David Hull

Journal of Optimization Theory and Applications -     

George Leitmann

Journal of Optimization Theory and Applications -     

Tips and Tricks for the Surface Engineering of Well-Ordered Morphologically Driven Silver-Based Nanomaterials

Particularly-shaped silver nanostructures are successfully applied in many scientific fields, such as nanotechnology, catalysis, (nano)engineering, optoelectronics, and sensing. In recent years, the production of shape-controlled silver-based nanostructures and the knowledge around this topic has grown significantly. Hence, on the basis of the most recent results reported in the literature, a critical analysis around the driving forces behind the synthesis of such nanostructures are proposed herein, pointing out the important role of surface-regulating agents in driving crystalline growth by favoring (or opposing) development along specific directions. Additionally, growth mechanisms of the different morphologies considered here are discussed in depth, and critical points highlighted.     

Fluorescent macrocyclic chemosensor for Zn(II) detection at alkaline pH values

ABSTRACT

The new macrocyclic ligand L (28,29-dimethoxy-27-oxa-8,11,14,17,25,26-hexaazatetracyclo[22.2.1.1(2,6).1(19,23)]nonacosa-2,4,6(28),19,21,23(29),24,26(1)-octaene) has been synthesised. It contains a tetramine chain and the 2,5-bis(2-methoxy-3-metyl-phenyl)-1,3,4-oxadiazole (PPD-OMe) chromophore, acting as coordinating and sensing units, respectively.

The fluorescent emission of L depends on the pH being highly fluorescent at pH = 2 and not emitting from pH >10. The studies highlighted that L is a PET mediated emitting chemosensor, being the PET effect regulated by the degree of the tetraamine protonation.

L coordinates metal ions (Cu(II), Zn(II) and Cd(II)) in water giving rise to an OFF-ON fluorescent response for the presence of Zn(II) ion thus signalling its presence in the medium. This response is particularly notable at pH = 9 allowing to extend the Zn(II) sensing also in the alkaline pH field.     

Approximate Entropy of Brain Network in the Study of Hemispheric Differences

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments.     

pH-Dependent Hydration Change in a Gd-Based MRI Contrast Agent with a Phosphonated Ligand

The heptadentate ligand L was shown to form an extremely stable Gd complex at neutral pH with a pGd value of 18.4 at pH 7.4. The X-ray crystal structures of the complexes formed with Gd and Tb displayed two very different coordination behaviors being, respectively, octa- and nonacoordinated. The relaxometric properties of the Gd complex were studied by field-dependent relaxivity measurements at various temperatures and by ¹⁷O NMR spectroscopy. The pH-dependence of the longitudinal relaxivity profile indicated large changes around neutral pH leading to a very large value of 10.1 mm ⁻¹⋅s⁻¹ (60 MHz, 298 K) at pH 4.7. The changes were attributed to an increase of the hydration number from one water molecule in basic conditions to two at acidic pH. A similar trend was observed for the luminescence of the Eu complex, confirming the change in hydration state. DOSY experiments were performed on the Lu analogue, pointing to the absence of dimers in solution in the considered pH range. A breathing mode of the complex was postulated, which was further supported by ¹H and ³¹P NMR spectroscopy of the Yb complex at varying pH and was finally modeled by DFT calculations.     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

The Skew Normal multivariate risk measurement framework

Computational Management Science - In this paper, we consider a random vector $$X=\left( X_1,X_2\right) $$ following a multivariate Skew Normal distribution and we provide an explicit formula for...