##### Numerical Method for the Perturbed Risk Model with Randomized Observation and Two-sided Jumps

Hua Dong

Asian Research Journal of Mathematics, Page 1-7
DOI: 10.9734/ARJOM/2018/43494

In this paper, we considered the perturbed risk model with two-sided jumps, where ruin can only occur at some Poisson times. A generalized Gerber-Shiu-type function is discussed involving the number of observations, the ruin time and the de cit at ruin. Integro-differential equations with certain boundary conditions are derived. As it is diffcult to get closed-form solutions, a numerical sinc method is proposed.

##### Non-linear Saturation Controller to Reduce the Vibrations of Vertical Conveyor Subjected to External Excitation

Y. A. Amer, A. T. EL-Sayed, M. N. Abd EL-Salam

Asian Research Journal of Mathematics, Page 1-26
DOI: 10.9734/ARJOM/2018/44590

In this article, We adjusted the equations by using non-linear saturation controller (NSC) to control the vibrations of vertical conveyor. The system described by a four-degree-of-freedom (4-DOF) including the cubic non-linear terms and external excitations. We applied the multiple scale perturbation technique (MSPT) to obtain the approximate solution. The time histories of the system are investigated numerically with and without NSC control. We investigated the frequency response equations at the simultaneous resonance case (Ω1≅ω1, Ω2≅ω2, ω1≅2ω3, ω2≅2ω4) numerically using Runge-Kutta of fourth order. We studied the numerical simulation to obtain the effectiveness of the different parameters on the system using MATLAB program. Finally, we submitted a comparison of previously published studies.

##### On T1-T2-g- Closed Sets in Bitopological Spaces

K. Vithyasangaran, P. Elango

Asian Research Journal of Mathematics, Page 1-8
DOI: 10.9734/ARJOM/2018/44752

In this paper, we introduced and studied a new kind of generalized closed set called $$\tau_1\tau_2-\bar{g}$$-closed set in a bitopological space $$(X,\tau_1, \tau_2)$$. The properties of this $$\tau_1\tau_2-\bar{g}$$-closed set are studied and compared with some of the corresponding generalized closed sets in general topological spaces and bitopological spaces. We also defined the $$\tau_1\tau_2-\bar{g}$$-continuous function and studied some its properties

##### Skill Comparison of Multiple-Linear Regression Model and Artificial Neural Network Model in Seasonal Rainfall Prediction-North East Nigeria

Ebiendele Ebosele Peter, Ebiendele Eromosele Precious

Asian Research Journal of Mathematics, Page 1-10
DOI: 10.9734/ARJOM/2018/44049

Seasonal Rainfall in Nigeria is usually complex due to the tremendous range of variation over a wide range of scales both in space and time. Forecasting techniques such as Multiple Linear Regression (MLR) and Artificial Neural Network (ANN) have been used to study rainfall. This study is motivated by the need to compare MLR and ANN models to know which one is more reliable in predicting Seasonal rainfall. The rainfall datasets used in this study were collected from the achieving of Nigeria meteorological agency from (1986-2017). The model comparison was based on four criteria; the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), prediction error and Correlation coefficient (r). The error measures are comparable for the two models. The analysis of the models performance shows that, overall, the ANN model performs better than the MLR model in terms of PE, RMSE, MAE and correlation coefficient. ANN had the minimum MAE=56.66 mm, RMSE=74.84 and PE=0.11209 respectively and in terms of correlation coefficient between the observed rainfall and predicted rainfall amount, ANN model had high correlation coefficient (0.93) compared to MLR model whose correlation coefficient was  (0.66).

##### Unsteady Oscillatory Couette Flow between Vertical Parallel Plates with Constant Radiative Heat Flux

K. W. Bunonyo, E. Amos, I. C. Eli

Asian Research Journal of Mathematics, Page 1-11
DOI: 10.9734/ARJOM/2018/44702

In the present study, Unsteady Oscillatory Couette Flow between vertical parallel plates with constant radiative heat flux is considered. The mathematically formulated governing equations are simplified with dimensionless variables and coupled ordinary differential equations were obtained. Rosseland approximation is used and the present study is therefore for a case of to an optically thick fluid like blood. The transformed set of coupled nonlinear ordinary differential equations is then solved analytically using the perturbation method, and the velocity and temperature functions are simulated. It is observed that increasing the thermal radiation parameter Rd increases the blood flow, in addition, the oscillatory frequency ω also improves the flow profiles such as temperature θ(y) and velocity w(y).