Synthesis,spectroscopic, DFT,biological studies and molecular docking of oxovanadium (IV), copper (II) and iron (III) complexes of a new hydrazone derived from heterocyclic hydrazide

A new Schiff base hydrazone (Z)‐2‐(2‐aminothiazol‐4‐yl)‐N′‐(2‐hydroxy‐3‐methoxybenzylidene) acetohydrazide (H₂L) and its chelates [VO (HL)₂]·5H₂O, [Cu (HL)Cl(H₂O)]·2H₂O and [Fe(L)Cl(H₂O)₂]·3H₂O have been isolated and characterized using different physico‐chemical methods, for example infrared (IR), electron paramagnetic resonance (EPR), thermogravimetric analysis and DTG in the solid state, and ¹H‐NMR, ¹³C‐NMR and UV in solution. Magnetic and UV–visible measurements proposed that the coordination environments are square pyramidal, tetrahedral and octahedral geometries for oxovanadium (IV), Cu (II) and Fe (III), respectively. The ligand acts as mono‐negative NO towards oxovanadium (IV) and Cu (II) ions, and bi‐negative ONO for Fe (III) ion. The geometries of the ligand and its complexes were performed using Gaussian 9 program with density functional theory. The EPR spectral data of oxovanadium (IV) and Cu (II) chelates confirmed the mentioned geometries. The molecular modeling was done, and illustrated bond lengths, bond angles, molecular electrostatic potential, Mulliken atomic charges and chemical reactivity for the inspected compounds. Theoretical IR and ¹H‐NMR of the free ligand were calculated. Furthermore, thermodynamic and kinetic parameters for thermal decomposition steps were studied. Docking study of H₂L was applied against the proteins of both bacterial strains Staphylococcus aureus and Escherichia coli, as well as the protein of xanthine oxidase as antioxidant agent by Schrödinger suite program utilizing XP glide protocol. Furthermore, antimicrobial, antioxidant and DNA‐binding activities of the compounds have been carried out.     

Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

Birnbaum‐Saunders distribution: A review of models,analysis, and applications

Birnbaum and Saunders introduced a two‐parameter lifetime distribution to model the fatigue life of a metal, subject to cyclic stress. Since then, extensive work has been done on this model providing different interpretations, constructions, generalizations, inferential methods, and extensions to bivariate, multivariate, and matrix‐variate cases. More than 200 papers and one research monograph have already appeared describing all these aspects and developments. In this paper, we provide a detailed review of all these developments and, at the same time, indicate several open problems that could be considered for further research.     

Targeted Construction of Amorphous MoSx with an Inherent Chain Molecular Structure for Improved Pseudocapacitive Lithium-Ion Response

Owing to low ion/electron conductivity and large volume change, transitional metal dichalcogenides (TMDs) suffer from inferior cycle stability and rate capability when used as the anode of lithium-ion batteries (LIBs). To overcome these disadvantages, amorphous molybdenum sulfide (MoS_x) nanospheres were prepared and coated with an ultrathin carbon layer through a simple one-pot reaction. Combining X-ray photoelectron spectroscopy (XPS) with theoretical calculations, MoS_x was confirmed as having a special chain molecular structure with two forms of S bonding (S²⁻ and S₂²⁻), the optimal adsorption sites of Li⁺ were located at S₂²⁻. As a result, the MoS_x electrode exhibits superior cycle and rate capacities compared with crystalline 2H-MoS₂ (e.g., delivering a high capacity of 612.4 mAh g⁻¹ after 500 cycles at 1 A g⁻¹). This is mainly attributed to more exposed active S₂²⁻ sites for Li storage, more Li⁺ transfer pathways for improved ion conductivity, and suppressed electrode structure pulverization of MoS_x derived from the inherent chain-like molecular structure. Quantitative charge storage analysis further demonstrates the improved pseudocapacitive contribution of amorphous MoS_x induced by fast reaction kinetics. Moreover, the morphology contrast after cycling demonstrates the dispersion of active materials is more uniform for MoS_x than 2H-MoS₂, suggesting the MoS_x can well accommodate the volume stress of the electrode during discharging. Through regulating the molecular structure, this work provides an effective targeted strategy to overcome the intrinsic issues of TMDs for high-performance LIBs.     

Impact of C=C/B−N Replacement on the Diels–Alder Reactivity of Curved Polycyclic Aromatic Hydrocarbons

The influence of the replacement of C=C bonds by isoelectronic B−N moieties on the reactivity of π-curved polycyclic aromatic hydrocarbons has been computationally explored by means of density functional theory calculations. To this end, we selected the Diels–Alder cycloaddition reactions of the parent corannulene and its BN-doped counterparts with either cyclopentadiene or maleic anhydride. In addition, the analogous reactions involving larger buckybowls, such as BN-hemifullerene, BN-circumtrindene, and BN-fullerene, have been also considered. It has been found that whereas corannulene behaves as a dienophile, its BN counterpart better acts as a diene. In contrast, the larger BN-curved systems cannot be used as dienes in Diels–Alder reactions, but undergo facile (i.e., low barrier) cycloaddition reactions with cyclopentadiene. The observed trends in reactivity, which cannot be directly explained by using typical frontier molecular orbital arguments, are quantitatively described in detail by means of state-of-the-art computational methods, namely the activation strain model of reactivity combined with the energy decomposition analysis method. The results of our calculations highlight the crucial role of the curvature of the system on the reactivity and its influence on the strength of the orbital interactions between the deformed reactants during their transformations.     

“Dial-In” Emission from a Unique Flexible Material with Polarization Tuneable Spectral Intensity

The development of organic photoluminescent materials, which show promising roles as catalysts, sensors, organic light-emitting diodes, logic gates, etc., is a major demand and challenge for the global scientific community. In this context, a photoclick polymerization method is adopted for the growth of a unique photoluminescent three-dimensional (3D) polymer film, E, as a model system that shows emission tunability over the range 350–650 nm against the excitation range 295–425 nm. The DFT analysis of energy calculations and π-stacking supports the spectroscopic observations for the material exhibiting a broad range of emission owing to newly formed chromophoric units within the film. Full polarization spectroscopic Mueller matrix studies were employed to extract and quantify the molecular orientational order of both the ground (excitation) and excited (emission) state anisotropies through a set of newly defined parameters, namely the fluorescence diattenuation and fluorescence polarizance. The information contained in the recorded fluorescence Mueller matrix of the organic polymer material provided a useful way to control the spectral intensity of emission by using pre- and post-selection of polarization states. The observation was based on the assumption that the longer lifetime of the excited dipolar orientation is attributed to the compactness of the film.     

Side-on-End-on Coordination of Dinitrogen on a Polynuclear Vanadium Nitride Cluster Anion [V5N5]−

The side-on-end-on coordination of N₂ can be very important to activate and functionalize this very stable molecule. However, such coordination has rarely been reported. This study reports a gas-phase species (a polynuclear vanadium nitride cluster anion [V₅N₅]⁻) that can capture N₂ efficiently (12 %), and the quantum chemistry modelling suggests an unusual side-on-end-on coordination. The cluster anions were generated by laser ablation and the reaction with N₂ has been characterized by mass spectrometry, photoelectron imaging spectroscopy, and density functional theory calculations. The back-donation interactions between the localized d–d bonding orbitals on the low-coordinated dual metal (V) sites and the antibonding π* orbitals of N₂ are the driving forces to adsorb N₂ with a high binding energy (about 2.0 eV).     

Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.