##### Binding Visualization Method and Numeric Method Together to Analyze Large Data - With a Case Study

Yousuo Zou, Zhiqiang Chen, Jinhe Xu

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/19773

In this paper, the authors combine a data visualization method and a numeric analysis method, binding them together to analyze large data (Big Data). Also included is a case study selected from the water transportation industry – A port on the Yangtze River and its annual import & export productivity (104 tons /year) – used to show how our methods work step by step. Theoretical and practical efforts in this paper suggest that the proposed methods (or algorithms) are efficient for data analysis and data prediction.

##### A Study of the Estimation of the Gini Coefficient of Income Using Lorenz Curve

Kwasi A. Darkwah, Ezekiel N. N. Nortey, Felix O. Mettle, Isaac Baidoo

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/24494

Aims: This paper compares the Boole and Weddle numerical integration methods to estimate the Lorenz curve and Gini Coefficient of income in Ghana.

Study Design:  Research Paper.

Place and Duration of Study: Ghana, Secondary data for 2013 Ghana Living Standard Survey.

Methodology: The Lorenz curve and Gini coefficients of income were estimated using Rasche, Gaffney and Obst function and polynomial function according to numerical integration methods such as Boole and Weddle methods. The Bias and relative error was used to compare the numerical integration methods used.

Results: The results showed that the estimated Lorenz curve and Gini coefficients using Rasche, Gaffney and Obst function and polynomial function according to the Boole and Weddle method of integration resulted in positive and negative biases respectively with the Boole method producing the highest absolute relative error of 1.8082%.

Conclusion: This study showed that both the Boole and Weddle method of numerical integration are not uniformly optimal in estimating the Gini coefficient of income but the Weddle’s method is better as compared to Boole method of numerical integration in estimating the Gini coefficient of income.

##### The Use of Spatial Distribution of the Local Histogram Based Features for Finger's Veins Biometrics

Ruaa E. Fadhil, Loay E. George

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/24729

Finger vein authentication is a new biometric technique utilizing the vein patterns inside of fingers for personal identity verification. Vein patterns are different for each finger belong to each person; and as they are hidden underneath the skin’s surface, this makes finger vein detection a secure biometric for individual identification. The vein grid images are acquired using infrared (IR) cameras. The acquired images are of low contrast and blurred in nature; so, an effective contrast enhancement step is required to expand the values of brightness range in the input vein image. The deal with low quality finger vein image represents the major concern of this work, beside to the selection of proper features to efficiently distinguish between individuals.

In this paper a feature vector of the local histogram moments of gray finger image is proposed to represent the veins attributes; the main reason for used local moments is their ability to reflect the statistical behavior of veins variation at each part of finger image.  The extracted features are assembled as a feature vector; which, in turn, is used to distinguish different individuals. Nearest Neighbor classifier are used to make recognition decisions in the matching stage. The system is tested using a database consisting of 3,816 images. This dataset was constructed by capturing 6 samples for each of the 3fingers (i.e., index, middle and ring) that belong to one of the 2 hands of the 106 subjects. The achieved identification results of the proposed system indicate high recognition performance which is 99.52%, while the verification test results indicate error rate 0.003%.

##### Invariant Subspace Method and Some Exact Solutions of Time Fractional Modi ed Kuramoto-Sivashinsky Equation

A. Ouhadan, E. H. El Kinani

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/BJMCS/2016/25215

In this paper, we construct the exact solutions of the modified nonlinear time fractional Kuramoto-Sivashinsky equation by suing the invariant subspace method. As a result, the obtained reduced system of nonlinear ordinary fractional equations is solved by the Laplace transform method and with using of some useful properties of Mittag-Leffler functions. Then, some exact solutions of the time fractional nonlinear studied equation are found.

##### Harmonic Solution of a Weakly Non-linear Second Order Differential Equation Governed the Motion of a TM-AFM Cantilever

A. M. Elnaggar, K. M. Khalil, A. S. Rahby

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/24725

The harmonic solution of a weakly non-linear second order differential equation governed the dynamic behavior of a micro cantilever based on TM (Tapping mode) AFM (Atomic force microscope) is investigated analytically by applying the method of multiple scales (MMS). The modulation equations of the amplitude and the phase are obtained, steady state solutions, frequency response equation, the peak amplitude with its location and the approximate analytical expression are determined. The stability of the steady state solutions is calculated. Numerical solutions of the frequency response equation and its stability condition are carried out for different values of the parameters in the equation. Results are presented in a group of figures. Finally discussion and conclusion are given.

##### On Minimal Non-elementary Groups and Proper NF-groups

Yıldız Aydın, Ali Pancar

Journal of Advances in Mathematics and Computer Science, Page 1-4
DOI: 10.9734/BJMCS/2016/25010

Relations between a subgroup having F-supplement and a minimal non-elementary group are investigated and as a conclusion some conditions are given for a minimal non-elementary group to be an F-group. Then proper NF-groups which are also F-groups are studied.

##### A New Uniform Fourth Order One-Third Step Continuous Block Method for the Direct Solutions of y′′ = f (x, y, y′)

E. A. Areo, M. A. Rufai

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/24310

In this study, we applied the approach of collocation and interpolation to develop a new fourth order continuous one-third hybrid block method for the solutions of general second order initial value problems of ordinary differential equations. Three discrete schemes were derived from the continuous schemes. The discrete method was analyzed based on the properties of linear multistep methods and the method is found to be zero-stable, consistent and convergent. We reported an improved performance of the new method over the existing methods in the literature by solving four numerical examples and the approximate solutions obtained confirmed the superiority of our new developed scheme when compared with some latest existing approaches.