On the Classification of <Emphasis Type="Italic">N</Emphasis>-Points Concentrating Solutions for Mean Field Equations and the Symmetry Properties of the <Emphasis Type="Italic">N</Emphasis>-Vortex Singular Hamiltonian on the Unit Disk

Motivated by the analysis of the multiple bubbling phenomenon (Bartolucci et al. in Commun. Partial Differ. Equ. 29(7–8):1241–1265, 2004) for a singular mean field equation on the unit disk (Bartolucci and Montefusco in Nonlinearity 19:611–631, 2006), for any N≥3 we characterize a subset of the 2π/N-symmetric part of the critical set of the N-vortex singular Hamiltonian. In particular we prove that this critical subset is of saddle type. As a consequence of our result, and motivated by a recently posed open problem (Bartolucci et al. in Commun. Partial Differ. Equ. 29(7–8):1241–1265, 2004), we can prove the existence of a multiple bubbling sequence of solutions for the singular mean field equation.     

A new necessary and sufficient condition for the strong duality and the infinite dimensional Lagrange multiplier rule

Throughout this paper, the authors introduce a new condition, defined by Assumption  S^′$S^{\prime }$, which establishes a necessary and sufficient condition for the validity of the strong duality between a convex optimization problem and its Lagrange dual. This work will be focused on the context of emptiness of the interior of the ordering cone and convexity of the equality constraints. Moreover, this new condition will be necessary and sufficient for the infinite dimensional Lagrange multiplier rule. This new principle will find application to the elastic–plastic torsion problem, to the continuum model of transportation and to a problem with quadratic equality constraint with connected to evolutionary illumination and visibility problems.     

Angular and chromatic dispersion in Kerr-driven conical emission

We report measurements of ultrashort optical pulse filamentation in Kerr media with normal dispersion. We measure the angular dispersion of spontaneously generated colored conical emission and show that for large frequency shifts from the input pump frequency, it is well described by a relation between angle and frequency with slope determined solely by material chromatic dispersion. This measurement is in agreement with recent models that interpret filamentation dynamics in terms of the spontaneous formation of nonlinear X-waves. Finally, experimental results of filamentation in air show, for the first time, that the interpretation of CE in terms of X-waves may be also extended to gaseous media.     

On the absence of rapidly decaying solutions for parabolic operators whose coefficients are non-Lipschitz continuous in time

We find minimal regularity conditions on the coefficients of a parabolic operator, ensuring that no nontrivial solution tends to zero faster than any exponential.

     

Synthesis and Characterization of HgII/Se/CuI Multinuclear Compounds from Mercury(II) Bis(p‐aminobenzeneselenolate) – Hg(SeC6H4NH2‐p)2

In this paper we explore an amino functionalized selenolate unit for the synthesis of new multinuclear compounds with promising interesting properties and potential precursors of semiconductors. We present for the first time the X‐ray crystallographic structure of [Hg(SeC₆H₄NH₂)₂]₂ · diox ( 1· diox) and its copper(I) derivatives: HgCu₂X₂(SeC₆H₄NH₂)₂(PPh₃)₄ · 4diox [X = Br ( 2· 4diox) and I ( 3· 4diox)]. The compounds 1 and 2 , 3 can be considered as the starting material and intermediates, respectively, for the synthesis of ternary Hg^II/Se/Cu^I nanoclusters. We also provide IR and NMR spectroscopic data and evaluate the optical features of these compounds by difuse reflectance UV/Vis spectroscopy.     

The Hydrolysis of the Anhydride of 2-Cyano-2-phenylpropanoic Acid Triggers the Repeated Back and Forth Motions of an Acid–Base Operated Molecular Switch

This work aimed to render phenomenologically autonomous the otherwise stepwise operation of a catenane-based molecular switch, which is chemically triggered by the decarboxylation of 2-cyano-2-phenylpropanoic acid ( 2 ). Given that any amount of 2 in stoichiometric excess with respect to the catenane is consumed in a side reaction, the authors resorted to the corresponding anhydride 5 , the slow hydrolysis of which, due to adventitious water in dichloromethane, continuously produces in situ the actual fuel 2 . As a consequence, the machine does not require a reloading after each cycle, but switches back and forth as long as fuel is present.     

Ti3C2Tx-Modified PEDOT:PSS Hole-Transport Layer for Inverted Perovskite Solar Cells

PEDOT:PSS is a commonly used hole-transport layer (HTL) in inverted perovskite solar cells (PSCs) due to its compatibility with low-temperature solution processing. However, it possesses lower conductivity than other conductive polymers and metal oxides, along with surface defects, limiting its photovoltaic performance. In this study, we introduced two-dimensional Ti₃C₂T_x (MXene) as an additive in the PEDOT:PSS HTL with varying doping concentrations (i.e., 0, 0.03, 0.05, and 0.1 wt.%) to tune the electrical conductivity of PEDOT:PSS and to modify the properties of the perovskite film atop it. We noted that the grain size of the CH₃NH₃PbI₃ (MAPI₃) perovskite layer grown over an optimal concentration of MXene (0.03 wt.%)-doped PEDOT:PSS increased from 250 nm to 400 nm, reducing charge recombination due to fewer grain boundaries. Ultraviolet photoelectron spectroscopy (UPS) revealed increased work function (WF) from 4.43 eV to 4.99 eV with 0.03 wt.% MXene doping, making the extraction of holes easier due to a more favorable energy level alignment with the perovskite. Quantum chemical investigations based on density functional theory (DFT) were conducted at the ωB97XD/6-311++G(d,p) level of theory to provide more insight into the stability, bonding nature, and optoelectronic properties of the PEDOT:PSS–MXene system. The theoretical investigations revealed that the doping of PEDOT:PSS with Ti₃C₂T_x could cause a significant effect on the electronic properties of the HTL, as experimentally demonstrated by an increase in the electrical conductivity. Finally, the inverted PSCs employing 0.03 wt.% MXene-doped PEDOT:PSS showed an average power conversion efficiency (PCE) of 15.1%, up from 12.5% for a reference PSC employing a pristine PEDOT:PSS HTL. The champion device with a 0.03 wt.% MXene–PEDOT:PSS HTL achieved 15.5% PCE.     

Role of the Hydroxyl Radical-Generating System in the Estimation of the Antioxidant Activity of Plant Extracts by Electron Paramagnetic Resonance (EPR)

The scavenging activity of hydroxyl radicals, produced by the Fenton reaction, is commonly used to quantify the antioxidant capacity of plant extracts. In this study, three Fenton systems (Fe/phosphate buffer, Fe/quinolinic acid and Fe/phosphate buffer/quinolinic acid) and the thermal degradation of peroxydisulfate were used to produce hydroxyl radicals; the hydroxyl radical scavenging activity of plant extracts (ginger, blueberry juices and green tea infusion) and chemical compounds (EGCG and GA) was estimated by spin trapping with DMPO (5,5-dimethyl-1-pyrroline N-oxide) and EPR (Electron Paramagnetic Resonance) spectroscopy. Phosphate buffer was used to mimic the physiological pH of cellular systems, while quinolinic acid (pyridine-2,3-dicarboxylic acid) facilitates the experimental procedure by hindering the spontaneous oxidation of Fe(II). The EC₅₀ (the concentration of chemical compounds or plant extracts which halves the intensity of the DMPO–OH adduct) values were determined in all the systems. The results show that, for both the chemical compounds and the plant extracts, there is not a well-defined order for the EC₅₀ values determined in the four hydroxyl radical generating systems. The interactions of phosphate buffer and quinolinic acid with the antioxidants and with potential iron-coordinating ligands present in the plant extracts can justify the observed differences.