PROTONATION CONSTANTS AND SOLVENT DEPENDENT SPIN-CROSSOVER BEHAVIOUR OF IRON(II)-2-(2′-PYRIDYL)BENZIMIDAZOLE COMPLEXES

Abstract

2-(2′-Pyridyl)benzimidazole (pybzim = LH) coordinates to iron(II) as a bidentate and forms the tris-ligated complex, [Fe(pybzim)₃]²⁺ as isolated in the solid. Titration of [Fe(pybzim)₃]²⁺ with base demonstrates the successive deprotonation of the imino hydrogens of the coordinated ligands. Protonation constants for the free ligand, pybzim (Iog₁₀ K ^H = 11.33) and the complex, [Fe(pybzim)₃]²⁺ (log₁₀ K ^H ₁ = 9.58, log₁₀ K ^H ₂ = 8.13 and log₁₀ K ^H ₃ = 6.97) were measured in 30% (v/v) H₂O/EtOH. Results show that coordination to iron(II) increases the acidity of the imino hydrogen of the ligand. Spin-crossover behaviour of the complex were studied in different solvents ME, AC, AN, NM, NB, DMF, DMSO and ANL. The complex shows strong spin-crossover behaviour which is solvent dependent. Values of the spin-equilibrium constant (K _sc) and the associated thermodynamic parameters (ΔH _sc = 18.1–21.3 kJ mol^?1 and δS _sc = 69.6–84.4JK^?1 mol^?1) were calculated. An increase of the enthalpy is observed with increasing donor number (DN) of the solvent.     

Planar Digraphs of Digirth Five Are 2‐Colorable

Neumann‐Lara (1985) and ?krekovski conjectured that every planar digraph with digirth at least three is 2‐colorable, meaning that the vertices can be 2‐colored without creating any monochromatic directed cycles. We prove a relaxed version of this conjecture: every planar digraph of digirth at least five is 2‐colorable. The result also holds in the setting of list colorings.     

Mathematical analysis of the dynamics of COVID-19 in Africa under the influence of asymptomatic cases and re-infection

Coronavirus pandemic (COVID-19) hit the world in December 2019, and only less than 5% of the 15 million cases were recorded in Africa. A major call for concern was the significant rise from 2% in May 2020 to 4.67% by the end of July 15, 2020. This drastic increase calls for quick intervention in the transmission and control strategy of COVID-19 in Africa. A mathematical model to theoretically investigate the consequence of ignoring asymptomatic cases on COVID-19 spread in Africa is proposed in this study. A qualitative analysis of the model is carried out with and without re-infection, and the reproduction number is obtained under re-infection. The results indicate that increasing case detection to detect asymptomatically infected individuals will be very effective in containing and reducing the burden of COVID-19 in Africa. In addition, the fact that it has not been confirmed whether a recovered individual can be re-infected or not, then enforcing a living condition where recovered individuals are not allowed to mix with the susceptible or exposed individuals will help in containing the spread of COVID-19.     

Dynamical analysis of age-structured pertussis model with covert infection

An age-structured pertussis model with covert infection is proposed to understand the effect of covert infection on the recurrence of pertussis. It is found that vaccination only for young children does not have a decisive effect on whooping cough control. It is shown that although the vaccine coverage rate is relatively high, the model has a backward bifurcation for a larger covert infection rate. In addition, sufficient conditions for the disease-free steady state to be globally asymptotically stable are obtained.     

The minimum forcing number of perfect matchings in the hypercube

Let $M$ be a perfect matching in a graph. A subset $S$ of $M$ is said to be a forcing set of $M$, if $M$ is the only perfect matching in the graph that contains $S$. The minimum size of a forcing set of $M$ is called the forcing number of $M$. Pachter and Kim (1998) conjectured that the forcing number of every perfect matching in the $n$-dimensional hypercube is $2^{n?2}$, for all $n\ge 2$. This was revised by Riddle (2002), who conjectured that it is at least $2^{n?2}$, and proved it for all even $n$. We show that the revised conjecture holds for all $n\ge 2$. The proof is based on simple linear algebra.     

Accuracy of high‐order density‐based compressible methods in low Mach vortical flows

At low Mach numbers, Godunov‐type approaches, based on the method of lines, suffer from an accuracy problem. This paper shows the importance of using the low Mach number correction in Godunov‐type methods for simulations involving low Mach numbers by utilising a new, well‐posed, two‐dimensional, two‐mode Kelvin–Helmholtz test case. Four independent codes have been used, enabling the examination of several numerical schemes. The second‐order and fifth‐order accurate Godunov‐type methods show that the vortex‐pairing process can be captured on a low resolution with the low Mach number correction applied down to 0.002. The results are compared without the low Mach number correction and also three other methods, a Lagrange‐remap method, a fifth‐order accurate in space and time finite difference type method based on the wave propagation algorithm, and fifth‐order spatial and third‐order temporal accurate finite volume Monotone Upwind Scheme for Conservation Laws (MUSCL) approach based on the Godunov method and Simple Low Dissipation Advection Upstream Splitting Method (SLAU) numerical flux with low Mach capture property. The ability of the compressible flow solver of the commercial software, ANSYS FLUENT , in solving low Mach flows is also demonstrated for the two time‐stepping methods provided in the compressible flow solver, implicit and explicit. Results demonstrate clearly that a low Mach correction is required for all algorithms except the Lagrange‐remap approach, where dissipation is independent of Mach number. © 2013 Crown copyright. International Journal for Numerical Methods in Fluids. © 2013 John Wiley & Sons, Ltd.     

Nondimensional frequency scaling of aerodynamically-tensioned membranes

Membrane wings have applications that involve low Reynolds number flyers such as micro air vehicles. The time-averaged and time-dependent deformations of the membrane affect the aerodynamic characteristics of the wing, primarily in the region beyond the maximum aerodynamic efficiency of the wing. This paper investigates an appropriate nondimensional vibration frequency scaling of a spanwise tensioned membrane with free (unattached) leading and trailing edges at low Reynolds numbers relative to nondimensional aeroelastic parameters. Silicone rubber membranes with varying spanwise pre-tension, aerodynamic tension (due to wing angle-of-attack and flow dynamic pressure), modulus of elasticity, span, and thickness are studied. Experimental results are compared to a proposed scaling that simplifies the aerodynamic loading as a uniform pressure distribution acting on the membrane. Data is further compared and discussed relative to previous published results of membrane wings with finite wing spans (three-dimensional flow) and fixed (rigid) leading edges.     

Modeling and character analyzing of multiple fractional-order memcapacitors in parallel connection

Recently,the memory elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behaviors.Thus,the modeling and characterizing of the mem-elements become essential.In this paper,the analysis of the multiple fractional-order voltage-controlled memcapacitors model in parallel connection is studied.Firstly,two fractional-order memcapacitors are connected in parallel,the equivalent model is derived,and the characteristic of the equivalent memcapacitor is analyzed in positive or negative connection.Then a new understanding manner according to different rate factor K and fractional orderαis derived to explain the equivalent modeling structure conveniently.Additionally,the negative order appears,which is a consequence of the combination of memcapacitors in different directions.Meanwhile,the equivalent parallel memcapacitance has been drawn to determine that multiple fractional-order memcapacitors could be calculated as one composite memcapacitor.Thus,an arbitrary fractional-order equivalent memcapacitor could be constructed by multiple fractional-order memcapacitors.