##### Parameter Estimation for a Mixture of Two Univariate Gaussian Distributions: A Comparative Analysis of The Proposed and Maximum Likelihood Methods

Cliff Richard Kikawa, Michael Yu Shatalov, Petrus Hendrik Kloppers, Andrew Mkolesia

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2016/16617

Two approaches to parameter estimation for a mixture of two univariate Gaussian distributions are numerically compared. The proposed method (PM) is based on decomposing a continuous function into its odd and even components and estimating them as polynomials, the other is the usual maximum likelihood (ML) method via the expected maximisation (EM) algorithm. An overlapped mixture of two univariate Gaussian distributions is simulated. The PM and ML are used to re-estimate the known mixture model parameters and the measure of performance is the absolute percentage error. The PM produces comparable results to those of to the ML approach. Given that the PM produces good estimates, and knowing that the ML always converges given good initial guess values (IGVs), it is thus recommended that the PM be used symbiotically with the ML to provide IGVs for the EM algorithm.

##### Machine Interference Problem with Reliable Server under Multiple Vacations Policy

S. A. Ojobor, N. O. Ogini

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/19209

The machine interference problem with reliable server under multiple vacations policy is considered. There are M similar machines that are subject to breaks down with a single server who is responsible for repairing the failed machines under multiples vacations. The failed machines arrive for service according to Poisson distribution with rate λ. The service time distributions of the failed machines are assumed to be exponentially distributed with state dependent service rate µn, where n is the number of failed machines. The differential difference equations obtained for the reliable server is solved through in MATLAB to obtain transient probability for the system. The transient probabilities are used to compute the operational measures of performance for the systems. The effects of failure rate, service rate and vacation length for the system were studied. We show that with the same service rate μ , failure rate λ and vacation length θ, as the number of operating machine in the system increases the variance also increases. We also found that the variance under multiple vacations system is slightly less than that of single vacation. This means that the multiple vacations models may be preferred to the single vacation. The result also shows that the CPU time for the machine interference problem with reliable server under single vacation is slightly lower than that of machine interference problem with an unreliable server under single vacation policy.

##### Weak Implication on Monadic Heyting Algebras

Aldo V. Figallo, Gustavo Pelaitay

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/20464

In this paper, we introduce an implication operation, called weak implication, which will be quite useful in order to characterize subdirectly irreducible monadic Heyting algebras. Furthermore, it is shown that deductively semisimple algebras are the non trivial ones such that the subalgebra of constants is a Tarski algebra with rst element, i.e. a Boolean algebra, as it is mentioned by A. Monteiro and O. Varsavsky in 1957 (Algebras de Heyting monádicas, Actas de las X Jornadas de la Unión Matemática Argentina, Bahía Blanca, (1957), (52-62). Finally, it is stated that some of the results established for monadic Heyting algebras are also valid for monadic generalized Heyting algebras.

##### Hausdorff Graphs

V. Seena, Raji Pilakkat

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/20509

A simple graph G is said to be Hausdorff if for any two distinct vertices u and v of G, one of the following conditions hold:
1. Both u and v are isolated
2. Either u or v is isolated
3. There exist two non-adjacent edges e1 and e2 of G such that e1 is incident with u and e2 is incident with v:
In this paper we discuss Hausdorff graphs and some examples of it. This paper also deals with the sucient conditions for Kmn, join of two graphs, middle graph of a graph and corona of two graphs to be Hausdorff. The line graph of a given Hausdorff graph is Hausdorff is proved. Moreover, the relations between Hausdorff graph with its incidence matrix and its adjacency matrix are discussed.

##### A Personal Identification Method Based on the Geometrical Patterns of Veins Grid in a Finger

Ruaa E. Fadhil, Loay E. George, Asmaa Q. Shareef

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2016/20268

As a new biometric technique, finger recognition has attracted lots of attentions and used in wide range of applications. Finger vein recognition is a physiological characteristics-based biometric technique; it uses vein patterns of human finger to perform identity authentication. Vein patters are network of blood vessels under a person’s skin. Even in the case of identical twins the finger-vein patterns are believed to be quite unique. This makes finger vein detection a secure biometric for individual identification. In this paper a feature set based on the local binary projections of veins grid body is proposed to be used for personal identification. The proposed system consists of three main stages, which are: preprocessing, feature extraction, and matching. Since near infrared NIR vein images suffer from low contrast, and low noise; which make the extraction task of accurate veins grid become hard. For this reason a sophisticated preprocessing process needs to be accomplished to ensure high identification rates. The applied steps in preprocessing stage are: histogram equalization (to improve the contrast of the image). Also the brightness compensation step is applied to suppress the background and to make grid body more visible, and to make the segmentation task easier. Finally two levels of thinning are applied to make the grid appearance more localized.

Due to fast implementation, and both rotation and scale invariant features requirements; a feature set based on the local binary projection (in four directions: vertical, horizontal, main diagonal, and second diagonal) is adopted. The geometrical moments are calculated for the four direction projections which represent the discriminating local finger vein features.

The developed system was tested over SDUMLA-HMT finger-vein database collected from 106 volunteers using their index, middle and ring fingers of both hands. The collection for each of the 6 fingers is repeated for 6 times to obtain 6 finger vein images. The test results indicated that the equal error rate of our proposed is 99.2%. Increasing the number of learning sample leads to improvement the identification rate up to (100%).

##### Fixed Point Results for Generalized Weakly C- contractive Mappings in Ordered G-partial Metric Spaces

Kanayo Stella Eke

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/18991

We introduced the class of generalized weakly C-contractive mappings in G-partial metric spaces by combining the characteristics of Hardy and Rogers maps with weak contraction maps. The existence and uniqueness of xed point for those maps in ordered G-partial metric spaces are established. Examples are given to support the validity of our results. Our results generalize some results in the literature.

##### An Automated System for Atlas Based Multiple Organ Segmentation of Abdominal CT Images

Sanjay Saxena, Neeraj Sharma, Shiru Sharma, S. K. Singh, Ashish Verma

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2016/20812

In this paper, an efficient atlas based approach for multiple abdominal organ segmentation is presented. This automatic segmentation of different organs such as spine, kidneys, liver, aorta, spleen of abdominal image is based on allocation of spine as landmark. In current years several researches has been done for developing automatic segmentation techniques of abdominal CT images however still it is an incredibly challenging task to segment this efficiently and appropriately. This paper proposed a fully automatic system for abdominal image segmentation by marking spine as landmark to extract different organs using a fuzzy based system. The proposed technique uses the fact that multiple organs of abdominal images are situated at a particular distance and in particular range of angles from the spine and spine is the solitary organ which is frequent in the slices of CT image data set. In this paper we focused for the segmentation of liver, kidney, aorta, spine, spleen. This system is evaluated on the data of several patients (152 CT images which consist all such organs) and obtained significant results by comparing the computed results to the boundaries manually traced by experts.