Open Access Original Research Article

Blow-up of Solutions for a Reaction-diffusion Equation with Nonlinear Nonlocal Boundary Condition

Sen Zhou, Zuodong Yang

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2016/25746

This paper deals with a reaction-diffusion equation subject to nonlinear nonlocal boundary condition and with nonlocal reaction source. We investigate the global existence and blow up in finite time of a nonnegative solution by using a sub-super solution method.

Open Access Original Research Article

Comparative Design and Analysis of PIDA Controller Using Kitti's and Jung-Dorf Approach for Third Order Practical Systems

D. K. Sambariya, Deepak Paliwal

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/BJMCS/2016/26223

In this paper, PIDA controller is designed for third-order control systems using Novel Analytical methods. These approaches are based on Jung-Dorf method and Kittis method. This paper demonstrated the PIDA controller design for application of DC motor, Induction motor and AVR power system. The PIDA controller is an extension to the PID controller. The additional term A stands for acceleration, with this new term, a closed-loop system can respond faster with less overshoot. Originally, the PIDA controller design utilizes the Dominant pole concept proceeded in the s-plan.

Open Access Original Research Article

Defect Prediction Framework Using Neural Networks for Software Enhancement Projects

Vipul Vashisht, Manohar Lal, G. S. Sureshchandar

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/26337

So far, various approaches have been proposed for effective and accurate prediction of software defects, yet most of these approaches have limited adoption in practice. The objective of this paper is to provide a framework which is expected to be more user-friendly, effective and acceptable for predicting the defects in multiple phases across software enhancement projects. This communication describes a process of applying computational intelligence technologies, in particular neural networks in formulating defect prediction models early in the software development life cycle. A series of empirical experiments are carried out based on input and output measures extracted from 50 'real world' project subsystems. In order to increase the adoption and make the prediction framework easily accessible to project managers, a graphical user interface (GUI) based tool has been designed and implemented that allows input data to be fed easily.

The proposed framework uses historical data for training model and as a result provides a defect range (minimum, maximum) based output instead of a definite defect count based output. This is done in view of the fact that exact-count prediction has less probability of being correct as compared to range based predictions. The defect predictions can be used for taking informed decisions including prioritizing software testing efforts, planning additional round of code reviews, allocating human and computer resources, planning for risk mitigation strategy and other corrective actions. The claim of effectiveness of proposed framework is established through results of a comparative study, involving the proposed framework and some well-known models for software defect prediction.

Open Access Original Research Article

The Behavior of two Coupled Mechanical Oscillators in Non-linear Fields and the Possibility of Obtaining Controlled Halts

Nicuşor Nistor, Constantin Gheorghieş, Nelu Cazacu, Gabriela Tudor

Journal of Advances in Mathematics and Computer Science, Page 1-23
DOI: 10.9734/BJMCS/2016/24446

The proposed mechanical system consists of two magnetic oscillating subsystems, which are mechanically coupled. The first one consists of a spring-magnet-mass subsystem and the other one is a spring-mass subsystem. The non-linear symmetric field created by two other fixed magnets, oriented for attraction, acts only upon the first subsystem. The entire system can oscillate horizontally, without friction and without loss of energy. Oscillations occur with conservation of kinetic energy and potential energy stored in the springs. During the movement, depending on the amplitude of oscillations, the main body stops for a period and this can be controlled by the physical constants of the system. The reason for these controlled halts of oscillations is the transfer of mechanical impulse, due to both oscillators entering in the frequencies equalizing status with different initial frequencies. The frequency of the main oscillator gets synchronized with the frequency of the second oscillator, by its deeper or more superficial presence in a non-linear magnetic field, which is strongly dependent on distance. This paper will apply linear algebra transformation methods, on the R3 vector spaces, for differential equations systems, that are applicable to non-linear systems only if we consider some special conditions. The general case will be solved and the method will be verified through a numerical application.

Open Access Original Research Article

The Metrics of Multiple Inheritance and the Reusability of Code – Java and C++

Fawzi Albalooshi

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/25851

One of the fundamental notions in object-oriented systems is multiple inheritance which enables developers to combine concepts and increase the reusability of resulting software. Two of the widely used object-oriented languages are Java and C++ that each has its own mechanism to implement multiple inheritance. The paper investigates the difference between the two languages’ implementation of this important notion. CK software metrics have been widely used to measure object-oriented software designs and implementations and are well-known in the software engineering community. In this paper they are used to assess the two implementations of an object-oriented system having multiple inheritance relationships and in particularly the reusability factor. Reusability is evaluated using a combination of the CK metrics that have been designed specifically for the purpose. The results clearly show that the Java implementation compared to C++ has increased coupling and software complexity and lacks cohesion resulting to reduced software reusability.

Open Access Original Research Article

Exact Solutions with Bounded Periodic Amplitude for Kundu Equation and Derivative Nonlinear Schrödinger Equation

Changfu Liu, Jinmei Liu, Ping Zhou, Min Chen

Journal of Advances in Mathematics and Computer Science, Page 1-6
DOI: 10.9734/BJMCS/2016/25570

In this paper, exact solutions with bounded periodic amplitude to Kundu equation are obtained through transformation, direct integration method and trial function method when the parameters satisfy certain conditions. By the way, exact solutions for the derivative nonlinear Schrödinger equation are also obtained. Two solutions' images are displayed. These results greatly enrich the solutions' structural diversity for these equations.

Open Access Original Research Article

Improve the Mean Square Solution of Second-order Random Differential Equations by Using Homotopy Analysis Method

A. R. Khudair, S. A. M. Haddad, S. L. Khalaf

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2016/25673

The Homotopy analysis method is implemented by Golmankhanehi et al. to find the expectation and variance of the approximate solutions of the second-order random differential equations [1]. In this note, we reused the Homotopy analysis method to solve the same problem and we draw some very important improvements and comments on the paper [1]. The results in this paper are coinciding with the results in [2, 3, 4, 5].