Direct electrochemistry and bioelectrocatalysis of a class II non-symbiotic plant haemoglobin immobilised on screen-printed carbon electrodes

In this study, direct electron transfer (ET) has been achieved between an immobilised non-symbiotic plant haemoglobin class II from Beta vulgaris (nsBvHb2) and three different screen-printed carbon electrodes based on graphite (SPCE), multi-walled carbon nanotubes (MWCNT-SPCE), and single-walled carbon nanotubes (SWCNT-SPCE) without the aid of any electron mediator. The nsBvHb2 modified electrodes were studied with cyclic voltammetry (CV) and also when placed in a wall-jet flow through cell for their electrocatalytic properties for reduction of H₂O₂. The immobilised nsBvHb2 displayed a couple of stable and well-defined redox peaks with a formal potential (E°′) of ?33.5 mV (vs. Ag|AgCl|3 M KCl) at pH 7.4. The ET rate constant of nsBvHb2, k _s, was also determined at the surface of the three types of electrodes in phosphate buffer solution pH 7.4, and was found to be 0.50 s^?1 on SPCE, 2.78 s^?1 on MWCNT-SPCE and 4.06 s^?1 on SWCNT-SPCE, respectively. The average surface coverage of electrochemically active nsBvHb2 immobilised on the SPCEs, MWCNT-SPCEs and SWCNT-SPCEs obtained was 2.85?×?10^?10 mol cm^?2, 4.13?×?10^?10 mol cm^?2 and 5.20?×?10^?10 mol cm^?2. During the experiments the immobilised nsBvHb2 was stable and kept its electrochemical and catalytic activities. The nsBvHb2 modified electrodes also displayed an excellent response to the reduction of hydrogen peroxide (H₂O₂) with a linear detection range from 1 μM to 1000 μM on the surface of SPCEs, from 0.5 μM to 1000 μM on MWCNT-SPCEs, and from 0.1 μM to 1000 μM on SWCNT-SPCEs. The lower limit of detection was 0.8 μM, 0.4 μM and 0.1 μM at 3σ at the SPCEs, the MWCNT-SPCEs, and the SWCNT-SPCEs, respectively, and the apparent Michaelis–Menten constant, $ {\hbox{K}}_{\rm{M}}^{\rm{app}} $ , for the H₂O₂ sensors was estimated to be 0.32 mM , 0.29 mM and 0.27 mM, respectively.     

Functionalization of Graphene Oxide with 3‐Mercaptopropyltrimethoxysilane and Its Electrocatalytic Activity in Aqueous Medium

In this work, a highly dispersed graphene oxide (GO) was successfully functionalized with 3‐mercaptopropyltrimethoxysilane (MPTS) molecule by silanization method. The chemically generated GO and MPTS functionalized GO (MPTS‐GO) were structurally characterized by thermogravimetric analysis (TGA), X‐ray diffraction analysis (XRD), scanning electron microscope (SEM), energy dispersive X‐ray (EDAX), fourier transform infrared spectroscopy (FT‐IR) and ultraviolet visible spectroscopy (UV‐Vis) techniques. The MPTS‐GO is highly suspensable in water. The thermal and conductivity results for MPTS‐GO are significantly increased compared to GO. Moreover, glassy carbon electrode modified with MPTS‐GO hybrid (MPTS‐GO/GCE) was prepared by casting of the MPTS‐GO solution on GCE. The MPTS‐GO/GCE showed an excellent electrocatalytic activity towards methionine (Met). This was understood from the observed less positive oxidation potential and higher oxidation current when compared to bare GC electrode. The MPTS‐GO has excellent electrocatalytic activity, making it an ideal candidate for sensor applications.     

Two-dimensional quaternion wavelet transform

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several examples of the CQWT. As an application we derive a Heisenberg type uncertainty principle for these extended wavelets.     

Morse index of some min-max critical points. I. Application to multiplicity results

We give here a general result on lower bounds for Morse indices of critical points obtained by some min-max principles. Combining this information with a semi-classical inequality yields sharp estimates on the growth of some critical values, from which we deduce new multiplicity results for solutions of semi-linear second-order elliptic equations.     

A result on the sum of element orders of a finite group

Let G be a finite group and $$\psi (G)=\sum _{g\in {G}}{o(g)}$$. There are some results about the relation between $$\psi (G)$$ and the structure of G. For instance, it is proved that if G is a group of order n and $$\psi (G)>\dfrac{211}{1617}\psi (C_n)$$, then G is solvable. Herzog et al. in (J Algebra 511:215–226, 2018) put forward the following conjecture: Conjecture. If G is a non-solvable group of order n, then $$\begin{aligned} {\psi (G)}\,{\le }\,{{\dfrac{211}{1617}}{\psi (C_n)}}, \end{aligned}$$with equality if and only if $$G \cong A_5$$. In particular, this inequality holds for all non-Abelian simple groups. In this paper, we prove a modified version of Herzog’s Conjecture.     

Multiplicatively and non-symmetric multiplicatively norm-preserving maps

Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖ _X and ‖.‖ _Y denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖ _Y = ‖fg‖ _X , for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖ _X = ‖Tf Tg + α‖ _Y , f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,

Slant Submanifolds of Almost Contact Metric 3-Structure Manifolds

In this paper we introduce the notion of slant submanifold of an almost contact metric 3-structure manifold. We give some examples and characterize these submanifolds. Moreover, Sasakian slant submanifolds of an almost contact 3-structure manifold are defined and studied. We also establish a sharp inequality including the squared mean curvature and Ricci curvature of a Sasakian slant submanifold.     

Decarboxylative ipso Amination of Activated Benzoic Acids

In the presence of a bimetallic Pd/Cu system with 1,10‐phenanthroline as the ligand and either air or N‐methylmorpholine N‐oxide as the oxidant, electron‐deficient benzoic acids undergo oxidative decarboxylative coupling with unprotected amines. This operationally simple aniline synthesis is widely applicable with respect to the amine and gives good yields, even on multigram scale. The orthogonality of this reaction to other Pd‐catalyzed cross‐couplings allows the concise synthesis of multisubstituted arenes by sequential C?C, C?Cl, and C?N functionalizations. Mechanistic investigations suggest the intermediacy of a hypervalent Pd species.