Mathematic analysis

øVWDQEXO 7HFKQLFDO 8QLYHUVLW\ ,QVWLWXWH RI ,QIRUPDWLFV 0DVODN øVWDQEXO NDKUDPDQ#EHLWXHGXWU øVWDQEXO 7HFKQLFDO 8QLYHUVLW\ &RPSXWHU (QJLQHHULQJ 'HSDUWPHQW 0DVODN øVWDQEXÔ NXUWJRNPHQ`#FHLWXHGXWU Abstract. This paper presents a novel algorithm for license plate detection and license plate character segmentation problems by using the Gabor transform in detection and local vector quantization in segmentation. As of our knowledge this is the first application of Gabor filters to license plate segmentation problem. Even though much of the research efforts are devoted to the edge or global thresholding-based approaches, it is more practical and efficient to analyze the image in certain directions and scales utilizing the Gabor transform instead of error-prone edge detection or thresholding. Gabor filter response only gives a rough estimate of the plate boundary. Then binary split tree is used for vector quantization in order to extract the exact boundary and segment the plate region into disjoint characters which become ready for the optical character recognition.

In this paper we propose general nonlinear models for off-line and on-line parameters identification in dynamic systems. These numerical filters can be applied to any nonlinear system represented by a state equation and an observation equation both nonlinear. The theory of hidden Markov models is used to derive these algorithms starting from a of Baum & Welch type method. The proposed identification algorithm has two levels: the first level is an iterative and global algorithm (IGA), it estimates iteratively the parameters from a block of data. The second level is an ergodic recursive algorithm (ERA), it estimates the parameters in an adaptive manner. The estimators defined by these algorithms converge almost surely to the true values of the model parameters studied in [A. Khoukhi, T. Aliziane, M. Souilah, Un Algorithme Multi-Niveau d'Identification d'un Canal en Communication Nume´rique, JESA 36(4) (2002) 519-537; M. Souilah, A. Khoukhi, T. Aliziane, A new multi-level algorithm for identification and stochastic adaptive control of industrial manipulators, Eng. Simulation 26(4) (2004) 83-98; M. Souilah, A new strategy for identification and control of mobile robots, Eng. Simulation 28(3) (2006) 35-48]. The advantage of the proposed nonlinear filters in relation to classical autoregressive models is the fact that the nonlinearity of the model is taken into account as it is and no linearizations are made around a nominal position. The variances of the added noises are also estimated. The mathematical convergence of the algorithms IGA and ERA is an open problem in the general case. We propose to this end an interesting conjecture based on ergodic theory. These algorithms are applied to identify the parameters of a transmission channel in data communication. Some simulation results showing the convergence of these algorithms are given. r

In this paper we propose general nonlinear models for off-line and on-line parameters identification in dynamic systems. These numerical filters can be applied to any nonlinear system represented by a state equation and an observation equation both nonlinear. The theory of hidden Markov models is used to derive these algorithms starting from a of Baum & Welch type method. The proposed identification algorithm has two levels: the first level is an iterative and global algorithm (IGA), it estimates iteratively the parameters from a block of data. The second level is an ergodic recursive algorithm (ERA), it estimates the parameters in an adaptive manner. The estimators defined by these algorithms converge almost surely to the true values of the model parameters studied in [A. Khoukhi, T. Aliziane, M. Souilah, Un Algorithme Multi-Niveau d'Identification d'un Canal en Communication Nume´rique, JESA 36(4) (2002) 519-537; M. Souilah, A. Khoukhi, T. Aliziane, A new multi-level algorithm for identification and stochastic adaptive control of industrial manipulators, Eng. Simulation 26(4) (2004) 83-98; M. Souilah, A new strategy for identification and control of mobile robots, Eng. Simulation 28(3) (2006) 35-48]. The advantage of the proposed nonlinear filters in relation to classical autoregressive models is the fact that the nonlinearity of the model is taken into account as it is and no linearizations are made around a nominal position. The variances of the added noises are also estimated. The mathematical convergence of the algorithms IGA and ERA is an open problem in the general case. We propose to this end an interesting conjecture based on ergodic theory. These algorithms are applied to identify the parameters of a transmission channel in data communication. Some simulation results showing the convergence of these algorithms are given.

The consistency of the approximation of a double-layer potential when using a boundary-element method and approximating the curved boundary by a polygonal curve in two-dimensional problems or by a polyhedral surface in three-dimensional ones is investigated. The results are applied to the numerical analysis of the approximation of a model problem: the diffraction of a time-harmonic acoustic wave by a penetrable object.

In this paper, we prove the existence and uniqueness of the global solution to the reaction diffusion system SKT with homogeneous Newmann boundary conditions. We use the lower and upper solution method and its associated monotone iterations where the reaction functions are locally Lipschitz .We study the blowing-up property of the solution, we give a sufficient condition on the reaction parameters of the model to ensure the blow-up of the solution continuous functions spaces.