Showing papers in "IOSR Journal of Mathematics in 2014"

Estimation of the Effect of Multicollinearity on the Standard Error for Regression Coefficients

Abstract: This research was set to examine the effect Multicollinearity has, on the standard error for regression coefficients when it is present in a Classical Linear Regression model (CLRM). A classical linear regression model was fitted into the GDP of Nigeria ,and the model was examined for the presence of Multicollinearity using various techniques such as Farrar-Glauber test, Tolerance level, Variance inflation factor, Eigen values etc and the result obtained shows that Multicollinearity has contributed to the increase of the standard error for regression coefficients, thereby rendering the estimated parameters less efficient and less significant in the class of Ordinary Least Squares estimators. Tolerance levels of 0.012, 0.005, 0.002 and 0.001 forβ1, β2, β3 ,and β4 respectively clearly shown a very low tolerance among all the explanatory variables with very high Variance Inflation Factors of 84.472, 191.715,502.179 and 675.633 respectively. A Coefficient of determination (RSquare) of 99%, though signaled a very high validity for the CLRM but it is equally an indications of a very high degree of Multicollinearity among the explanatory variables. The Eigen values of 0.431, 0.005, 0.002 and 0.000 for β0, β1, β2, β3 ,and β4 respectively clearly shown a very low Eigen value among the explanatory variables, which are closer to zero with very high Condition index of 30.983, 49.759 and 100.810 for β2, β3 ,and β4 respectively which indicate that the Multicollinearity present is due greatly to the influence of regressors X2, X3, and X4..

On Consistency and Limitation of paired t-test, Sign and Wilcoxon Sign Rank Test

Abstract: This article investigates the strength and limitation of t-test and Wilcoxon Sign Rank test procedures on paired samples from related population. These tests are conducted under different scenario whether or not the basic parametric assumptions are met for different sample sizes. Hypothesis testing on equality of means require assumptions to be made about the format of the data to be employed. The test may depend on the assumption that a sample comes from a distribution in a particular family. Since there is doubt about the nature of data, non-parametric tests like Wilcoxon signed rank test and Sign test are employed. Random samples were simulated from normal, gamma, uniform and exponential distributions. The three tests procedures were applied on the simulated data sets at various sample sizes (small, moderate and large) and their Type I error and power of the test were studied in both situations under study.

Alpha-Skew-Logistic Distribution

Abstract: Alpha-skew-Logistic distribution is introduced following the same methodology as those of Alpha- skew-normal distribution (Elal-Olivero, 2010) and Alpha-skew-Laplace distributions (Harandi and Alamatsaz, 2013). Cumulative distribution function (cdf), moment generating function (mgf), moments, skewness and kurtosis of the new distribution is studied. Some related distributions are also investigated. Parameter estimation by method of moment and maximum likelihood are discussed. Closeness of the proposed distribution with alpha-skew-normal distribution is studied. The suitability of the proposed distribution is tested by conducting data fitting experiment and comparing the values of log likelihood, AIC, BIC. Likelihood ratio test is used for discriminating between Alpha-skew-Logistic and logistic distributions. Mathematics Subject Classification: 60E05; 62E15; 62H10

Mathematical Study of Monthly and Annual Rainfall Trends in Nasarawa State, Nigeria

Abstract: Rainfall is very important for the economic growth and development of any nation; hence there is dire need to study the monthly and annual trends. This paper critically examines the mathematical study of monthly and annual rainfall patterns in Nasarawa State for 20 years (1993-2012) using data obtained from the archives of Meteorological Observatory at the College of Agriculture, Lafia, Nasarawa State. Statistical techniques like time series analysis, mean and standard deviation were employed to depict the temporal distribution of rainfall over the area. The study shows that 1996 is the wettest year, while 2010 shows a year with the lowest negative rainfall deviation. In analyzing the months for the period, it was noticed that August recorded the highest rainfall value of 2498mm which is the month where clouds pervades the sky.

Supersonic Similitude for Oscillating Nonplanar Wedge

Abstract: A similitude has been obtained for a pitching oscillating Non planar wedge with attached bow shock at high angle of attack in supersonic flow. A strip theory in which flow at a span wise location is two dimensional and independent of each other is being used. This combines with the similitude to lead to a one- dimensional piston theory. Closed form of simple relations is obtained for stiffness and damping derivatives in pitch. The present theory is valid only when the shock wave is attached with the nose of the wedge. From the theory developed some of the results are obtained for wide range of Mach number and angle of attack with remarkable computational ease. From the results it is found that when convexity is introduced in the non-planar wedge, this results in shifting of the center of pressure towards the leading edge, and the stiffness as well as the damping derivative decreases with the increase in the Mach number for all the values of the semi vertex angles.

Adomian Decomposition Method for Solving Delay Differential Equations of Fractional Order

Abstract: In this paper, we implement Adomian decomposition method for solving numerically non-linear delay differential equations of fractional order. The fractional derivative will be in the Caputo sense. In this approach, the solutions are found in the form of a convergent power series with easily computed components. Some numerical examples are presented to illustrate the accuracy and ability of the proposed method.

Estimation of stability derivatives for a planar wedge in the newtonian limit

Abstract: The present work contains an analytical method derived using Ghosh’s Hypersonic similitude to predict the aerodynamic stability derivatives of a Planar Wedge in the Newtonian limit. It uses the strip theory developed by Ghosh’s where span wise strips are independent of each other, to obtain the expressions for stiffness and damping derivatives in pitch for a planar wedge in the Newtonian limit. The present theory predicts the stability derivatives of a planar wedge for a wide range of geometrical and flow parameters. The knowledge of these stability derivatives is essential to freeze and arrive at the geometrical as well as the kinematic similarity parameters before we go for exhaustive computations and experimental studies. The present method predicts the stability derivatives in pitch for a planar wedge with remarkable computational ease, which is very handy at the design stage. The expressions derived for stability derivatives become exact in the Newtonian limit. It is found that stiffness derivative linearly varies with the pivot position. It is also observed that the centre of pressure moves towards the trailing edge and this shift is quite high at high angles of attack. Hence, this behavior could be utilized to stabilize the aerospace vehicle from the static stability point of view. In the case of damping derivative since the expression for the damping derivative is non-linear and the same has been reflected in the results. However, the behavior remains linear till angle of attack fifteen degrees, later the trend is non-linear.

Some Properties of Soft Connected Spaces and Soft Locally Connected Spaces

Abstract: In this paper we will introduced soft disjoint sets, soft separated sets ,soft connected space , soft disconnected space ,and study the relation between soft disjoint sets and soft separated sets, define soft hereditary property and study soft hereditary property on soft connected spaces , study the product of two soft disconnected spaces and the product of soft connected with soft disconnected .

Comparative Study of Elliptic and Hyper elliptic Curve Cryptography in Discrete Logarithmic Problem

Abstract: Binary and prime fields are being considered for practical implementation on both Elliptic and Hyperelliptic curves for software curve implementation. The main operations like scalar multiplication and group operations are compared in both hyperelliptic and elliptic cryptography. ECC and HECC are implemented on different binary fields and also compare the encryption and decryption system in discrete logarithmic problem.

Numerical Solution of Integro-Differential Equation Using Adomian Decomposition and Variational Iteration Methods

Abstract: In this paper, a comparative study of Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM) were considered on various types of integrodifferential equation; which are Fredholm, Volterra and Fredholm-Volterra equations. From the examples considered, it was observed that these methods were compared favorably with the exact solution. VIM has an advantage over ADM due to non-requirement of Adomian polynomial and hence converges faster to the exact solution for some nonlinear problems.

Cluster Information of Non-Sampled Area In Small Area Estimation

Abstract: Empirical Best Linear Unbiased Predictor (EBLUP) has been widely used to predict parameters in area with small or even zero sample size. The problem is when this model should be used to predict the parameters of non-sampled area. Ordinary EBLUP predicted the parameters using synthetic model which ignore the area random effects because lack of non-sampled area information. Thus, those prediction will be distorted based on a single line of the synthetic model. One of idea that developed in this paper is to modify the prediction model by adding cluster information by assuming that there are similiarities among particular areas. These information will be added into the model to modify the intercept of prediction model. Another approach is by adding random effects of auxiliary variable into the previous model in order to modify both intercept and slope of the prediction model. In this paper, simulation process is carried out to study the performance of the proposed models compared with ordinary EBLUP. All models evaluated based on the value of Relative Bias (RB) and Relative Root Mean Squares Error (RRMSE). The results show that the addition of cluster information can improve the ability of the model to predict on non-sampled areas.

Queueing Analysis of Patient Flow in Hospital

Abstract: Waiting on a queue is not usually interesting, but reduction in this waiting time usually requires planning and extra investments. The increasing population and health-need due to adverse environmental conditions have led to escalating waiting times and congestion in hospitals especially in the Emergency and Accident Departments (EAD). It is universally acknowledged that a hospital should treat its patients, especially those in need of critical care, in timely manner. Incidentally, this is not achieved in practice particularly in government owned health institutions because of high demand and limited resources in these hospitals. To enhance the level of admittance to care, optimal beds required in hospital is needed and this can be achieved by adequate knowledge of patient flow. In this paper, we show that queue theory can accurately model the flow of in-patient in hospital; we determine the optimal bed count and its performance measure.

An Appliaction of Generalized Fuzzy Soft Matrices in Decision Making Problem

Abstract: After development of fuzzy soft matrices, it has been applying in many fields of real life scenarios The problems which are unable to solve by ordinary matrices can be solved by fuzzy soft matrices In this paper our main aim is to define generalized fuzzy soft matrices and to study a few of its properties Finally, we presented a decision making problem based on one of the operation of generalized fuzzy soft matrices

Convergence Analysis of shifted Fourth kind Chebyshev Wavelets

Abstract: The aim of this paper is to state and prove the uniform convergence theorem and accuracy estimation for shifted fourth kind Chebyshev wavelets.

Application of Fuzzy Measure and Fuzzy Integral in Students Failure Decision Making

Abstract: The present paper discusses an application of fuzzy measure and corresponding fuzzy integral for the evaluation of students failure reasons. From the result it is clearly seen that Choquet Integral has a good choice in Decision making.

Effect of Angle of Attack on Stability Derivatives of a Delta Wing with Straight Leading Edge in Supersonic Flow

Abstract: In the Present paper effect of angle of incidence on pitching derivatives of a delta wing with Straight leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which strips at different span wise location are independent. This combines with similitude to give a piston theory. From the results it is seen that with the increase in the Mach number, there is a decrement of stiffness as well as the damping derivatives in pitch for all the Mach number tested, however, the magnitude of decrement for different inertia level will differ. It is seen that with the increase in the angle of attack both stiffness and damping derivatives increase linearly, nevertheless, this linear behavior limit themselves for different Mach numbers. For Mach number M = 2, this limiting value of validity is fifteen degrees, for Mach 2.5 & 3, it is twenty five degrees, whereas, for Mach 3.5 & 4 it becomes thirty five degrees. When these stability derivatives were considered at various pivot positions, namely h = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. After scanning the results it was observed that with the shift of the pivot position from the leading edge to the trailing edge, the magnitude of both the stability derivatives were decreasing progressively with the pivot position. Results have been obtained for supersonic flow of perfect gases over a wide range of angle of attack and Mach number. The effect of real gas, leading edge bluntness of the wing, and secondary wave reflections are neglected.

Investigating Daily Naira/Dollar Exchange Rate Volatility: A Modeling using GARCH and Asymmetric Models

Abstract: Exchange rates are important financial problem that is receiving attention globally. This study investigated the volatility of daily Dollar/Naira exchange rate using GARCH (1, 1), GJR-GARCH (1, 1), TGARCH (1, 1) and TS-GARCH (1, 1) models by using daily data over the period June 1, 2000 to July 26, 2011 consisting of 4083 observations. The results from all the models show that volatility was persistent (i.e. exceed 1) indicating GARCH (1, 1), GJR-GARCH (1, 1), and TS-GARCH (1, 1) models variances are not stationary but for TGARCH (1, 1) model (i.e. below 1) indicating the variance is stationary. The GJR-GARCH (1, 1) and TGARCH (1, 1) models show the existence of statistically significant asymmetry effect. The results from all the asymmetry models rejected the hypothesis of leverage effect. The TGARCH (1, 1) and TS-GARCH (1, 1) models are found to be the best models, they have all the parameters of the variance being significant and with lower information criteria.

Refinement of Iterative Methods for the Solution of System of Linear Equations Ax=b

Abstract: In this paper we present a survey of three iterative refinement methods for the solution of system of linear equations. The result of this paper shows that the refinement of generalized Jacobi method is much more efficient than the refinement of Jacobi iterative method and is as fast as the refinement of Gauss-Seidel method considering their performance, number of iterations required to converge, storage and level of accuracy. This research will help to appreciate the use of iterative techniques for understanding linear equations.

Ordering Generalized Hexagonal Fuzzy Numbers Using Rank, Mode, Divergence and Spread

Abstract: The Fuzzy set theory has been applied in many fields such as management, engineering and almost in every business enterprise as well as day to day activities. Ordering fuzzy numbers plays an important role in approximate reasoning, optimization, forecasting, decision making, risk analysis, controlling, scheduling and various other usages in our day to day activities. This paper describes a ranking method for ordering fuzzy numbers based on Area, Mode, divergence, Spreads and Weights of generalized (non-normal) hexagonal fuzzy numbers.

Strongly * Continuous Functions in Topolgical Spaces

Abstract: The Purpose Of This Paper Is To Introduce Strongly And Perfectly  *Continuous Maps And Basic Properties And Theorems Are Investigated. Also, We Introduced  * Open And Closed Maps And Their Properties Are Discussed. Mathematics Subject Classifications: 54ao5

Application of Exp(())-expansion Method to Find the Exact Solutions of Nonlinear Evolution Equations

Abstract: In this paper, we explore new applications of the )) ( exp(    -expansion method for finding exact traveling wave solutions of generalized Klein-Gordon Equation and right-handed nc-Burgers equation. By means of this method three new solutions of each equations is obtained including the hyperbolic functions, exponential functions and rational function solutions. The proposed method is very effective, efficient and applicable mathematical tools for nonlinear evolution equations (NLEEs). So this method can be used for many other nonlinear evolution equations.

Unsteady MHD Poiseuille Flow between Two Infinite Parallel Plates in an Inclined Magnetic Field with Heat Transfer

Abstract: Unsteady MHD Poiseuille flow between two infinite parallel porous plates in an inclined magnetic field with heat transfer has been studied. The pressure gradient is considered negligible. The lower plate alone is porous. The momentum and energy equations were solved by variable separable technique. The fluid velocity is expressed in terms of Hartmann number while temperature is in terms of Prandlt number. The effects of various magnetic inclinations to velocity and skin friction with various Prandlt number to temperature and Nulsselt number are discussed by graphs and tables.

Application of Homotopy and Variational Iteration Methods to the Atmospheric Internal Waves Model

Abstract: Atmospheric internal waves can be represented by a nonlinear system of partial differential equation (PDE) under shallow-fluid assumption. In this paper, we exploited the homotopy analysis method (HAM) and variational iteration method (VIM) to obtain an approximate analytical solutions of the system. The results of both methods are then compared with numerical method. It is shown that both HAM and VIM are efficient in approximating the numerical solutions.

A deteriorating inventory model for quadratic demand and constant holding cost with partial backlogging and inflation

Abstract: In most of the deteriorating items inventory model, demand rate has considered as a constant function. But in realistic situation these cost varying according to time. So in this paper, we developed a deterministic deteriorating inventory model with inflation in which demand rate are quadratic function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved numerically by minimizing the total inventory cost for cycle. Keywords: inventory, deteriorating items, shortages, time dependent demand, partial backlogging, constant holding cost and inflation.

The Value Distribution of Some Differential Polynomials

Abstract: We prove a value distribution theorem for meromorphic functions having few poles, which improves several results of C.C.Yang and others.Also we obtain a generalized form of Clunie's result.      

An investigation of temporal adaptive solution of Richards' equation for sharp front problems

Abstract: Accurate, reliable, efficient, and robust simulation of groundwater flow in the unsaturated zone for the problems that characterized by sharp fronts in both space and time is computationally expensive. The accurate numerical solution of these problems by standard approaches with uniform spatial and temporal discretization usually inefficient and simulation is too costly. Moreover, it is very difficult to obtain explicit solution of Richards' equation by using standard time integration unless very small time steps are used in the integration process. Economical and robust solution may be achieved with variable time step size instead of constant time step size use. In this study, adaptive method in time is used to solve Richards' equation with finite difference technique. Temporal adaptation is accomplished by using variable order, variable step size approximation. We show how a differential algebraic equation can give accurate solution, have good mass balance properties and more economical for a wide range solution accuracy. The accuracy and computational efficiency of the method are evaluated by comparison with a uniform spatial discretization that is adaptive in time for three problems simulating one-dimensional flow processes in unsaturated porous media. The results indicate that the method is quite competitive with spatially and temporally adaptive approach. We conclude that the method can be effectively implemented and efficient alternative to standard approaches for simulating

Some Coding Theorems on Fuzzy Entropy Function Depending Upon Parameter R and Ѵ

Abstract: In the literature of information theory several types of coding theorems involving fuzzy entropy functions exists. In this paper, some new fuzzy coding theorems have been obtained involving utilities. The fuzzy coding theorems obtained here are not only new but also generalizes some well known results available in the literature.

Radiation and thermal diffusion effect on a steady MHD free convection heat and mass transfer flow past an inclined stretching sheet with Hall current and heat generation

Abstract: In the present paper is an investigation of steady MHD free convection, heat and mass transfer flow of an incompressible electrically conducting fluid past an inclined stretching sheet under the influence of an applied uniform magnetic field with Hall current and radiation effect. Using suitable similarity transformations the governing fundamental boundary layer equations are transformed to a system of non-linear similar ordinary differential equations for momentum, thermal energy and concentration equations which are then solved numerically by the shooting method along with Runge- Kutta fourth-fifth order integration scheme. The results presented graphically illustrate that primary velocity field decrease due to increase of magnetic parameter, Angle of inclination, Dufour number, Prandtl number, Heat generation and Soret number while secondary velocity also decrease for Hall parameter . Other parameters increase the velocities of the fluid flow. Temperature field increases in the presence of Dufour number, heat generation, Schmidt number, Magnetic parameter, Grashof number & Modified Grashof number and decreases for other parameters. Also, concentration profiles decreases for increasing the values of Dufour number, Schmidt number, Heat generation, Soret number, Grashof number & Modified Grashof number but concentration increases for other parameters. The numerical results concerned with the primary velocity, secondary velocity, temperature and concentration profiles effects of various parameters on the flow fields are investigated and presented graphically. Also the skin friction coefficient, the local Nusselt number and the local Sherwood number are presented in Tables 1-3.

Sirs-Si Model of Malaria Disease with Application of Vaccines, Anti-Malarial Drugs, and Spra)'ing

Abstract: Malaria is a deadly disease transmitted to humans through the bite of infected female mosquitoes .It can also be transmitted from an infected mother (congenitally) or through blood transfusion. In this paper, we discussed the transmission of malaria featuring in the framework of an SIRS-SI model with treatments are given to humans and mosquitoes. We here utilized the use of vaccines, the use of anti-malarial drugs, and the use of spraying as treatment efforts. A stability analysis was then performed and numerical simulation was provided to clarify the result. It is shown that treatments affect the dynamics of human and mosquito populations. In addition, we proposed the Homotopy Analysis Method (HAM) to construct the approximate solution of the model.