Open Access Original Research Article

Effect of Sample Size on the Performance of Ordinary Least Squares and Geographically Weighted Regression

Mitra L. Devkota, Gary Hatfield, Rajesh Chintala

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/BJMCS/2014/6050

A recently developed spatial analytical tool, Geographically Weighted Regression (GWR) was used to deal with spatial nonstationarity in modeling the crop residue yield potential for North Central region of the USA. Average of daily mean temperature and total precipitation of crop growing season were the explanatory variables. In this study, the model performance of Ordinary Least Squares (OLS) and GWR were compared in terms of coefficient of determination (R2) and corrected Akaike Information Criterion (AICc). Moran’s I and Geary’s C were used to test the spatial autocorrelation of OLS and GWR residuals. The explanatory power of the models was assessed by approximate likelihood ratio test. Furthermore, the test of spatial heterogeneity of the GWR parameters was conducted by using data sets with small and large samples. The comparative study of R2and AICc between the models showed that all the GWR models performed better than the analogous OLS models. Test of spatial autocorrelation of residuals revealed that the OLS residuals had higher degrees of spatial autocorrelation than the GWR residuals indicating that GWR mitigated the spatial autocorrelation of residuals. Results of the approximate likelihood ratio test showed that GWR models performed better than the OLS models suggesting that the OLS relationship was not constant across the space of interest. More importantly, it was demonstrated that the data set would have to be large enough for the individual parameters of GWR models to be spatially heterogeneous.

Open Access Original Research Article

A Novel Approach for Sphere Decoder MIMO System

Garima Mathur, MohammadSalim ., R.P. Yadav

Journal of Advances in Mathematics and Computer Science, Page 22-32
DOI: 10.9734/BJMCS/2014/5614

In sphere decoding techniques, it was seen that the generalized sphere decoder algorithms have been applied to decode the MIMO systems. The transmitted vector is determined by decoding a sequence of determined sub problems.In this paper, the proposed sphere decoder has promised considerable performance as compared to the generalized sphere decoder. The proposed sphere decoding algorithm follows an adaptive radius selection approach for reducing the computational complexity as compared to the generalized sphere decoding algorithm and with the ideal ML decoder which applies on the QPSK signaling. Also it has proven that the proposed sphere decoder has given the performance near optimal like the ML decoder. The performance comparison is done under the Flat Rayleigh fading environment. We substantiate our new proposed reduced complexity near optimal sphere decoding algorithm with simulations.

Open Access Original Research Article

Fitting Quadratic Curves to Data Points

N. Chernov, Q. Huang, H. Ma

Journal of Advances in Mathematics and Computer Science, Page 33-60
DOI: 10.9734/BJMCS/2014/6016

Fitting quadratic curves (a.k.a. conic sections, or conics) to data points (digitized images) is a fundamental task in image processing and computer vision. This problem reduces to minimization of a certain function over the parameter space of conics. Here we undertake a thorough investigation of that space and the properties of the objective function on it. We determine under what conditions that function is continuous and differentiable. We identify its discontinuities and other singularities and determined what effect those have on the performance of minimization algorithms. Our analysis shows that algebraic parameters of conics are more suitable for minimization procedures than more popular geometric parameters, for a number of reasons. First, the space of parameters is naturally compact, thus their estimated values cannot grow indefinitely causing divergence. Second, with algebraic parameters minimization procedures can move freely and smoothly between conics of different types allowing shortcuts and faster convergence. Third, with algebraic parameters one avoids known issues occurring when the fitting conic becomes a circle. To support our conclusions we prove a dozen of mathematical theorems and provide a plenty of illustrations.

Open Access Original Research Article

Conceptual Framework for Integration of Organisation Information Processing Theory and Activity Theory in Enterprise Systems Implementation

Clement Mayieko Nyandiere, Faustin Kamuzora, Ismail Ateya Lukandu, Vincent Omwenga

Journal of Advances in Mathematics and Computer Science, Page 61-72
DOI: 10.9734/BJMCS/2014/5181

Implementation processes of systems in organizations follow different strategies and one of these strategies is to understand the uncertainties associated with the integration of the new system into an existing system environment so as to limit any challenges that may arise during the system implementation. Systems are implemented to address specific organizational needs, that is, activities the organization engages in. This paper explores organization information processing theory (OIPT) and activity theory in enterprise resource planning (ERP) systems implementation. A framework for the ERP implementation has been developed from a conceptual model on the interaction of organizational culture and structure. The modified model incorporates the activity theory and the OIPT and provides a formal way of bringing on board various interplaying variables in the system implementation process, more so for ERP systems.

Open Access Original Research Article

A General Inequality Related to Variational Inequalities and Its Consequences

B. B. Sahoo, G. K. Panda

Journal of Advances in Mathematics and Computer Science, Page 73-89
DOI: 10.9734/BJMCS/2014/3465

Let X  be a Hausdorff topological vector space with dual X*  and K  a nonempty closed and convexsubset of X. Let the value of u E X*  at x E  be denoted by (u,x). Let g:K - R   be a map (possibly nonlinear). The classical minimization problem for the pair(g,K)  is to find xE K   such that

g(xo) = min g(y).

If we define a function f : K X K-R as f (x,y) =g (y)-g(x) for all x,yEK , then the above problem reduces to the problem of finding xo E K  such that f (xo,y) > 0 for all y E K .

 

 

 

Open Access Original Research Article

Solving Nonlinear Systems Using Fourth Order Iterative Method

M. A. Hafiz, A. E. Alamir

Journal of Advances in Mathematics and Computer Science, Page 90-103
DOI: 10.9734/BJMCS/2014/5175

In this paper, an efficient decomposition method is constructed and used for solving system of nonlinear equations. These methods based on the modified homotopy technique of Noor [1]. This technique is revised to solve the system of nonlinear equations. Our approach yields third and fourth order iterative methods which are more efficient than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods.

Open Access Original Research Article

A Generalized Non-Stationary 4-Point b-ary Approximating Scheme

Pakeeza Ashraf, Ghulam Mustafa

Journal of Advances in Mathematics and Computer Science, Page 104-119
DOI: 10.9734/BJMCS/2014/4120

A generalized non-stationary 4-point b-ary approximating subdivision scheme is presented for even integer b≥2. Lagrange trigonometric polynomial plays a key role in computation of mask of the generalized scheme. The proposed schemes can be considered as non-stationary counterpart of existing stationary approximating schemes. Asymptotic equivalence technique is used for convergence analysis of the proposed schemes. Efficiency of proposed schemes is illustrated with the help of some examples.

Open Access Original Research Article

Fuzzy Cost Computations of M/M/1 and M/G/1 Queueing Models

M. Jeeva, E. Rathnakumari

Journal of Advances in Mathematics and Computer Science, Page 120-132
DOI: 10.9734/BJMCS/2014/4353

In this paper two models of planning queuing system and its effect on the cost of the each system by using two fuzzy queuing models of M/M/1 and M/G/1 are studied. These two fuzzy queuing models based on the cost of each model are compared and fuzzy ranking methods are used to select the optimal model due to the resulted complexity. Fuzzy queuing is more practical and realistic than deterministic queuing models. The basic idea is to transform a fuzzy queuing cost problem to a family of conventional crisp queue cost problem by applying the α-cut approach and Zadeh’s extension principle. A set of parametric nonlinear programs are developed to calculate the lower and upper bound of the minimal expected total cost per unit time at α, through which the membership function of the total cost is constructed. Numerical example is illustrated to check the validity of the proposed method.

Open Access Original Research Article

A New Class of Odd-Point Ternary Non-Stationary Schemes

Ghulam Mustafa, Mehwish Bari

Journal of Advances in Mathematics and Computer Science, Page 133-152
DOI: 10.9734/BJMCS/2014/3736

In this paper we generate a new family of odd point ternary non-stationary interpolating subdivision schemes by using Lagrange identities. It is to be observed that the limiting ellipse, generated by proposed schemes compared to the existing non-stationary interpolating schemes, has less deviation from being an exact ellipse. The proposed non-stationary schemes are asymptotically equivalent to converging stationary schemes [1,2,3,4,5,6]. The performance and comparison of the schemes are verified by examples.

Open Access Original Research Article

Modeling and Parameter Sensitivity Analysis of Population Dynamics in Uganda

Jimmy Omony

Journal of Advances in Mathematics and Computer Science, Page 153-161
DOI: 10.9734/BJMCS/2014/5981

Keeping track of the human population is essential for proper planning for facilities such as healthcare, infrastructure, education, and other essential needs. There are various ways by which the government can ensure that service provision is improved and maintained for its citizens and very often this starts by knowing the changes in demography as a function of time.In this work mathematical modeling and simulations are used to study the population dynamics of Uganda. The models are used for prediction of the county’s population and how its dynamics changes in time. Parameter sensitivity analysis was performed using population census data and the results shows huge influence of variations of the model parameters. The results show that the difference between the per capita birth and death rate parameters is crucial for changes in the country’s population. Such findings can also be analogously applied to countries with a similar population structure and economy.