Equivalent partial differential equations of a lattice Boltzmann scheme

We show that when we formulate the lattice Boltzmann equation with a small time step $\Delta$t and an associated space scale $\Delta$x, a Taylor expansion joined with the so-called equivalent equation methodology leads to establish macroscopic fluid equations as a formal limit. We recover the Euler equations of gas dynamics at the first order and the compressible Navier-Stokes equations at the second order. 1) Discrete geometry $\bullet$ We denote by d the dimension of space and by L a regular d-dimensional lattice. Such a lattice is composed by a set L 0 of nodes or vertices and a set L 1 of links or edges between two vertices. From a practical point of view, given a vertex x, there exists a set V (x) of neighbouring nodes, including the node x itself. We consider here that the lattice L is parametrized by a space step $\Delta$x > 0. For the fundamental example called D2Q9 (see e.g. Lallemand and Luo, 2000), the set V (x) is given with the help of the family of vectors (e j) 0$\le$j$\le$J defined by J = 8, (1.1) e j = 0 0 , 1 0 , 0 1 , --1 0 , 0 --1 , 1 1 , --1 1 , --1 --1 , 1 --1 and the vicinity (1.2) V (x) = { x + $\Delta$x e j , 0 $\le$ j $\le$ J }

Knowledge Extraction for Discriminating Male and Female in Logical Reasoning from Student Model

The learning process is a process of communication and interaction between the teacher and his students on one side and between the students and each others on the other side. Interaction of the teacher with his students has a great importance in the process of learning and education. The pattern and style of this interaction is determined by the educational situation, trends and concerns, and educational characteristics. Classroom interaction has an importance and a big role in increasing the efficiency of the learning process and raising the achievement levels of students. Students need to learn skills and habits of study, especially at the university level. The effectiveness of learning is affected by several factors that include the prevailing patterns of interactive behavior in the classroom. These patterns are reflected in the activities of teacher and learners during the learning process. The effectiveness of learning is also influenced by the cognitive and non cognitive characteristics of teacher that help him to succeed, the characteristics of learners, teaching subject, and the teaching methods. This paper presents a machine learning algorithm for extracting knowledge from student model. The proposed algorithm utilizes the inherent characteristic of genetic algorithm and neural network for extracting comprehensible rules from the student database. The knowledge is used for discriminating male and female levels in logical reasoning as a part of an expert system course.Comment: 10 pages IEEE format, International Journal of Computer Science and Information Security, IJCSIS 2009, ISSN 1947 5500, Impact Factor 0.423, http://sites.google.com/site/ijcsis

Fuzzy equilibrium existence for Bayesian abstract fuzzy economies and applications to random quasi-variational inequalities with random fuzzy mappings

In this paper, we introduce a Bayesian abstract fuzzy economy model and we prove the Bayesian fuzzy equilibrium existence. As applications, we prove the existence of the solutions for two types of random quasi-variational inequalities with random fuzzy mappings and we also obtain random fixed point theorems.Comment: 25 page

On effective human robot interaction based on recognition and association

Faces play a magnificent role in human robot interaction, as they do in our daily life. The inherent ability of the human mind facilitates us to recognize a person by exploiting various challenges such as bad illumination, occlusions, pose variation etc. which are involved in face recognition. But it is a very complex task in nature to identify a human face by humanoid robots. The recent literatures on face biometric recognition are extremely rich in its application on structured environment for solving human identification problem. But the application of face biometric on mobile robotics is limited for its inability to produce accurate identification in uneven circumstances. The existing face recognition problem has been tackled with our proposed component based fragmented face recognition framework. The proposed framework uses only a subset of the full face such as eyes, nose and mouth to recognize a person. It's less searching cost, encouraging accuracy and ability to handle various challenges of face recognition offers its applicability on humanoid robots. The second problem in face recognition is the face spoofing, in which a face recognition system is not able to distinguish between a person and an imposter (photo/video of the genuine user). The problem will become more detrimental when robots are used as an authenticator. A depth analysis method has been investigated in our research work to test the liveness of imposters to discriminate them from the legitimate users. The implication of the previous earned techniques has been used with respect to criminal identification with NAO robot. An eyewitness can interact with NAO through a user interface. NAO asks several questions about the suspect, such as age, height, her/his facial shape and size etc., and then making a guess about her/his face