Numerical simulation of unsteady 3D magneto-Sisko fluid flow with nonlinear thermal radiation and homogeneous–heterogeneous chemical reactions

In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan–Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.     

Bentonite-modified electrochemical sensors: a brief overview of features and applications

Bentonites are promising materials for electrochemical sensing because of their unique physicochemical properties. They have relatively high surface area, good adsorption and ion-exchange ability, highly tunable surface and interlayer composition, non-toxic nature, and excellent biocompatibility. Moreover, they are outstanding substrates for stable immobilization of different functional moieties. The primary focus of this review article is to highlight the applications of bentonite-modified electrodes for the analysis of organic and inorganic analytes in different matrices. A brief summary on the necessity of analysis of different compounds is provided. For the first time, features and applications of bentonite-modified electrodes are critically appraised. The key features of bentonite-modified electrodes that enhance their electrocatalytic activity toward detection of certain target analytes are highlighted. At the end, an account of current status of bentonite-modified electrodes along with future research directions is provided.     

Tris(2‐aminoethyl)amine‐based ferrocene‐terminated dendrimers as burning rate catalysts for ammonium perchlorate‐based propellant decomposition

Ferrocene‐based derivatives show potential application as burning rate catalysts (BRCs) for solid composite propellants. However, migration problems of simple ferrocene‐based derivatives limit their application as BRCs in solid composite propellants. To overcome the migration problems of ferrocene‐based BRCs and to enhance the burning rate of ammonium perchlorate (AP)‐based propellants, zero‐ to second‐generation tris(2‐aminoethyl)amine‐based ferrocene‐terminated dendrimers (G0, G1 and G2) were synthesized. The structures of G0, G1 and G2 were confirmed using ¹H NMR, Fourier transform infrared and UV–visible spectroscopies. The electrochemical behavior of G0, G1 and G2 was investigated using cyclic voltammetry. It was found that G0, G1 and G2 showed redox behavior due to the presence of ferrocene and this redox behavior was diffusion controlled over the investigated scan range. The burning rate catalytic effect of G0, G1 and G2 on thermal decomposition of AP was investigated using thermogravimetry and differential thermogravimetry. G0, G1 and G2 showed good catalytic effect on the thermal decomposition of AP. Anti‐migration studies showed that migration of G0, G1 and G2 was much slower than that of 2,2‐bis(ethylferrocenyl)propane (catocene) and ferrocene.     

Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.     

Three-step iterations for nonlinear accretive operator equations

In this paper, we suggest and analyze a three-step iterative scheme for solving nonlinear strongly accretive operator equation Tx=f without continuous condition in a uniformly smooth Banach space. Our results include the Ishikawa, Mann and Noor iterations as special cases. The results presented in this paper improve and extend almost all the current results in the more general setting.     

Resolvability in circulant graphs

A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u, v ∈ V (G) there is a vertex w ∈ W such that d(u, w) ≠ d(v, w). A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G, denoted by dim(G). For a vertex u of G and a subset S of V (G), the distance between u and S is the number min s∈S d(u, s). A k-partition Π = {S 1 , S 2 , . . . , S k } of V (G) is called a resolving partition if for every two distinct vertices u, v ∈ V (G) there is a set S i in Π such that d(u, Si )≠ d(v, Si ). The minimum k for which there is a resolving k-partition of V (G) is called the partition dimension of G, denoted by pd(G). The circulant graph is a graph with vertex set Zn , an additive group of integers modulo n, and two vertices labeled i and j adjacent if and only if i-j (mod n) ∈ C , where CZn has the property that C =-C and 0 ■ C. The circulant graph is denoted by Xn, Δ where Δ = |C|. In this paper, we study the metric dimension of a family of circulant graphs Xn, 3 with connection set C = {1, n/2 , n-1} and prove that dim(Xn, 3 ) is independent of choice of n by showing that dim(Xn, 3 ) ={3 for all n ≡ 0 (mod 4), 4 for all n ≡ 2 (mod 4). We also study the partition dimension of a family of circulant graphs Xn,4 with connection set C = {±1, ±2} and prove that pd(Xn, 4 ) is independent of choice of n and show that pd(X5,4 ) = 5 and pd(Xn,4 ) ={3 for all odd n ≥ 9, 4 for all even n ≥ 6 and n = 7.     

Quantum Information of the Aharanov–Bohm Ring with Yukawa Interaction in the Presence of Disclination

We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.     

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

Acta Mathematica Sinica, English Series - In this research article, we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators...