Open Access Original Research Article

Full Observability Criteria for Linear Impulsive Control Systems with Application to Diabetes Type I Dynamics

P. S. Rivadeneira

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2017/37398

The main goal of this paper is to derive a full characterization of the observability of linear time-invariant impulsive systems. Two cases are studied. The firrst case considers continuous outputs. A suitable adapted Kalman criterion is shown to characterize properly the observability. In the second case, only discrete-time measurements of the outputs are available. A new rank condition based on the structure of the impulses is shown to characterize observability. Finally, these results are tested and illustrated both on academic examples and on the dynamical model of diabetic type I patients. The latter provides a nice case study for an impulsive system with discrete time measurements as the meals may be approximated by some impulse inputs and the glycemia measurement is usually done in real life at various times through the day.

Open Access Original Research Article

Novel Technique for IRFPA Blind Pixels Detection

Abdulaziz Mohammed Algamdi, Ahmad Abbas Ahmad Adas

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2017/38072

Infrared focal plane array (IRFPA) is a bi-dimensional infrared detector which is a matrix of micro detectors referred as pixels. Physical pixel failure (blind pixel) is a serious issue in case of utilizing IRFPA as a measuring tool or a surveillance system to monitors hot objects. Scene-based non-uniformity correction (SBNUC) technique for uncooled IRFPA depends on the correction algorithm strength to estimate the correction parameters and to eliminate the need for using the reference-based non-uniformity correction (RBNUC) technique which requires doing a lab calibration instead of self-calibration. SBUNC’s have disadvantages of ghosting artifacts which be complex when a new blind pixel appears. This research aims to enhance SBNUC techniques by changing the detection technique blind pixels and apply it in an earlier stage of system operation and to eliminate the need for adding a complex layer of the algorithm over original SBUNC codes for blind pixels detection, only. This research focuses on studying the electrical aspects of IRFPA detector to examine the effect of skimming reference voltage on the global image contrast. This research found out that exciting Vsk by voltage values close to its boundaries could separate blind pixels from the image background which become very exposed and simple to detect and correct. This research proposes a combination of electrical circuit modification, a routine of Vsk voltage excitation along with image acquisition. This research applies Otsu’s method as a global thresholding technique to detect blind pixels. Researchers found out that this proposed technique could detect all blind pixels successfully without the need for RBNUC which avoid SBNUC's techniques of lab calibration process to detect the blind pixels.

Open Access Original Research Article

1P-ABC, a Simplified ABC Variant for Continuous Optimization Problems

George Anescu

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2017/38065

In this paper a novel simplified and fast variant of the ABC algorithm is proposed, 1 Population ABC (1P-ABC), with the aim to increase the efficiency of the ABC algorithm by using only one population of bees, the employed bees, while maintaining a good e ectiveness of the algorithm in solving dicult nonlinear optimization problems. The novel 1P-ABC algorithm was tested, both regarding the efficiency and the success rate, against three known variants of ABC, the original ABC algorithm, an improved variant, Gbest-guided Artificial Bee Colony (GABC), and another improved variant, Fast ABC (F-ABC). The testing was conducted by employing an original testing methodology over a set of 11 scalable, multimodal, continuous optimization functions (10 unconstrained and 1 constrained) most of them with known global solutions. The novel proposed 1P-ABC algorithm outperformed the other ABC variants in efficiency, while for the success rate the results were mixed.

Open Access Original Research Article

Modelling the Dynamics of Smoking Epidemic

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

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/JAMCS/2017/37328

Our study is made up two sections: Non-smokers, problem- smokers, smokers-in-treatment and counselling, and removed-smokers (SPTcR) mathematical model that explains the dynamics of smoking epidemic without considering the recovery class to susceptible class transferring followed by modelling smoking epidemic where the recovery class is considered to revert to susceptible class to become problem smokers again after treatment and recovery respectively. We discussed the existence and stability of the smoking-free and endemic equilibria of both models. Our mathematical analysis of both models establish that the global dynamics of smoking epidemic transmission can be determined by the basic reproductive number. The smoking-free equilibrium was locally asymptotically stable if R0 < 1 and unstable if R0 > 1 in both models. Global stability of smoking-free and endemic equilibria was also discussed in our first model, using Lassalle’s invariance principle of Lyapunov functions. Numerical simulations were conducted using Matlab software to confirm our analytic results in both models. Our findings were that reducing the contact rate between the non-smokers and problem smokers, increasing the number of smokers that go into treatment and educating smokers to refrain from smoking can be useful in combating the smoking epidemic.

Open Access Original Research Article

On the Stability Analysis of MDGKN Systems with Control Parameters

Ubong D. Akpan, Moses O. Oyesanya

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/JAMCS/2017/35326

In this work, we study linear systems with Mass, Damping Force, Gyroscopic Force, Stiffness and Circulatory Force (MDGKN systems) with control parameters. The relationship between the parameters determines the stability or otherwise of the system. The Lyapunov direct method is used to analyse MDGKN system. Stability theorem for determining the stability or otherwise of MDGKN is formulated. The results are illustrated on a 2x2 and a 3x3 matrix systems to show the effectiveness of the results obtained.