PARTIAL SUMS OF GENERALIZED CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING A GAUSSIAN HYPERGEOMETRIC FUNCTION
The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to its sequences of partial sums by involving the Gaussian hypergeometric function. Relevant connections of the results presented here with various known results are briefly indicated. We also mention results which are associated with certain classical orthogonal polynomials (deduced from some of the main results) exhibiting the usefulness of the results presented in this paper.
Quasi Partial Sums of Harmonic Univalent Functions
In this work, we obtain some conditions under which the quasi partial sums of the generalized Bernardi integral operator consisting of the harmonic univalent functions belongs to a similar class.
Multivariate Image Texture by Multivariate Variogram for Multispectral Image Classification
Traditional image texture measure usually allows a texture description of a single band of the spectrum, characterizing the spatial variability of gray-level values within the singleband image. A problem with the approach while applied to multispectral images is that it only uses the texture information from selected bands. In this paper, we propose a new multivariate texture measure based on the multivariate variogram. The multivariate texture is computed from all bands of a multispectral image, which characterizes the multivariate spatial autocorrelation among those bands. In order to evaluate the performance of the proposed texture measure, the derived multivariate texture image is combined with the spectral data in image classification. The result is compared to classifications using spectral data alone and plus traditional texture images. A machine learning classifier based on Support Vector Machines (SVMs) is used for image classification. The experimental results demonstrate that the inclusion of multivariate texture information in multispectral image classification significantly improves the overall accuracy, with 5 to 13.5 percent of improvement, compared to the classification with spectral information alone. The results also show that when incorporated in image classification as an additional band, the multivariate texture results in high overall accuracy, which is comparable with or higher than the best results from the existing single-band and two-band texture measures, such as the variogram, cross variogram and Gray-Level Co-occurrence Matrix (GLCM) based texture. Overall, the multivariate texture provides the useful spatial information for land-cover classification, which is different from the traditional single band texture. Moreover, it avoids the band selection procedure which is prerequisite to traditional texture computation and would help to achieve high accuracy in the most classification tasks.