Uniqueness and symmetry results for solutions of a mean field equation on 𝕊2 via a new bubbling phenomenon

Motivated by the study of gauge field vortices, we consider a mean field equation on the standard sphere 𝕊² involving a Dirac distribution supported at a point P ∈ 𝕊². Consistently with the physical applications, we show that solutions “concentrate” precisely around the point P for some limiting value of a given parameter. We use this fact to obtain symmetry (about the axis ) and uniqueness property for the solution. The presence of the Dirac measure makes such a task particularly delicate to handle from the analytical point of view. In fact, the bubbling phenomenon about the singularity allows the existence of solution sequences with a double‐peak profile near P. The new and more delicate part of this paper is to exclude this possibility by using the method of moving planes together with the Alexandrov‐Bol inequality. © 2011 Wiley Periodicals, Inc.     

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.     

On the nonlinear effects of the mean wind force on the galloping onset in shallow cables

Nonlinear Dynamics - The critical aeroelastic behavior of horizontal, suspended, and shallow cables is analyzed via a continuous model accounting for both external and internal damping....     

Characterization of Basil Volatile Fraction and Study of Its Agronomic Variation by ASCA

Basil is a plant known worldwide for its culinary and health attributes. It counts more than a hundred and fifty species and many more chemo-types due to its easy cross-breeds. Each species and each chemo-type have a typical aroma pattern and selecting the proper one is crucial for the food industry. Twelve basil varieties have been studied over three years (2018–2020), as have four different cuts. To characterize the aroma profile, nine typical basil flavour molecules have been selected using a gas chromatography–mass spectrometry coupled with an olfactometer (GC–MS/O). The concentrations of the nine selected molecules were measured by an ultra-fast CG e-nose and Principal Component Analysis (PCA) was applied to detect possible differences among the samples. The PCA results highlighted differences between harvesting years, mainly for 2018, whereas no observable clusters were found concerning varieties and cuts, probably due to the combined effects of the investigated factors. For this reason, the ANOVA Simultaneous Component Analysis (ASCA) methodology was applied on a balanced a posteriori designed dataset. All the considered factors and interactions were statistically significant (p < 0.05) in explaining differences between the basil aroma profiles, with more relevant effects of variety and year.     

Modified edge finite elements for photonic crystals

We consider Maxwell’s equations with periodic coefficients as it is usually done for the modeling of photonic crystals. Using Bloch/Floquet theory, the problem reduces in a standard way to a modification of the Maxwell cavity eigenproblem with periodic boundary conditions. Following [8], a modification of edge finite elements is considered for the approximation of the band gap. The method can be used with meshes of tetrahedrons or parallelepipeds. A rigorous analysis of convergence is presented, together with some preliminary numerical results in 2D, which fully confirm the robustness of the method. The analysis uses well established results on the discrete compactness for edge elements, together with new sharper interpolation estimates.     

Behaviour of Bu(CH2—CHCH2)SnCl2 in water and water-cosolvent media: An approach to understanding the chemical degradation of organotins in aquatic environments

The behaviour of allylbutyltin dichloride in water, water–ethanol and water–hexane media, under either homogeneous or heterogeneous conditions, has been studied. 1,3-Diallyl-1,3-dibutyl-1,3-dichlorodistannoxane, butyltin di(hydroxy)chloride and butyltin trichloride arise from the solvolytic, acid–base and degradation processes. The degradation process involving the cleavage of the tin–carbon allyl bond has been interpreted to occur via an intramolecular reaction at the expense of the cation [Bu(CH₂=CHCH₂)Sn(OH)(H₂O)_n]⁺. The mechanistic pathway is ascribable to an internal interaction of the electrophilic cation with a bonded water molecule. This mechanistic proposal may be of some help with understanding of the chemical degradation of diorganotin derivatives in aquatic environments.     

A convenient synthesis of unsymmetrically substituted terphenyls of biologically active stilbenes via a double Suzuki cross-coupling protocol

A double Suzuki cross-coupling protocol has been devised as a practical route to a variety of terphenyls. Good chemoselectivity was observed. Unsymmetrically substituted triphenylenes were also easily prepared.     

Evidence of nuclear motion in H<Subscript>2</Subscript>-like molecules by means of high harmonic generation

The dynamics of hydrogen-like molecules is investigated beyond the usual fixed nuclei approximation. The nuclear motion introduces in the familiar spectrum of emitted radiation additional regular lines whose separation is essentially given by the vibrational frequency of nuclear motion. A wavelet analysis of the emitted spectrum shows that the intensity of the harmonic lines is modulated with the same period of the nuclear motion; this suggests the possibility of the real-time control of the nuclear dynamics.     

An electroanalytical investigation of the olefin isomerization reaction promoted by electrogenerated cationic nickel(I) complexes

Summary Evidence for the ability of the electrogenerated cationic nickel(I) complex [Ni(PPh₃)₄]⁺ to promote the isomerization of allylbenzene is reported. However, the corresponding triethylphosphitenickel(I) complex displays no catalytic activity, apparently due to the poor leavinggroup character exhibited by the phosphite. The involvement of a -allylnickel hydride in the isomerization reaction is inferred from a comparison of the results obtained with those for the same reaction promoted by nickel hydride.