An Algorithmic Approach for Stability of an Autonomous System

Many phenomena in biology can be modeled as a system of first order differential equations x = ax + by, y=cx+dy. An example of such a system is the prey-predator model. To interpret the results we have to obtain full information on the system of equations such as the stability of the equilibrium points of the system. This requires in depth knowledge of differential equations. The literature often emphasizes on the analytical methods to obtain results regarding the stability of the equilibrium points. This is possible to achieve for small systems such as a 2 x 2 system. The non-mathematician researchers often do not have the analytical tools to understand the model fully. Very often what they are interested in is the information regarding the critical points and their stability without going through the tedious mathematical analysis. This calls for user friendly tools for the non-mathematicians to use in order to answer their problem at hand. The objective of this research is to establish an algorithm to determine the stability of a more general system. By doing so we will be able to help those who are not familiar with analytical methods to establish stability of systems at hand The following algorithm is' employed in developing the software: L 1. Search for critical point is conducted. L2. Eigenvalues of the linear system are computed. These values are obtained from the characteristic equation IA - All = 0 , where A. is an eigenvalue and F or the nonlinear system, linearization process around the critical points are carried out. L3. Stability of system is determined. L4. Trajectory of the system is plotted in the phase plane. To develop the software we use the C programming language. It is hoped that the software developed will be of help to researchers in the field of mathematical biology to understand the concept of stability in their model

Review methods for image segmentation from computed tomography images

Image segmentation is a challenging process in order to get the accuracy of segmentation, automation and robustness especially in medical images. There exist many segmentation methods that can be implemented to medical images but not all methods are suitable. For the medical purposes, the aims of image segmentation are to study the anatomical structure, identify the region of interest, measure tissue volume to measure growth of tumor and help in treatment planning prior to radiation therapy. In this paper, we present a review method for segmentation purposes using Computed Tomography (CT) images. CT images has their own characteristics that affect the ability to visualize anatomic structures and pathologic features such as blurring of the image and visual noise. The details about the methods, the goodness and the problem incurred in the methods will be defined and explained. It is necessary to know the suitable segmentation method in order to get accurate segmentation. This paper can be a guide to researcher to choose the suitable segmentation method especially in segmenting the images from CT scan

Evaluation of performance for different filtering methods in CT brain images

This paper presents the comparison of filtering methods for a contrast enhancement of computed tomography (CT) brain images. Each method consists of three filter consecutively which is a combination of the low order linear filter such as Gaussian filter, disk filter, average filter and median filter with an adaptive filter method and unsharp filter. The process starts with filtering the CT brain image using low order linear filter, then proceeds with adaptive averaging filter and ends with unsharp filter. In this paper, there are two criteria, peak signal to noise ratio and mean square error, that were adopted for performance assessment. Our preliminary results showed that the combination of Gaussian filter with adaptive filter and unsharp filter gives the good result in removing the noise and edge detection. This method improved the CT brain image and the gyri and sulci can be easily identified

On the properties of class of pvalent functions defined by Salagean differential operator,

Abstract Salagean [3] defined the operato

P A COEFFICIENT BOUNDS FOR A CLASS MULTIVALENT FUNCTION DEFINED BY SALAGEAN OPERATOR

Abstract: The aim of the present paper is to define a subclass of analytic p-valent function in the open unit disk U = {z : |z| < 1} namely S λ p (A, B, b). For the class defined, we obtain the upper bounds for the Fekete Szego functional,|a p+2 − µa 2 p+1 |