Geometric representation of the mean–variance–skewness portfolio frontier based upon the shortage function

The literature suggests that investors prefer portfolios based on mean, variance and skewness rather than portfolios based on mean–variance (MV) criteria solely. Furthermore, a small variety of methods have been proposed to determine mean–variance–skewness (MVS) optimal portfolios. Recently, the shortage function has been introduced as a measure of efficiency, allowing to characterize MVS optimal portfolios using non-parametric mathematical programming tools. While tracing the MV portfolio frontier has become trivial, the geometric representation of the MVS frontier is an open challenge. A hitherto unnoticed advantage of the shortage function is that it allows to geometrically represent the MVS portfolio frontier. The purpose of this contribution is to systematically develop geometric representations of the MVS portfolio frontier using the shortage function and related approaches.     

Combining the pair distribution function and computational methods to understand lithium insertion in Brookite (TiO2)

X-ray pair distribution function (PDF) methods and first-principles calculations have been combined to probe the structure of electrochemically lithiated TiO(2) Brookite. Traditional powder diffraction studies suggest that Brookite amorphizes upon lithium insertion, with the Bragg reflections disappearing. However, PDF analysis indicates that the TiO(2) framework connectivity is maintained throughout lithium intercalation, with expansions along the a and b axes. The Li(+) ions within the framework are poorly observed in the X-ray PDF, which is dominated by contributions from the more strongly scattering Ti and O atoms. First-principles calculations were used to identify energetically favorable Li(+) sites within the Brookite lattice and to develop a complete structural model of the lithiated material. This model replicates the local structure and decreased intermediate range order observed in the PDF data. The analysis suggests that local structural distortions of the TiO(2) lattice accommodate lithium in five-coordinate sites. This structural model is consistent with the observed electrochemical behavior.     

Sorption efficiency of a new sorbent towards uranyl: phosphonic acid grafted Merrifield resin

A novel sorbent resin consisting of a Phosphonic Acid grafted on Merrifield Resin (PA-MR) for the extraction of uranyl from nitrate media is described. The sorption behaviour of uranyl cation on PA-MR was investigated using batch equilibrium technique. The effects of parameters such as shaking speed, pH levels, contact time, metal concentrations, ionic strength and temperature were reported. The results show that the sorption capacity increases with increasing both initial uranyl ion concentration and temperature and decreases with increasing ionic strength. Therefore, the optimum condition for the present study should be using 6.6 mg adsorbent per 1.0 mg uranyl in solution with pH 3.6 and shaking at 250 rpm for 180 min. The adsorption behavior of the system was also investigated and found to be in line with Langmuir isotherm. The kinetic data was well described by the pseudo second-order. Thermodynamics data leads to endothermic process ∆H = + 31.03 kJ⁻¹ mol⁻¹, ∆S = + 146.64 J mol⁻¹ K⁻¹ and ∆G = −11.96 kJ mol⁻¹ at 20 K. ∆G decreased to negatives values with increasing temperature indicating that the process was more favoured at high temperature.     

Part two: Analytical optimisation of a procedure for lead detection in milk by means of bismuth-modified screen-printed electrodes

This work reports the optimisation of a new analytical method for lead ion detection in milk; the electrochemical detection scheme is based on the method that was described in Part I [1]. It features the use of a disposable, environmentally friendly bismuth film electrode to replace the traditionally used (toxic) mercury one while here we report an arduous development of sample treatment so that the simple device can be applied as a screening tool in many settings. For this purpose, a milk pre-treatment procedure by means of wet digestion with HCl, HClO₄, and H₂O₂ combined with an ultrasonic treatment was developed. The detection of lead ions in treated milk was then carried out using a disposable screen-printed electrode modified with Nafion^® and an “in situ” bismuth film, with the analysis being performed in anodic stripping voltammetry mode. The analytical method developed allows the detection of milk contaminated with lead ions at a concentration of 20 μg Kg⁻¹ (legal limit) and it can be proposed as a screening method for routine analysis of lead ions in milk with the advantage of employing inexpensive and portable instrumentation. Moreover, dedicated software supported by a portable instrument introduces procedures that are essential to avoid distortion from ambient lead contamination and also makes it possible for an unskilled operator to carry out each step of the analysis.     

Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold

We establish inequalities for the eigenvalues of the sub-Laplace operator associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR manifold. Our inequalities extend those obtained by Niu and Zhang (Pac J Math 208(2):325–345, 2003 [26]) for the Dirichlet eigenvalues of the sub-Laplacian on a bounded domain in the Heisenberg group and are in the spirit of the well known Payne–Pólya–Weinberger and Yang universal inequalities.     

A new class of lithium and sodium rechargeable batteries based on selenium and selenium-sulfur as a positive electrode

A new class of selenium and selenium-sulfur (Se(x)S(y))-based cathode materials for room temperature lithium and sodium batteries is reported. The structural mechanisms for Li/Na insertion in these electrodes were investigated using pair distribution function (PDF) analysis. Not only does the Se electrode show promising electrochemical performance with both Li and Na anodes, but the additional potential for mixed Se(x)S(y) systems allows for tunable electrodes, combining the high capacities of S-rich systems with the high electrical conductivity of the d-electron containing Se. Unlike the widely studied Li/S system, both Se and Se(x)S(y) can be cycled to high voltages (up to 4.6 V) without failure. Their high densities and voltage output offer greater volumetric energy densities than S-based batteries, opening possibilities for new energy storage systems that can enable electric vehicles and smart grids.     

Existence Results for Critical Semi-linear Equations on Heisenberg Group Domains

Following the work of G. Citti and F. Uguzzoni who studied Yamabe type problems on Heisenberg group domains, we consider here the following critical semi-linear equation on domains of the Heisenberg group ${{\mathbb{H}^1}}$ : $$(P) \left\{\begin{array}{lll}-{\Delta_{H}}u\quad =\quad K{u^{3}}\quad\,{\rm in}\,\,\Omega,\\ \quad\quad\,{u}\quad > \quad0\qquad\,\,\,\,{\rm in}\,\,\Omega,\\ \quad\quad\,{u}\quad = \quad 0 \quad\quad\,\,\,{\rm on}\,\partial \Omega, \end{array}\right. $$ where Δ _H is the sublaplacian on ${{\mathbb{H}^1}}$ and K is a C ³ positive function defined on Ω. Using a version of the Morse Lemma at infinity, we give necessary conditions on K to insure the existence of solutions for (P).     

Cytotoxicity of new secondary metabolites,fatty acids and tocols composition of seeds of Ducrosia anethifolia (DC.) Boiss

Two new monoterpene Ducrosin A (1) and sesquiterpene Ducrosin B (2) were isolated along with three known compounds, stigmasterol (3) and two furanocoumarins (4 and 5), from the dichloromethane extract of the seeds of Ducrosia anethifolia (DC.) Boiss. Their structures were determined using extensive 1D and 2D NMR, (ES)-HRMS and IR spectroscopic analyses and by comparison with literature data. Gas chromatography analysis of the fatty acids (FAs) of D. anethifolia seed oils (DAOs) showed high percentages of elaidic acid (C18:1 Δ9t) 65% and oleic acid (C18:1 Δ9c) 15%. The total tocopherol (tocols) content in DAOs was found to be 164 mg/100 g. The cytotoxic effect of the isolates was also evaluated using the MTT assay against the HCT-116 and SKOV-3 cell lines. The results showed that compound 2 was the most cytotoxic agent followed by compounds 1 and 4, which has an epoxide moiety that most likely contributes to its activity.     

Effect of Shear Flow on Nanoparticles Migration near Liquid Interfaces

The effect of shear flow on spherical nanoparticles (NPs) migration near a liquid–liquid interface is studied by numerical simulation. We have implemented a compact model through which we use the diffuse interface method for modeling the two fluids and the molecular dynamics method for the simulation of the motion of NPs. Two different cases regarding the state of the two fluids when introducing the NPs are investigated. First, we introduce the NPs randomly into the medium of the two immiscible liquids that are already separated, and the interface is formed between them. For this case, it is shown that before applying any shear flow, 30% of NPs are driven to the interface under the effect of the drag force resulting from the composition gradient between the two fluids at the interface. However, this percentage is increased to reach 66% under the effect of shear defined by a Péclet number Pe = 0.316. In this study, different shear rates are investigated in addition to different shearing times, and we show that both factors have a crucial effect regarding the migration of the NPs toward the interfacial region. In particular, a small shear rate applied for a long time will have approximately the same effect as a greater shear rate applied for a shorter time. In the second studied case, we introduce the NPs into the mixture of two fluids that are already mixed and before phase separation so that the NPs are introduced into the homogenous medium of the two fluids. For this case, we show that in the absence of shear, almost all NPs migrate to the interface during phase separation, whereas shearing has a negative result, mainly because it affects the phase separation.