Blog Analysis with Fuzzy TFIDF

These days blogs are becoming increasingly popular because it allows anyone to share their personal diary, opinions, and comments on the World Wide Wed. Many blogs contain valuable information, but it is a difficult task to extract this information from a high number of blog comments. The goal is to analyze a high number of blog comments by clustering all blog comments by their similarity based on keyword relevance into smaller groups. TF-IDF weight has been used in classifying documents by measuring appearance frequency of each keyword in a document, but it is not effective in differentiating semantic similarities between words. By applying fuzzy semantic to TF-IDF, TF-IDF becomes fuzzy TF-IDF and has the ability to rank semantic relevancy. Fuzzy VSM can be effective in exploring hidden relationship between blog comments by adapting fuzzy TF-IDF and fuzzy semantic for extending Vector Space Model to fuzzy VSM. Therefore, fuzzy VSM can cluster a high number of blog comments into small number of groups based on document similarity and semantic relevancy

Numerical methods for systems of conservation laws of mixed type using flux splitting

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed

Numerical experiments on the accuracy of ENO and modified ENO schemes

Further numerical experiments are made assessing an accuracy degeneracy phenomena. A modified essentially non-oscillatory (ENO) scheme is proposed, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives comparable results with the original ENO schemes for discontinuous problems

Numerical study of the small scale structures in Boussinesq convection

Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate Essentially Nonoscillatory (ENO) scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. The numerical results suggest that the collapse of the bubble cap is unlikely to occur in resolved calculations. The strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. We also found that the cascade of energy to small scales is dominated by the formulation of thin and sharp fronts across which density jumps

Resolution properties of the Fourier method for discontinuous waves

In this paper we discuss the wave-resolution properties of the Fourier approximations of a wave function with discontinuities. It is well known that a minimum of two points per wave is needed to resolve a periodic wave function using Fourier expansions. For Chebyshev approximations of a wave function, a minimum of pi points per wave is needed. Here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its Fourier coefficients. In our recent work on overcoming the Gibbs phenomenon, we have shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficient of a rapidly converging Gegenbauer expansion. We therefore study the resolution properties of a Gegenbauer expansion where both the number of terms and the order increase