Asian Research Journal of Mathematics

This paper studied the behavior of two companies using predator prey model as the basis. As the companies are competing constantly, it affects them because their interaction determines the availability of resources for their growth. Considering growth of these companies, the parameters  which were respectively the carrying capacity and competitive impact of either of the competing companies on each other were included in the model. Equilibrium point and their existence criteria were analyzed to find the threshold that will guarantee the coexistence of both companies or collapse of either of them or both. It was shown that both companies can grow and rise simultaneously, (coexist) by dividing their resources correspondingly or that even the slightest change in their competition coefficient can lead to adverse situation, which may cause complete disappearance of one of the companies or both. We conclude that as long as these companies did not operate beyond their effective carrying capacity and equally maintain their respective competitive advantage, coexistence might be achieved. Some simulations are also given to illustrate our results.

The paper is devoted to construction of some closed inductive sequence of models of the generalized second-order Dedekind theory of real numbers with exponentially increasing powers. These models are not isomorphic whereas all models of the standard second-order Dedekind theory are. The main idea in passing to generalized models is to consider instead of superstructures with the single common set-theoretical equality and the single common set-theoretical belonging superstructures with several generalized equalities and several generalized belongings for rst and second orders. The basic tools for the presented construction are the infraproduct of collection of mathematical systems different from the factorized Los ultraproduct and the corresponding generalized infrafiltration theorem. As its auxiliary corollary we obtain the generalized compactness theorem for the generalized second-order language.

This paper presented a class of A-stable Runge-Kutta collocation methods with three free parameters for the solution of rst order ordinary dierential equations. Power series was considered as its basis function, adoption of interpolation and collocation of the approximate solution at some selected grid points to give system of equations was also considered. Gaussian Elimination method was used to solve for the unknown parameters and substituted into the approximate solution to give the continuous method. The three cases considered are the Guass, the Lobatto, and the Radau types. Analysis of the methods was made based on order, zero stability, consistence and convergence. The derived schemes were implemented in the Predictor-Corrector mode. Comparison with existing methods showed that the new developed Schemes compete favorably.

The present study aims to obtain infinite fractional power series solution vectors of fractional Cauchy-Riemann systems equations with initial conditions by the use of vectorial iterative fractional Laplace transform method (VIFLTM). The basic idea of the VIFLTM was developed successfully and applied to four test examples to see its effectiveness and applicability. The infinite fractional power series form solutions were successfully obtained analytically. Thus, the results show that the VIFLTM works successfully in solving fractional Cauchy-Riemann system equations with initial conditions, and hence it can be extended to other fractional differential equations.

Biometric recognition for human identification plays a key role in the rapid development of computer vision and pattern recognition research areas. The biometrics, refers to the automatic identification of a person based behavioral characteristics, physiological properties or traits. Signature recognition is one such human identification method and can be performed either in offline or online mode. This paper proposed an offline handwritten signature recognition which is based on image processing technique, scale-invariant feature transform (SIFT) and speeded-up robust features (SURF) features and support vector machines (SVMs). The handwritten signature images were then recognized through the proposed method that involves identification of regions of interest and representation of those regions as SIFT or SURF, construction of codebooks and the multi-class classification of the feature histograms using support vector machines (SVMs). Experiments have been carried out with our dataset of 1600 samples and a recognition rate in excess of 95% was obtained over the ten-fold cross validations.