Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te

An Analytic Approach to the Wave Packet Formalism in Oscillation Phenomena

We introduce an approximation scheme to perform an analytic study of the oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian wave packets, we show that the oscillation is bounded by a time-dependent vanishing function which characterizes the slippage between the mass-eigenstate wave packets. We also demonstrate that the wave packet spreading represents a secondary effect which plays a significant role only in the non-relativistic limit. In our analysis, we note the presence of a new time-dependent phase and calculate how this additional term modifies the oscillating character of the flavor conversion formula. Finally, by considering Box and Sine wave packets we study how the choice of different functions to describe the particle localization changes the oscillation probability.Comment: 16 pages, 7 figures, AMS-Te

Phytochemical Characterization of Citrus-Based Products Supporting Their Antioxidant Effect and Sensory Quality

The increasing attention on the impact of food on human and environmental health has led to a greater awareness about nutrition, food processing, and food waste. In this perspective, the present work deals with the investigation of the chemical non-volatile and volatile profiles of two Citrus-based products, produced through a conscious process, using Citrus peels as natural gelling agents. Moreover, the total polyphenol content (TPC) and the antioxidant properties were evaluated, as well as their sensorial properties. Chemical and antioxidant results were compared with those of Citrus fresh fruits (C. reticulata, C. sinensis, and C. limon). Concerning the non-volatile fingerprint, the two samples showed a very similar composition, characterized by flavanones (naringenin, hesperetin, and eriodyctiol O-glycosides), flavones (diosmetin and apigenin C-glucosides), and limonoids (limonin, nomilinic acid, and its glucoside). The amount of both flavonoids and limonoids was higher in the Lemon product than in the Mixed Citrus one, as well as the TPC and the antioxidant activity. The aroma composition of the two samples was characterized by monoterpene hydrocarbons as the main chemical class, mainly represented by limonene. The sensorial analysis, finally, evidenced a good quality of both the products. These results showed that the most representative components of Citrus fruits persist even after the transformation process, and the aroma and sensorial properties endow an added value to Citrus preparations

Remarks upon the mass oscillation formulas

The standard formula for mass oscillations is often based upon the approximation $t \approx L$ and the hypotheses that neutrinos have been produced with a definite momentum $p$ or, alternatively, with definite energy $E$. This represents an inconsistent scenario and gives an unjustified reduction by a factor of two in the mass oscillation formulas. Such an ambiguity has been a matter of speculations and mistakes in discussing flavour oscillations. We present a series of results and show how the problem of the factor two in the oscillation length is not a consequence of gedanken experiments, i.e. oscillations in time. The common velocity scenario yields the maximum simplicity.Comment: 9 pages, AMS-Te

The HERMES Dual-Radiator Ring Imaging Cerenkov Detector

The construction and use of a dual radiator Ring Imaging Cerenkov(RICH) detector is described. This instrument was developed for the HERMES experiment at DESY which emphasizes measurements of semi-inclusive deep-inelastic scattering. It provides particle identification for pions, kaons, and protons in the momentum range from 2 to 15 GeV, which is essential to these studies. The instrument uses two radiators, C4F10, a heavy fluorocarbon gas, and a wall of silica aerogel tiles. The use of aerogel in a RICH detector has only recently become possible with the development of clear, large homogeneous and hydrophobic aerogel. A lightweight mirror was constructed using a newly perfected technique to make resin-coated carbon-fiber surfaces of optical quality. The photon detector consists of 1934 photomultiplier tubes for each detector half, held in a soft steel matrix to provide shielding against the residual field of the main spectrometer magnet.Comment: 25 pages, 23 figure

Timelapse

We discuss the existence in an arbitrary frame of a finite time for the transformation of an initial quantum state into another e.g. in a decay. This leads to the introduction of a timelapse $\tilde{\tau}$ in analogy with the lifetime of a particle. An argument based upon the Heisenberg uncertainty principle suggests the value of $\tilde{\tau}=1 / M_0$. Consequences for the exponential decay formula and the modifications that $\tilde{\tau}$ introduces into the Breit-Wigner mass formula are described.Comment: 5 pages [2 figs], ReV-Te

Jellyfish Polysaccharides for Wound Healing Applications

Jellyfishes are considered a new potential resource in food, pharmaceutical and biomedical industries. In these latter cases, they are studied as source of active principles but are also exploited to produce marine collagen. In the present work, jellyfish skin polysaccharides (JSP) with glycosaminoglycan (GAG) features were extracted from Rhizostoma pulmo, a main blooming species of Mediterranean Sea, massively augmented by climate leaded “jellyfishication” of the sea. Two main fractions of R. pulmo JSP (RP-JSPs) were isolated and characterized, namely a neutral fraction (RP-JSP1) and a sulphate rich, negatively charged fraction (RP-JSP2). The two fractions have average molecular weights of 121 kDa and 590 kDa, respectively. Their sugar composition was evaluated through LC-MS analysis and the result confirmed the presence of typical GAG saccharides, such as glucose, galactose, glucosamine and galactosamine. Their use as promoters of wound healing was evaluated through in vitro scratch assay on murine fibroblast cell line (BALB/3T3 clone A31) and human keratinocytes (HaCaT). Both RP-JSPs demonstrated an effective confluency rate activity leading to 80% of scratch repair in two days, promoting both cell migration and proliferation. Additionally, RP-JSPs exerted a substantial protection from oxidative stress, resulting in improved viability of treated fibroblasts exposed to H2O2. The isolated GAG-like polysaccharides appear promising as functional component for biomedical skin treatments, as well as for future exploitation as pharmaceutical excipients

Performance of the Two Aerogel Cherenkov Detectors of the JLab Hall A Hadron Spectrometer

We report on the design and commissioning of two silica aerogel Cherenkov detectors with different refractive indices. In particular, extraordinary performance in terms of the number of detected photoelectrons was achieved through an appropriate choice of PMT type and reflector, along with some design considerations. After four years of operation, the number of detected photoelectrons was found to be noticeably reduced in both detectors as a result of contamination, yellowing, of the aerogel material. Along with the details of the set-up, we illustrate the characteristics of the detectors during different time periods and the probable causes of the contamination. In particular we show that the replacement of the contaminated aerogel and parts of the reflecting material has almost restored the initial performance of the detectors.Comment: 18 pages, 9 Figures, 4 Tables, 44 Reference

Strong Correlations in a nutshell

We present the phase diagram of clusters made of two, three and four coupled Anderson impurities. All three clusters share qualitatively similar phase diagrams that include Kondo screened and unscreened regimes separated by almost critical crossover regions reflecting the proximity to barely avoided critical points. This suggests the emergence of universal paradigms that apply to clusters of arbitrary size. We discuss how these crossover regions of the impurity models might affect the approach to the Mott transition within a cluster extension of dynamical mean field theory.Comment: 45 pages, 14 figures. To appear in Journal of Physics: Condensed Matte

Double Quantum Dots as Detectors of High-Frequency Quantum Noise in Mesoscopic Conductors

We propose a measurement set-up for detecting quantum noise over a wide frequency range using inelastic transitions in a tunable two-level system as a detector. The frequency-resolving detector consists of a double quantum dot which is capacitively coupled to the leads of a nearby mesoscopic conductor. The inelastic current through the double quantum dot is calculated in response to equilibrium and non-equilibrium current fluctuations in the nearby conductor, including vacuum fluctuations at very low temperatures. As a specific example, the fluctuations across a quantum point contact are discussed.Comment: 4 pages, 4 figures. Final version to appear in Physical Review Letter