

Articles
by
Mbaitiga Zacharie 
Total Records (
5 ) for
Mbaitiga Zacharie 





Mbaitiga Zacharie


his study describes the Adaptive Resonance Theory 1 (ART1), an efficient algorithm that emulates the selforganizing pattern recognition and hypothesis testing properties of the ART neural network architecture for horizontal and vertical classification of 09 digits recognition. In our approach the ART1 model can selforganize in real time producing stable and clear recognition while getting input patterns beyond those originally stored. It can also preserve its previously learned knowledge while keeping its ability to learn new input patterns that can be saved in such a fashion that the stored patterns cannot be destroyed or forgotten. A parameter called the attentional vigilance parameter determines how fine the categories will be. If vigilance increases or decreases due to environmental control feedback, then the system automatically searches for and learns fine recognition categories. 




Mbaitiga Zacharie


Problem statement: Research into robot motion control offers research opportunities that will change scientists and engineers for year to come. Autonomous robots are increasingly evident in many aspects of industry and everyday life and a robust robot motion control can be used for homeland security and many consumer applications. This study discussed the adaptive fuzzy knowledge based controller for robot motion control in indoor and outdoor environment. Approach: The proposed method consisted of two components: the process monitor that detects changes in the process characteristics and the adaptation mechanism that used information passed to it by the process monitor to update the controller parameters. Results: Experimental evaluation had been done in both indoor and outdoor environment where the robot communicates with the base station through its Wireless fidelity antenna and the performance monitor used a set of five performance criteria to access the fuzzy knowledge based controller. Conclusion: The proposed method had been found to be robust. 




Mbaitiga Zacharie


Problem statement: The purpose of any robotic is to perform tasks that a human would prefer not to do or hopefully do it with precision in order to avoid mistakes or when a human is out of duty due to fatigue or health reasons. The research into human detection into images has paid the way be aware of what is going on around the houses or buildings where a frontline security is needed 24 h a day. In this research a human detection security robot based on Gaussian distribution histogram was proposed. Approach: The proposed method consisted of three steps: (1) the RGB color space histogram was created by subdividing a color space into certain number of bins and then counted the number of pixels that each bin contains. (2) The created RGB histogram was converted into HSV color histogram using Gaussian distribution method. (3) The bellshape curve of the Gaussian distribution was used to calculate the detection probability between the standard deviation. Results: Experimental evaluation had been tested on the images sequences where the experimental results revealed that the proposed method was less sensitive to changes in the scene achieving higher performance detection than traditional method of histogram creation and had been found to be robust. Conclusion: The results showed that the histogram based human detection resists to any changes in the image scenes. 





Mbaitiga Zacharie


This study shows the use of gamma function to prove the Riemann functional equation. Two approaches had been used to solve this problem: first the value of t in the definition of the gamma function had been changed to pi nu x if only if sigma is greater than zero in the complex plane. Secondly, the Poisson summation formula is used to show that zeta has a simple pole at s = 1 with residue 1, we had found that Riemann zeta function depended intimately on properties of gamma function, which was a new gate for solving complex problems related to zeta function. 




Mbaitiga Zacharie


Problem statement: In the prime number the Riemann zeta function is unquestionable and undisputable one of the most important questions in mathematics whose many researchers are still trying to find answer to some unsolved problems such as Riemann Hypothesis. In this study we proposed a new method that proves the analytic extension theorem for zeta function. Approach: Abel transformation was used to prove that the extension theorem is true for the real part of the complex variable that is strictly greater than one and consequently provides the required analytic extension of the zeta function to the real part greater than zero and Euler product was used to prove the real part of the complex that are less than zero and greater or equal to one. Results: From this proposed study we noted that the real values of the complex variable are lying between zero and one which may help to understand the relation between zeta function and its properties and consequently can pay the way to solve some complex arithmetic problems including the Riemann Hypothesis. Conclusion: The combination of Abel transformation and Euler product is a powerful tool for proving theorems and functions related to Zeta function including other subjects such as radio atmospheric occultation. 





