The h-Integrability and the Weak Laws of Large Numbers for Arrays

In this paper, the concept of weak laws of large numbers for arrays (WLLNFA) is studied, and a new notion of uniform integrability referred to as h-integrability is introduced as a condition for WLLNFA in obtaining the main results

On a Survey of Uniform Integrability of Sequences of Random Variables

This paper presents explicitly a survey of uniformly integrable sequences of random variables. We also study extensively several cases and conditions required for uniform integrability, with the establishment of some new conditions needed for the generalization of the earlier results obtained by many scholars and researchers, noting the links between uniform integrability and pointwise convergence of a class of polynomial functions on conditional based

Analytical Solutions of the Navier-Stokes Model by He’s Polynomials

Navier-Stokes models are of great usefulness in physics and applied sciences. In this paper, He’s polynomials approach is implemented for obtaining approximate and exact solutions of the Navier-Stokes model. These solutions are calculated in the form of series with easily computable components. This technique is showed to be very effective, efficient and reliable because it gives the exact solution of the solved problems with less computational work, without neglecting the level of accuracy. We therefore, recommend the extension and application of this novel method for solving problems arising in other aspect of applied sciences. Numerical computations, and graphics done in this work, are through Maple 18

Analytic and Numerical Solutions of Time-Fractional Linear Schrödinger Equation

Fractional Schrödinger equation is a basic equation in fractional quantum mechanics. In this paper, we consider both analytic and numerical solutions of time-fractional linear Schrödinger Equations. This is done via a proposed semi-analytical method upon the modification of the classical Differential Transformation Method (DTM). Some illustrative examples are used; the results obtained converge faster to their exact forms. This shows that this modified version is very efficient, and reliable; as less computational work is involved, even without given up accuracy. Therefore, it is strongly recommended for both linear and nonlinear time-fractional partial differential equations (PDEs) with applications in other areas of applied sciences, management, and finance

Stochastic Analysis of Stock Market Price Models: A Case Study of the Nigerian Stock Exchange (NSE)

In this paper, stochastic analysis of the behaviour of stock prices is considered using a proposed log- normal distribution model. To test this model, stock prices for a period of 19 years were taken from the Nigerian Stock Exchange (NSE) for simulation, and the results reveal that the proposed model is efficient for the prediction of stock prices. Better accuracy of results via this model can be improved upon when the drift and the volatility parameters are structured as stochastic functions of time instead of constants parameters

Suitability of rice husk ash mould additive for thin wall ductile iron graphite characteristics

Thin wall ductile iron (TWDI) components are used in automobile and related sectors owing to weight savings without sacrificing functional properties. However, its application is hampered by low ductility owing to carbide precipitation and poor nodule characteristics in as-cast structure. In this study, mould thermal characteristics are adjusted using rice husk ash (RHA). Green sand was blended with 1-6 wt. % RHA to produce moulds for casting of 4 mm TWDIs, samples obtained were subjected to microstructural (Optical, SEM and EDS), hardness and strength analyzes. Elemental composition of carbide precipitates showed iron and carbon. Nodularity ratings > 90%, nodule count >1000 nodules/mm2 and strength of 596 MPa were observed in samples cast in 4 wt. % RHA sand mix. Ductility of 6.1 occurred in 6 wt. % RHA/sand mix. The sand-RHA mix offers cooling rate control, reduction of precipitation of deleterious carbides and superior graphite characteristics in 4 mm TWDI castings.Keywords: cooling rate, carbide precipitate, nodules, properties, san

A Semi-Analytical Method for Solutions of a Certain Class of Second Order Ordinary Differential Equations

This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous and nonhomogeneous cases. For the robustness and efficiency of the method, four examples are considered. The results indicate that the DTM is reliable and accurate when compared to the exact solutions of the solved problems

The influence of steel die parameter and micro-structural investigation on AA6063 aluminum alloy

The study investigated the influence of steel die parameter and the microstructural evaluation of AA 6063 aluminum alloy extruded at room temperature using different die entry angles. Mild and tool steel dies of entry angles of 15o, 30o, 45o, 60o, 75o and 90o were used to extrude the work sample. Microstructural analysis, coupled with ram velocity, elongation, hardness, and maximum extrusion pressure of the extruded samples, were de-termined. It was observed that theaximum extrusion pressure required for extrusion and hardness of extruded samples increased with increasing die entry angle .Experimental results show that aluminum alloy deforms better when the die material is made of mild steel with die entry angles of 45o, 75o and 90o as compared to tool stee

Some Methods of Numerical Solutions of Singular System of Transistor Circuits

In this paper, observer design in generalized state space also known as singular system of transistor circuits is solved using the Differential transform method (DTM) and the Picard iterative technique (PIT). The numerical results obtained via these methods converge rapidly to their associated exact solutions upon comparison. It is obvious that these results are in excellent agreement with those already in literature via other numerical methods. However, the DTM reveals the ease of application and fewer computations compared to other numerical methods. Whereas, the PIT requires the Lipschitzian continuity condition to be satisfied

Parameter Estimation of Local Volatility in Currency Option Valuation

In quantitative finance and option pricing, one of the basic determinants of option prices is the volatility of the underlying asset. In this paper, we therefore, present a concise study of volatility in option pricing in the sense of Dupire’s approach. Thereafter, we outspread such study via the application of Ito formula to the modelling and valuation of currency option with local volatility. For the purpose of efficiency, we use the daily historical prices of stock-S&P 500 for a certain period to estimate the corresponding historical volatility. Graphical representation of the analysed daily historical data of stock prices with respect to a local volatility is presente