This paper provides a procedure for estimating Stochastic Volatility (SV) in financial time series via latent autoregressive in a Bayesian setting. A Gaussian distributional combined prior and posterior of all hyper-parameters (autoregressive coefficients) were specified such that the Markov Chain Monte Carlo (MCMC) iterative procedure via the Gibbs and Metropolis-Hasting sampling method was used in estimating the resulting exponentiated forms (quadratic forms) from the posterior kernel density. A case study of Naira to eleven (11) exchangeable currencies’ rates by Central Bank of Nigeria (CBN) was subjected to the estimated solutions of the autoregressive stochastic volatility. The posterior volatility estimates at 5%, 50%, and 95% quantiles of \({e^{\frac{\mu }{2}}}\) = (0.130041, 0.1502 and 0.1795) respectively unveiled that the Naira-US Dollar exchange rates has the highest rates bartered by fluctuations.

This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms.

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

In this present study, the transient magnetohydrodynamics free convection heat and mass transfer of Casson nanofluid past an isothermal vertical flat plate embedded in a porous media under the influence of thermal radiation is studied. The governing systems of nonlinear partial differential equations of the flow, heat and mass transfer processes are solved using implicit finite difference scheme of Crank-Nicolson type. The numerical solutions are used to carry out parametric studies. The temperature as well as the concentration of the fluid increase as the Casson fluid and radiation parameters as well as Prandtl and Schmidt numbers increase. The increase in the Grashof number, radiation, buoyancy ratio and flow medium porosity parameters causes the velocity of the fluid to increase. However, the Casson fluid parameter, buoyancy ratio parameter, the Hartmann (magnetic field parameter), Schmidt and Prandtl numbers decrease as the velocity of the flow increases. The time to reach the steady state concentration, the transient velocity, Nusselt number and the local skin-friction decrease as the buoyancy ratio parameter and Schmidt number increase. Also, the steady-state temperature and velocity decrease as the buoyancy ratio parameter and Schmidt number increase. Also, the local skin friction, Nusselt and Sherwood numbers decrease as the Schmidt number increases. However, the local Nusselt number increases as the buoyancy ratio parameter increases. It was established that near the leading edge of the plate), the local Nusselt number is not affected by both buoyancy ratio parameter and Schmidt number. It could be stated that the present study will enhance the understanding of transient free convection flow problems under the influence of thermal radiation and mass transfer as applied in various engineering processes.

Let \(G\) be a simple and finite graph. A graph is said to be decomposed into subgraphs \(H_1\) and \(H_2\) which is denoted by \(G= H_1 \oplus H_2\), if \(G\) is the edge disjoint union of \(H_1\) and \(H_2\). If \(G= H_1 \oplus H_2 \oplus \cdots \oplus H_k\), where \(H_1\), \(H_2\), …, \(H_k\) are all isomorphic to \(H\), then \(G\) is said to be \(H\)-decomposable. Furthermore, if \(H\) is a cycle of length \(m\) then we say that \(G\) is \(C_m\)-decomposable and this can be written as \(C_m|G\). Where \(G\times H\) denotes the tensor product of graphs \(G\) and \(H\), in this paper, we prove that the necessary conditions for the existence of \(C_6\)-decomposition of \(K_m \times K_n\) are sufficient. Using these conditions it can be shown that every even regular complete multipartite graph \(G\) is \(C_6\)-decomposable if the number of edges of \(G\) is divisible by \(6\).

In this research, we reported facile synthesis of efficient \(Ni_3Fe\) electrocatalyst nanostructures deposited on conducting carbon fibers surface by a simple chemical bath deposition method at moderate temperature. The composition, phase and electrocatalytic property of as-prepared binder-free electrocatalyst was characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), and electrochemical measurements. The as-synthesized \(Ni_3Fe@t-CF\) presented excellent performance and durability as water oxidation electrocatalyst in alkaline electrolyte owing to non-segregated deposition of \(Ni_3Fe\) nanostructures on conducting surface of carbon, high electrochemical surface area, and the fast absorption and desorption of water molecules during oxygen evolution reaction due to the \(3D\) architecture of conducting interlaced carbon fibers template.

Couroupita guianensis Aubl. (Lecythidaceae) “Cannonball tree” is a tropical plant with ethnobotanical uses. The present study is focused on analyzing the essential oil composition of Couroupita guianensis (C. guianensi) fresh flowers collected in El Salvador. Steam distillation, coupled with GC/FID and GC/MS analysis were employed to characterize the chemical composition and in vitro antioxidant activity study were carried out using DPPH assay. Eugenol was identified to be the most abundant constituent and quantified as \(46.20\)% of the total volatiles. Other constituents were found to be \(2\)-phenylethanol \((34.82\)%), \((E)-(E)\)-farnesol \((5.53\)%), nerol \((3.95\)%), geraniol \((3.20\)%), benzyl alcohol \((1.77\)%). \(DPPH\) assay showed a dose-dependent antioxidant activity. The study demonstrated that C. guianensis essential oil from El Salvador is a rich source of eugenol, which may be responsible for its antioxidant properties. Based on these results, further studies on the antibacterial and antifungal activity of C. guianensis essential oil are of fundamental importance.

The main difficulty in dealing with the basic differential equations of fluid momentum is in choosing an appropriate problem-solving methodology. In addition, it is necessary to correct minor errors incurred by neglecting some losses. However, in many cases, such methodologies suffer from long processing time (P-time). Therefore, this article focuses on the truncation technique involving an unsteady Eyring-Powell fluid towards a shrinking wall. The governing differential equations are converted to the non-dimensional from through similarity variables. It is seen that the present system is totally convergent in 8th-order approximate solution together with \(\hbar=-0.875\).

A topological index of graph \(G\) is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join \(\overline {G_1+G_2}\), tensor product \(\overline {G_1 \otimes G_2}\), Cartesian product \(\overline {G_1\times G_2}\), composition \(\overline {G_1\circ G_2}\), strong product \(\overline {G_1\ast G_2}\), disjunction \(\overline {G_1\vee G_2}\) and symmetric difference \(\overline {G_1\oplus G_2}\) will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.

A pseudo walk matrix \(\bf{W}_\bf{v}\) of a graph \(G\) having adjacency matrix \(\bf{A}\) is an \(n\times n\) matrix with columns \(\bf{v},\bf{A}\bf{v},\bf{A}^2\bf{v},\ldots,\bf{A}^{n-1}\bf{v}\) whose Gram matrix has constant skew diagonals, each containing walk enumerations in \(G\). We consider the factorization over \(\mathbb{Q}\) of the minimal polynomial \(m(G,x)\) of \(\bf{A}\). We prove that the rank of \(\bf{W}_\bf{v}\), for any walk vector \(\bf{v}\), is equal to the sum of the degrees of some, or all, of the polynomial factors of \(m(G,x)\). For some adjacency matrix \(\bf{A}\) and a walk vector \(\bf{v}\), the pair \((\bf{A},\bf{v})\) is controllable if \(\bf{W}_\bf{v}\) has full rank. We show that for graphs having an irreducible characteristic polynomial over \(\mathbb{Q}\), the pair \((\bf{A},\bf{v})\) is controllable for any walk vector \(\bf{v}\). We obtain the number of such graphs on up to ten vertices, revealing that they appear to be commonplace. It is also shown that, for all walk vectors \(\bf{v}\), the degree of the minimal polynomial of the largest eigenvalue of \(\bf{A}\) is a lower bound for the rank of \(\bf{W}_\bf{v}\). If the rank of \(\bf{W}_\bf{v}\) attains this lower bound, then \((\bf{A},\bf{v})\) is called a recalcitrant pair. We reveal results on recalcitrant pairs and present a graph having the property that \((\bf{A},\bf{v})\) is neither controllable nor recalcitrant for any walk vector \(\bf{v}\).