Open Access Original Research Article

Quality Inspection of Bag Packaging Red Beans (Phaseolus vulgaris) Using Fuzzy Clustering Algorithm

Ngatchou Alban, Bitjoka Laurent, Yemefack Martin, Boukar Ousman

Journal of Advances in Mathematics and Computer Science, Page 3369-3386
DOI: 10.9734/BJMCS/2014/12981

Food industry is currently focusing on fast and unsupervised quality inspection techniques. This paper deals with the development of new method for fast quality control of bag packaging red beans (Phaseolus vulgaris) using flatbed scanning. The proposed method combines fuzzy c means with spatial transformation (FCM_ST) to reduce FCM iteration. We used the labelled pixel, in the clustering image, for the evaluation of grain mixture in acquired image. The performance of the FCM_ST was compared to the standard FCM approach and it reveals itself very good for fast clustering and efficient detection of grain mixture. The detections accuracies of grain mixture in the bag packaging red beans (Phaseolus vulgaris) was 96% for acquired image with presence of other self-colour commercial beans type, 70% with presence of defected cotyledons beans, between 30% to 89% with presence of multi-coloured beans depending on their texture and between 10% to 15% with the presence of low discoloured red beans of same commercial type.

Open Access Original Research Article

Model Selection of Stochastic Simulation Algorithm Based on Generalized Divergence Measures

Papa Ngom, B. Don Bosco Diatta

Journal of Advances in Mathematics and Computer Science, Page 3387-3402
DOI: 10.9734/BJMCS/2014/12020

We consider the generalized divergence measure approach to compare different simulation strategies such as the Independent Sampler (IS), the Random Walk of Metropolis Hastings (RWMH), the Gibbs Sampler(GS), the Adaptive Metropolis (AM), and Metropolis within Gibbs (MWG). From a selected set of simulation algorithm candidates, the statistical analysis allows us to choose the best strategy in the sense of rate of convergence. We use the informational criteria such as the R´enyi divergence measure Rα(p, q), the Tsallis divergence Tα(p, q), and the -divergence Dα(p, q), where p and q are probability density functions, to show in some examples of synthetic models with target distributions in one dimensional, and two dimensional cases, the consistency and applicability of these -divergence measures for stochastic simulation selection.

Open Access Original Research Article

Paracontact Finsler Structures on Vector Bundles

Ahmet Kazan, H. Bayram Karadağ

Journal of Advances in Mathematics and Computer Science, Page 3403-3426
DOI: 10.9734/BJMCS/2014/13466

In this paper, we study the almost paracontact, almost paracontact metric, paracontact metric, K-paracontact and para-Sasakian Finsler structures on vector bundles and give some characterizations for these geometric structures. Also, the curvature of a paracontact Finsler manifold is given and some results for Ricci semi-symmetric para-Sasakian Finsler manifolds and para-Sasakian Finsler manifolds with η-parallel Ricci tensor are obtained with the aid of Ricci tensor and scalar curvature of Finsler structure.

Open Access Original Research Article

Price Dynamics of Maize in Ghana: An Application of Continuous –Time Delay Differential Equations

Martin Anokye, Francis T. Oduro

Journal of Advances in Mathematics and Computer Science, Page 3427-3443
DOI: 10.9734/BJMCS/2014/13484

This paper seeks to study the price dynamics of maize in Ghana, in the context of mathematical modelling using continuous-time cobweb models derived from linear and nonlinear delay differential equations. The stability conditions of two cobweb models: continuous-time linear and nonlinear models are discussed. The data is obtained from the Ministry of Food and Agriculture, Statistical Directorate Kumasi-Ghana, from 1994 to 2013.
The models performed on the assumptions that, maize has no equal substitutes and there are no exogenous shocks needed to generate price fluctuations so that market price would be determined by only the available supply in a single market.
From the results of the analysis performed on the real economic price and production data using numerical approach, the nonlinear delay differential model (formulated from linear demand and quadratic supply functions) showed oscillations between and around two equilibrium points and would neither converge. This result seems realistic as it appears to reflect real market conditions since an equilibrium price would not be compatible with the prevailing situation of high inflation, food insufficiency and/or producers’ sensitivity towards price.
The linear model (formulated from linear demand and linear supply functions) on the other hand showed little oscillations and then converged towards an equilibrium point (zero equilibrium price). However, this seems quite unrealistic.
Effects of delay parameter on oscillations are also discussed. It is observed that oscillations (price fluctuations) are suppressed for ≤0.5, using the nonlinear delay equation. This is an indication that price fluctuations are reduced, if and only if, factors affected by time lag, such as the time necessary for increasing supply, buying new inputs, hiring workers or transporting commodities to market centres, building warehouse and reducing effects of natural constraints on crop yields are improved. On the contrary, the linear delay differential equation, for >0.5 or ≤0.5, would still be in stable equilibrium.
We draw inferences from this study that researchers should rather use nonlinear models instead of linear models in solving most real-life economic problems to avoid misleading conclusions.

Open Access Original Research Article

Picture Maze Generation by Successive Insertion of Path Segment

Tomio Kurokawa

Journal of Advances in Mathematics and Computer Science, Page 3444-3463
DOI: 10.9734/BJMCS/2014/12048

Picture maze is a maze on which some picture appears when it is solved. This paper aims to present a very simple method to construct a picture maze. It is always possible to construct a spanning tree on a connected region of a binary picture. A spanning tree connects all vertices on the region. A 2-by-2 extended picture of a connected picture is the one such that each cell in the picture is transformed to four cells which constitute a square block with the cells. Then by analogy, it is always possible to construct a block spanning tree on the extended picture region, where a block is the square unit of four cells. Construction of the block spanning tree and the generation of the corresponding Hamiltonian path can be done at the same time. The Hamiltonian path is constructed along a data structure of a linked list in a simple manner. It traverses every cell on the 2-by-2 extended picture. The similar procedure but with the smaller block with two vertices, instead of four, can be applied to a non-extended picture, an ordinary one, which produces a near Hamiltonian path, which can then be a maze solution path. The near Hamiltonian path traverses nearly all the vertices on the picture, hence depicting a picture on the maze when it is solved. This paper demonstrates the method and its efficiency.

Open Access Original Research Article

Solution of Nonlinear Space–time Fractional Differential Equation via the Triple Fractional Riccati Expansion Method

E. A. B. Abdel-Salam, M. S. Jazmati

Journal of Advances in Mathematics and Computer Science, Page 3464-3475
DOI: 10.9734/BJMCS/2014/12974

In this paper, the triple fractional Riccati expansion method is applied to solve fractional differential equation. To illustrate the effectiveness of the method, the nonlinear space-time fractional Klein–Gordon equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time.

Open Access Original Research Article

Analytical Derivation of Latency in Computer Networks

Adelakun A. Adebiyi, Samuel N. John, Charles Ndujuiba

Journal of Advances in Mathematics and Computer Science, Page 3476-3488
DOI: 10.9734/BJMCS/2014/10770

This paper presents mathematical method of estimating the latency of a corporate computer network through broad classification into propagation, serialization and queue delays. The parameters of interest considered are the sending rates, arrival times, connection bandwidth and the speed of travelling in the medium. Simple and easily determined factors that are essential for computer networks’ quality of service QoS were used to derive the expressions for computing latencies. The expressions were tested with randomly varying packet sizes, variable mean service rates of nodal devices and varying packet arrival rates.

Open Access Original Research Article

Some Special Rogue Waves in One Type of Variable Coefficient Nonlinear Schrödinger Equations

Yue Wu, Jiuli Yin, Xingyu Feng, Qianqian Xing, Dan Li

Journal of Advances in Mathematics and Computer Science, Page 3489-3496
DOI: 10.9734/BJMCS/2014/12685

In this paper, a similarity transformation is devised to construct a Miura type transformations between one type of variable coefficient nonlinear Schrodinger equations and the cubic NLS equation. This transformation is devoted to obtain the travelling wave solutions of a complicated equation by using the solutions of a simpler equation directly. The result shows different rogue wave solutions of the variable coefficient nonlinear Schrodinger equations are given easily.

Open Access Original Research Article

Using the Average of the Extreme Values of a Triangular Distribution for a Transformation, and Its Approximant via the Continuous Uniform Distribution

H. I. Okagbue, S. O. Edeki, A. A. Opanuga, P. E. Oguntunde, M. E. Adeosun

Journal of Advances in Mathematics and Computer Science, Page 3497-3507
DOI: 10.9734/BJMCS/2014/12299

This paper introduces a new probability distribution referred to as a transformed triangular distribution (TTD) by using the average of the extreme values (minimum and maximum) of the triangular distribution. The TTD is being approximated by the continuous uniform distribution. The basic moments of the TTD and those of the continuous uniform distribution are compared respectively, and a relationship established. This can be used in modeling and simulation.

Open Access Original Research Article

The Stability and Convergence Analysis of a New Conjugate Gradient Method for Solving Nonlinear Optimization Problems

Nwaeze Emmanuel, Oko Nlia

Journal of Advances in Mathematics and Computer Science, Page 3508-3522
DOI: 10.9734/BJMCS/2014/13361

The development of any conjugate gradient method could be viewed from the perspective of approximating an objective function by a functional noting that the properties of the functional can be used to characterize the method. Using the functional , the new conjugate gradient method was developed and used to solve many nonlinear optimization problems with high efficiency and accuracy. The numeric analysis of its stability and convergence becomes imperative in order to establish the reliability of the method and satisfy the yearnings of its increasing users. In this paper, we present the stability and convergence analysis of the new conjugate gradient method.