectively, 19.22 ± 4.16 and 1.56 ± 0.21 mg/g for LA extract and 17.06 ± 3.31 and 1.41 ± 0.10 mg/g for LI extract. The qualitative analysis by liquid chromatography-electrospray tandem mass spectrometry (HPLC-ESI-MS) revealed that both the extracts were rich in phenolic acids and glycosylated flavonoids. The extracts exhibited radical scavenging, chelating, reducing activities, and inhibitory capacities on acetylcholinesterase and tyrosinase. The IC50 values against acetylcholinesterase and tyrosinase were, respectively, 5.35 ± 0.47 and 5.26 ± 0.02 mg/mL for LA, and 6.67 ± 0.12 and 6.56 ± 0.16 mg/mL for LI extracts. In conclusion, the oil-exhausted biomasses demonstrated to represent important sources of bioactive compounds, suitable for several applications in the food, cosmetic, and pharmaceutical industries.     

A Continuous-Time Random Walk Extension of the Gillis Model

We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional non-homogeneous random walk with a position-dependent drift known in the mathematical literature as Gillis random walk. This modified stochastic process allows to significantly change local, non-local and transport properties in the presence of heavy-tailed waiting-time distributions lacking the first moment: we provide here exact results concerning hitting times, first-time events, survival probabilities, occupation times, the moments spectrum and the statistics of records. Specifically, normal diffusion gives way to subdiffusion and we are witnessing the breaking of ergodicity. Furthermore we also test our theoretical predictions with numerical simulations.     

Flexible conducting polymer transistors with supercapacitor function

Planar organic electrochemical transistors (OECTs) using PEDOT:PSS as the channel material and nanostructured carbon (nsC) as the gate electrode material and poly(sodium 4‐styrenesulfonate (PSSNa) gel as the electrolyte were fabricated on flexible polyethylene terephthalate (Mylar^®) substrates. The nsC was deposited at room‐temperature by supersonic cluster beam deposition (SCBD). Interestingly, the OECT acts as a hybrid supercapacitor (to give a device that we indicate as transcap). The energy storage ability of transcaps has been studied with two cell configurations: one featuring PEDOT:PSS as the positive electrode and nsC as the negative electrode and another configuration with reversed electrode polarity. Potentiostatic charge/discharge studies show that both supercapacitors show good performance in terms of voltage retention, in particular, when PEDOT:PSS is used as the positive electrode. Galvanostatic charge–discharge characteristics show typical symmetric triangular shape, indicating a nearly ideal capacitive behavior with a high columbic efficiency (close to 100%). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 96–103     

Absolute and relative cut-off in adaptive approximation by wavelets

Given the wavelet expansion of a function v, a non-linear adaptive approximation of v is obtained by neglecting those coefficients whose size drops below a certain threshold. We propose several ways to define the threshold: all are based on the characterization of the local regularity of v (in a Sobolev or Besov scale) in terms of summability of properly defined subsets of its coefficients. A-priori estimates of the approximation error are derived. For the Haar system the asymptotic behavior of both the approximation error and the number of survived coefficients is thoroughly investigated for a class of functions having Hölder-type singularities.     

The N-terminal 1-16 peptide derived in vivo from protein seminal vesicle protein IV modulates alpha-thrombin activity: potential clinical implications

We have previously shown that seminal vesicle protein IV (SV-IV) and its 1-70 N-terminal fragment have anti-inflammatory activity and modulate anti-thrombin III (AT) activity. Moreover, mass spectrometry analysis of purified SV-IV has shown that the protein was found to be highly heterogeneous and 14% of the total SV-IV molecules are truncated forms, of particular interest the 1-16, 1-17, and 1-18 peptides. In this work we report experimental data which demonstrate that the 1-16 peptide (P1-16) possesses a marked effect on the AT activity by preventing the formation of the thrombin-AT complex. We found that the formation of thrombin-AT complex is markedly decreased in the presence of P1-16 used at equimolar concentration with thrombin as evaluated with SDS-PAGE. We also monitored the conformational changes of thrombin in the presence of different P1-16 concentrations, and calculated the K(d) of thrombin/P1-16 system by circular dichroism technique. The probable interaction sites of P1-16 with thrombin have been also evaluated by molecular graphics and computational analyses. These results have potential implications in the treatment of sterility and thrombotic diseases.     

Integrated Conversion of Lignocellulosic Biomass to Bio-Based Amphiphiles using a Functionalization-Defunctionalization Approach

Concerns over the sustainability and end-of-life properties of fossil-derived surfactants have driven interest in bio-based alternatives. Lignocellulosic biomass with its polar functional groups is an obvious feedstock for surfactant production but its use is limited by process complexity and low yield. Here, we present a simple two-step approach to prepare bio-based amphiphiles directly from hemicellulose and lignin at high yields (29 % w/w based on the total raw biomass and >80 % w/w of these two fractions). Acetal functionalization of xylan and lignin with fatty aldehydes during fractionation introduced hydrophobic segments and subsequent defunctionalization by hydrogenolysis of the xylose derivatives or acidic hydrolysis of the lignin derivatives produced amphiphiles. The resulting biodegradable xylose acetals and/or ethers, and lignin-based amphiphilic polymers both largely retained their original natural structures, but exhibited competitive or superior surface activity in water/oil systems compared to common bio-based surfactants.     

The Astrochemical Observatory: Molecules in the Laboratory and in the Cosmos

Astrochemistry is a discipline consolidated recently, although its roots extend back to the dawn of early civilization with the observation and mapping of the sky. The way to the understanding of the common natural laws on earth and in space paved by Galilei's observations by the telescope, has been extended in the last decades, by new technologies such as radioastronomy and space missions. Plenty of new chemistry was surprisingly discovered. Extreme rich information on the chemical “composition” of the universe is being obtained, either from the other planets and satellites in the Solar System, from meteorites and comets, or from the interstellar space. In this article we will present selected topics regarding the chemical structures and reactions being discovered. Particular attention will be devoted to aspects considered as relevant for the prebiotic processes on earth, such as those involving chirality and its role played in the origin and evolution of life.