On a Sufficient Condition for Weak Sharp Efficiency in Multiobjective Optimization

In this paper, we provide sufficient conditions entailing the existence of weak sharp efficient points of a multiobjective optimization problem. The approach uses variational analysis techniques, like regularity and subregularity of the diagonal subdifferential map related to a suitable scalar equilibrium problem naturally associated to the multiobjective optimization problem.     

On 3-way combinatorial identities

In this paper, we provide combinatorial meanings to two generalized basic series with the aid of associated lattice paths. These results produce two new classes of infinite 3-way combinatorial identities. Five particular cases are also discussed. These particular cases provide new combinatorial versions of Göllnitz–Gordon identities and Göllnitz identity. Seven q-identities of Slater and five q-identities of Rogers are further explored using the same combinatorial object. These results are an extension of the work of Goyal and Agarwal (Utilitas Math. 95 (2014) 141–148), Agarwal and Rana (Utilitas Math. 79 (2009) 145–155), and Agarwal (J. Number Theory 28 (1988) 299–305).     

Brownian Particle in a Poisson-Shot-Noise Active Bath: Exact Statistics,Effective Temperature,and Inference

The dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles is studied. The particle moves in a harmonic potential and experiences Poisson shot-noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker–Planck equation for the particle dynamics, the stationary solution for the displacement distribution is derived along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite-time first and second moments. An effective temperature is also computed through the fluctuation–dissipation theorem and show that equipartition theorem holds for all zero-mean kick distributions, including those leading to non-Gaussian stationary statistics. For the case of Gaussian-distributed active kicks, a re-entrant behavior from non-Gaussian to Gaussian stationary states and a heavy-tailed leptokurtic distribution across a wide range of parameters are found as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross-correlation functions. Fruits of the work is the development of an compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot-noise solely from the statistics the particle position.     

Analysis of the interface configuration and flow characteristics in tanks in a multiphase liquid–gas system using numerical simulation

A multiphase study was conducted using a turbulence model of large eddy simulation to investigate the interaction between the gaseous phase and the interface and its respective behaviour until the liquid phase movement was established, first in the near interface, as well as the presence of turbulent structures in the study of transport between phases. The results are shown for three surface configurations: a surface with waves in which the Reynolds number and friction velocity of the gaseous phase are, respectively, 210 and 0.25 m/s; a surface with small undulations, 86 and 0.10 m/s; and a flat surface, 43 and 0.05 m/s. Coherent structures are detected on both sides of the interface; these are intensified and less elongated for larger Reynolds numbers. Additionally, the interface exhibits distinct behaviour with regard to the examined phases. For the gaseous phase, it behaves like a no-slip surface.     

Volatolomics of Sardinian and Spanish Bituminaria: Characterization of Different Accessions Using Chemometrics

The present study aims to determine the volatile compositions of 15 different accessions of native Sardinian populations of Bituminaria morisiana (Pignatti & Metlesics) Greuter, Bituminaria bituminosa (L.) C. H. Stirt. (B. b.), and Spanish native accessions of B. bituminosa. Furthermore, we particularly focused on the essential oil characterization of these accessions and discriminated within populations with low furocoumarin content useful for fodder production in Mediterranean environments or furocoumarin extraction for pharmaceutical utilization. The plant extracts were analyzed by GC/MS, showing great variability in the content and composition. No differences were found in Bituminaria bituminosa (L.) C.H. Stirt. var. bituminosa essential oils, while the varieties Bituminaria bituminosa (L.) C.H. Stirt. var. crassiuscula P. Méndez, Fern. Galván & A. Santos and Bituminaria bituminosa (L.) C.H. Stirt. var. albomarginata P. Méndez, Fern. Galván & A. Santos are characterized by the presence of a high concentration of long-chain alcohols and of salicylic acid benzylic ester. In B. bituminosa var. albomarginata, we observed a different profile with predominance of a large concentration of alcohols as dodecanol and tetradecanol. The endemic B. morisiana can be identified for the predominant presence of farnesene. In methanolic fractions, we detected the presence of maltol, methyl citrate, methyl cumarate, santonin, and methyl linoleate. B. morisiana showed a low content of psoralens, and the accession of B. morisiana, from Siliqua indicated the presence of apocynin.     

Dynamical Instability Causes the Demise of a Supercooled Tetrahedral Liquid

We investigate the relaxation mechanism of a supercooled tetrahedral liquid at its limit of stability using isothermal isobaric (NPT) Monte Carlo simulations. In similarity with systems which are far from equilibrium but near the onset of jamming (O’Hern et al. in Phys Rev Lett 93:165702, 2004), we find that the relaxation is characterized by two time-scales: the decay of long-wavelength (slow) fluctuations of potential energy is controlled by the slope \([\partial (G/N)/\partial \phi ]\) of the Gibbs free energy (G) at a unique value of per particle potential energy \(\phi = \phi _{{\tiny mid}}\). The short-wavelength (fast) fluctuations are controlled by the bath temperature T. The relaxation of the supercooled liquid is initiated with a dynamical crossover after which the potential energy fluctuations are biased towards values progressively lesser than \(\phi _{{\tiny mid}}\). The dynamical crossover leads to the change of time-scale, i.e., the decay of long-wavelength potential energy fluctuations (intermediate stage of relaxation). Because of the condition [\(\partial ^2 (G/N)/\partial \phi ^2 = 0\)] at \(\phi = \phi _{{\tiny mid}}\), the slope \([\partial (G/N)/\partial \phi ]\) has a unique value and governs the intermediate stage of relaxation, which ends just after the crossover. In the subsequent stage, there is a relatively rapid crystallization due to lack of long-wavelength fluctuations and the instability at \(\phi _{{\tiny mid}}\), i.e., the condition that G decreases as configurations with potential energies lower than \(\phi _{{\tiny mid}}\) are accessed. The dynamical crossover point and the associated change in the time-scale of fluctuations is found to be consistent with the previous studies.     

Synthesis of novel 2,3-dihydro-4-pyridinones from bisdemethoxycurcumin under microwave irradiation

A novel synthesis of 2,3-dihydro-4-pyridinones via the reaction of bisdemethoxycurcumin and primary amines or amine acetates is demonstrated. The structures of the products were established by elemental analysis and from mass, ¹H and ¹³C NMR spectra.     

Enzymatic degradation of 3D scaffolds of starch-poly-(?-caprolactone) prepared by supercritical fluid technology

Starch-based polymers have been proposed for different tissue engineering applications due to their inherent properties. In this work, a polymeric blend of starch-poly-(?-caprolactone) (SPCL) was processed using supercritical fluid technology, namely, by supercritical assisted phase inversion. As SPCL is a biodegradable polymer, the matrices produced are susceptible of undergoing enzymatic degradation upon implantation in the human body. In vitro assessment of the enzymatic degradation of SPCL was carried out in different buffer solutions containing α-amylase and/or lipase. The effect of the presence of these enzymes was studied by monitoring different parameters in order to characterise both bulk and the surface of the scaffolds. As regards to bulk analysis, weight loss of the samples incubated for 1, 3, 7, 14 and 21 days was determined, further differential scanning calorimetry was carried out. The morphology of the scaffolds after these periods was analysed by micro-computed tomography (μ-CT) and surface chemistry was characterised by infra-red spectroscopy and contact angle measurements. Results suggest that SPLC scaffolds undergo bulk degradation, which is typically characterised by hydrolysis of chemical bonds in the polymer chain at the centre of the matrix, resulting in a highly porous material.     

Electron transfer processes on Ag and Au clusters supported on TiO2(110) and cluster size effects

The results of a detailed study of Li(+) neutralization in scattering on Ag and Au clusters and thin films supported on TiO(2) are presented. A very efficient neutralization is observed on small clusters with a decrease for the smallest clusters. These results closely follow the size-effects observed in the reactivity of these systems. The energy dependence of the neutralization was studied for the larger clusters (>4 nm) and observed to be similar in trend to the one observed on films and bulk (111) crystals. A general discussion of possible reasons of the enhancement in neutralization is presented and these changes are then tentatively discussed in terms of progressive modifications in the electronic structure of clusters as a function of reduction in size and as it evolves from metallic-like to discretised states. The highest neutralization efficiency would appear to correspond to clusters sizes for which a metal to nonmetal transition occurs. The relative position of the Li level and the highest occupied molecular orbital in the molecular cluster can be expected to strongly affect the electron transfer processes, which in this case should be described in a molecular framework.     

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C²-functions equipped with the Whitney Topology. To accomplish this, we combine Baire’s Lemma and the usual Transversality Theorem.