Abstract: In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.
Abstract: In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.
Abstract: In this paper, we propose a face recognition algorithm
using AAM and Gabor features. Gabor feature vectors which are well
known to be robust with respect to small variations of shape, scaling,
rotation, distortion, illumination and poses in images are popularly
employed for feature vectors for many object detection and
recognition algorithms. EBGM, which is prominent among face
recognition algorithms employing Gabor feature vectors, requires
localization of facial feature points where Gabor feature vectors are
extracted. However, localization method employed in EBGM is based
on Gabor jet similarity and is sensitive to initial values. Wrong
localization of facial feature points affects face recognition rate. AAM
is known to be successfully applied to localization of facial feature
points. In this paper, we devise a facial feature point localization
method which first roughly estimate facial feature points using AAM
and refine facial feature points using Gabor jet similarity-based facial
feature localization method with initial points set by the rough facial
feature points obtained from AAM, and propose a face recognition
algorithm using the devised localization method for facial feature
localization and Gabor feature vectors. It is observed through
experiments that such a cascaded localization method based on both
AAM and Gabor jet similarity is more robust than the localization
method based on only Gabor jet similarity. Also, it is shown that the
proposed face recognition algorithm using this devised localization
method and Gabor feature vectors performs better than the
conventional face recognition algorithm using Gabor jet
similarity-based localization method and Gabor feature vectors like
EBGM.
Abstract: Eye localization is necessary for face recognition and
related application areas. Most of eye localization algorithms reported
so far still need to be improved about precision and computational
time for successful applications. In this paper, we propose an eye
location method based on multi-scale Gabor feature vectors, which is
more robust with respect to initial points. The eye localization based
on Gabor feature vectors first needs to constructs an Eye Model Bunch
for each eye (left or right eye) which consists of n Gabor jets and
average eye coordinates of each eyes obtained from n model face
images, and then tries to localize eyes in an incoming face image by
utilizing the fact that the true eye coordinates is most likely to be very
close to the position where the Gabor jet will have the best Gabor jet
similarity matching with a Gabor jet in the Eye Model Bunch. Similar
ideas have been already proposed in such as EBGM (Elastic Bunch
Graph Matching). However, the method used in EBGM is known to be
not robust with respect to initial values and may need extensive search
range for achieving the required performance, but extensive search
ranges will cause much more computational burden. In this paper, we
propose a multi-scale approach with a little increased computational
burden where one first tries to localize eyes based on Gabor feature
vectors in a coarse face image obtained from down sampling of the
original face image, and then localize eyes based on Gabor feature
vectors in the original resolution face image by using the eye
coordinates localized in the coarse scaled image as initial points.
Several experiments and comparisons with other eye localization
methods reported in the other papers show the efficiency of our
proposed method.
Abstract: Initial values of reference vectors have significant influence on recognition accuracy in LVQ. There are several existing techniques, such as SOM and k-means, for setting initial values of reference vectors, each of which has provided some positive results. However, those results are not sufficient for the improvement of recognition accuracy. This study proposes an ACO-used method for initializing reference vectors with an aim to achieve recognition accuracy higher than those obtained through conventional methods. Moreover, we will demonstrate the effectiveness of the proposed method by applying it to the wine data and English vowel data and comparing its results with those of conventional methods.
Abstract: In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.
Abstract: A two dimensional three segments coupled pendulum system that mathematically models human arm configuration was developed along with constructing and solving the equations of motions for this model using the energy (work) based approach of Lagrange. The equations of motion of the model were solved iteratively both as an initial value problem and as a two point boundary value problem. In the initial value problem solutions, both the initial system configuration (segment angles) and initial system velocity (segment angular velocities) were used as inputs, whereas, in the two point boundary value problem solutions initial and final configurations and time were used as inputs to solve for the trajectory of motion. The results suggest that the model solutions are sensitive to small changes in the dynamic forces applied to the system as well as to the initial and boundary conditions used. To overcome the system sensitivity a new approach is suggested.
Abstract: In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Abstract: In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.