##### An Efficient CRT Based Reverse Converter for {22n+1-1, 2n-1, 22n-1} Moduli Set

Hassan Kehinde Bello, Kazeem Alagbe Gbolagade

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/JAMCS/2017/38517

This paper presents a reverse converter for the moduli set {22n+1-1, 2n-1, 22n-1} using a Chinese Remainder Theorem (CRT) algorithm and reverse method of data conversion. We compare our result with other converters found in literature that have the same Dynamic Range (DR) and our proposed algorithm has a better performance in terms of speed.

Aims: The aim of this study is to design a reverse converter for the moduli set {22n+1-1, 2n-1, 22n-1}, determine the speed and compare it with other moduli set with the same DR in literature.

Methodology: We applied Chinese Reminder Theorem algorithm for data conversion.

##### Simple Mathematical Model for Malaria Transmission

Mojeeb AL-Rahman EL-Nor Osman, Isaac Kwasi Adu

Journal of Advances in Mathematics and Computer Science, Page 1-24
DOI: 10.9734/JAMCS/2017/37843

Our model is made up of two sections: In the first section, we study a simple SEIR model, estimated the reproduction number, discussed the disease-free and endemic equilibria using the Routh-Hurwitz criterion and second additive compound matrix respectively. A global stability of disease-free and the endemic equilibria was performed using Lasselle’s invariance principle of Lyapunov functions. In the second section of our model, we considered SEIR-SEI model of malaria transmission between humans and mosquitoes. We estimated the reproduction number and discussed the stability of the disease-free and endemic equilibria. The disease-free equilibrium was locally asymptotically stable if the reproduction number is less than one and unstable if the reproduction number is greater than one in both models. Numerical simulations were conducted using Matlab software to confirm our analytic results. Our findings were that, Malaria may be controlled by reducing the contact rate between human and mosquito, the use of active malaria drugs, insecticides and mosquito treated nets can also help to reduce mosquitoes population and malaria transmission respectively.

##### Variants of Compatible Mappings in Menger Spaces

Balbir Singh, Pawan Kumar, Z. K. Ansari

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/JAMCS/2017/37973

In this paper, we introduce the notions of compatible mappings of type(R), type (K) and type (E) in Mengers paces and prove some common fixed point theorems for these mappings. In fact, we call these maps as variants of compatible mappings.

##### A Conceptual Approach to Resources Allocation Scheduling

A. A. Eludire, C. O. Akanbi

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2017/32569

The problem of scheduling and allocation of resources, both space and time, has generated a lot of issues and has become of great concerns in daily human activities. The choice of best or appropriate computational algorithms for solving this problem has been the subject of several seminars and conferences organized to discuss the allocation of resources in different fields. The problem of resource scheduling deals with various criteria that are involved in the allocation of resources and associated variation on how the resources are to be allocated. The scheduling of an allocation of resources requires proper management of resources and time for various users to avoid clashes in timing of events. This paper presents a conceptual framework for solving resource allocation scheduling problems using timetabling as a representative scheduling problem requiring proper management of resources and time for various users to avoid clashes in timing of events. The work identifies the constraints involved in algorithms that have been used to solve several timetabling problem like airplane roster, lecture schedules, etc. The paper attempts to identify a good framework for the use of fuzzy algorithm implementation that will be of great value to those resolving timetabling oriented problems.

##### Results of Existence Fixed Point for Integral Type Contractive Condition with ω-distance

S. J. Hosseini Ghoncheh, Khalil Nabizadeh Azar

Journal of Advances in Mathematics and Computer Science, Page 1-5
DOI: 10.9734/JAMCS/2017/29001

In this paper, we prove the existence of fixed point for mappings defined on complete metric spaces with ω-distance that satisfying a general contractive inequality of integral type.

##### One Step Trigonometrically-fitted Third Derivative Method with Oscillatory Solutions

A. O. Adeniran, I. O. Longe

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/JAMCS/2017/36509

A continuous one step Trigonometrically-fitted Third derivative method whose coefficients depend on the frequency and step size is derived using trigonometric basis function. The method obtained is use to solve standard problems with oscillating solutions. We also discuss the stability properties of the new method . Numerical result obtained via the implementation of the methods shows that the new method performs better than the one step Trigonometrically-fitted second derivative method proposed by Ngwane and Jator [1].

##### A Financial Prey-predator Model with Infection in the Predator

Letetia Mary Addison, Balswaroop Bhatt, David Owen

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2017/38379

A modified predator-prey model is proposed with logistic growth in both prey and predator populations and an infection in the predator population. This model uses ideas from the original biological Lotka-Volterra model in an attempt to imitate financial predation. Potential investors, the prey, interact with financial experts, the predators, who provide advice on purchasing financial instruments and investments. Some of these experts are honest while others are ‘infected’, in that, a portion of them attempt to deceive clients into making irrational investments for their own benefit, incurring losses to the client. Stability and Hopf bifurcation analyses are discussed analytically. The results have been verified using numerical simulations in MATLAB.  Using different datasets, the study shows that variation of different parameters can affect the stability of the system and the co-existence of potential investors and financial experts over time.

Aims: To determine regions of stability for the model by varying parameter values in simulated datasets.

Study Design:  Stability Analysis – Analytical and Numerical.

Methodology: The model is first studied analytically by solving for the positive, interior equilibrium point (once it exists) when the differential equations are solved simultaneously. Stability conditions are defined based on these results using the Routh – Hurwitz criteria. These results are verified numerically in MATLAB as an initial value problem, integrating with slight perturbation around the equilibrium point. Each parameter in the dataset is varied one at a time. The regions where the model remains stable for a particular parameter are recorded. The Hopf bifurcation points, where there are stability changes, are also noted and graphical simulations are produced using time series and three-dimensional (3D) plots for particular stable and unstable scenarios. The effect of three different pairs of financial expert - investor persuasion rates on the populations of investors, is also shown.

Results: Hopf bifurcation parameters for three simulated datasets were found to be associated with the investment persuasion rate, investor-expert interaction rates, expert interaction rate, expert interference constant and growth rate of experts. In particular, the population of potential investors increased drastically when the investor persuasion rate for dishonest investors was much greater than that for honest investors for the given dataset.

Conclusion: Variation of parameter values in the model allow for the analysis of model stability conditions. These enhance the creation of detection mechanisms to control the ‘infection’ of investment fraud among financial experts.

##### A Useful Result on the Covariance Between Ito Integrals

Tristan Guillaume

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/JAMCS/2017/38464

This article introduces a general result on the covariance between two Ito integrals driven by two different Brownian motions, which slightly generalizes the isometry property. This result finds applications in mathematical finance, e.g. it enables to determine the probability distribution of the integrated interest rate process in exponential-affine models of the yield curve.

##### Estimation of Community Views on Criminal Justice a Statistical Document Analysis Approach

Sujeong Seo, Ernest Fokoue

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/JAMCS/2017/38582

The Community Views on Criminal Justice System (CVCJS) initiative was established to collect a city community's perceptions on experiences with local Police Departments and other agencies in the criminal justice system, and share those findings to inform local Gun Involved Violence Elimination (GIVE) strategies in New York State. This paper reviews those findings via an empirical study with major text mining methods. Specifically, atomic/canonical words along with as n-grams are used to explore such text mining tasks as sentiment analysis, document clustering and topic modeling, all aimed at gaining insights into all the patterns underlying the community's perception of policing and criminal justice. We use Latent Dirichlet Allocation [LDA] analysis and Structural Topic Model [STM] analysis, which are currently among the most widely used topic modelling algorithms in the fields of computer science, statistics, and machine learning. Despite the very limited amount of data available for our study, the combination of sentiment analysis with document clustering and topic modelling helps extract and reveal very interesting patterns underlying the community's views of policing and criminal justice.

##### DRBEM Sensitivity Analysis and Shape Optimization of Rotating Magneto-Thermo-Viscoelastic FGA Structures Using Golden-Section Search Algorithm Based on Uniform Bicubic B-Splines

Mohamed Abdelsabour Fahmy

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/JAMCS/2017/38677

Aims: A practicalshape optimization technique is developed, using thedual reciprocity boundary element method (DRBEM) with the golden-section search algorithm based on uniform bicubic B-splines, for rotating magneto-thermo-viscoelastic functionally graded anisotropic (FGA) structures subjected to a moving heat source in the context of the Green and Naghdi theory of type III.

Study Design: Original Research Paper.

Place and Duration of Study: Jamoum University College, Mathematics Department, between July 2016 and August 2017.

Methodology: An implicit-implicit staggered algorithm was proposed for use with the DRBEM to obtain the final DRBEM coupled linear system of equations for displacements and temperature that describe the magneto-thermo-viscoelastic structural analysis problem. An implicit differentiation of the discretized dual reciprocity boundary integral equation with respect to design variables is used to calculate shape displacement sensitivities of anisotropic materials with very high accuracy. This method allows the coupling between optimization technique and a dual reciprocity boundary element method. The feasible direction method was developed and implemented for use with the one-dimensional golden-section search technique based on uniform bicubic B-splines, as a numerical optimization method for minimizing weight while satisfying all of the constraints.

Results: The optimum shape design of fillet in tension bars used as the numerical example in order to verify the formulation and the implementation of the proposed technique. The numerical results show our technique is efficient and precise.

Conclusion: From the research that has been performed, it is possible to conclude that the optimal shape of the top half of the fillet under stress constraint based on magneto-thermo-viscoelasticity is crucial when magneto-thermoviscoelastic field is sensitive to boundary shape. Also from this knowledge of the variation of the displacements and temperature sensitivities with time for magneto-thermo-viscoelastic FGA structures, we can design various magneto-thermoviscoelastic structures to meet specific engineering requirements and utilize within which to place new information can be more effective.

##### Iris Texture Analysis for Ethnicity Classification Using Self-Organizing Feature Maps

B. M. Latinwo, A. S. Falohun, E. O. Omidiora, B. O. Makinde

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/JAMCS/2017/29634

Ethnicity Classification from iris texture is a notable research in the field of pattern recognition that differentiates groups of people as distinct community by certain characteristics and attributes. Several ethnicity classification systems have been developed using Supervised Artificial Neural Network and Machine Learning algorithms. However, these systems are limited in their clustering ability and require prior definition of image classes which lowers its classification rate. Therefore, this work classified iris images from Nigeria, China and Hong Kong origin using Self-Organizing Feature Maps (SOFM) blended with Principal Component Analysis (PCA) based Feature extraction. Left and right irises of 240 subjects constituting 480 images were acquired online from CUIRIS (Nigeria), CASIA (China) and CUHK (Hong Kong) datasets, and normalized to a uniform size of 250 by 250 pixels. Three hundred and thirty six (336) images were used for training while the remaining 144 were used for testing. The system was implemented in Matrix Laboratory 8.1 (R2013a). The performance of the classification system was evaluated at varying thresholds (0.2, 0.4, 0.6 and 0.8) and 93.75% Correct Classification Rate (CCR) was obtained.

##### Some Commutativity Theorems for Prime Near-rings Involving Derivations

Moharram A. Khan, Abdu Madugu

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/JAMCS/2017/38097

The study depicts that a prime near-ring N is considered to be a commutative ring if there non-negative integers exist i.e., in such a way that N admits a non-zero derivation, where d satisfying one of the conditions like (C1) - (C8). For any x, y ∈ N , we define the following properties

In addition, an example is given to demonstrate the primeness of the hypothesis which is not superfluous. Finally, we can conclude it with some open problems.

##### A Stochastic Model of the Dynamics of Stock Price for Forecasting

A. I. O. Ofomata, S. C. Inyama, R. A. Umana, A. Omame

Journal of Advances in Mathematics and Computer Science, Page 1-24
DOI: 10.9734/JAMCS/2017/38014

In this work, a stochastic model of some selected stocks in the Nigerian Stock Exchange (NSE) is formulated. We considered four different stocks and their market prices. The likelihood of each change occurring in the stock prices was noted, the drift (the expectation) and the volatility (the covariance) of the change were computed leading to the formulation of stochastic differential equations. Changes in the prices of the stocks were studied for an average of 60 days. The drift and the volatility coefficients for the stochastic differential equations were determined and the Euler-Maruyama method for system of stochastic differential equations was used to simulate the stock prices. With the aid of the simulation we carried out a fore-cast of the prices of the stocks for a short time interval. A consideration of the different stock prices over a period of forty months, stock S1 seems to give the best return on investment compared with stocks S2, S3 and S4. The investor after observing the trend over longer period can invest in the stock that will yield the best returns. Our analysis enables us to compare as many as four stocks in order to advise the investor on where best to make investment.