We provide new concentration inequalities for functions of dependent variables. The work extends that of Janson (2004), which proposes concentration inequalities using a combination of the Laplace transform and the idea of fractional graph coloring, as well as many works that derive concentration inequalities using the entropy method (see, e.g., (Boucheron et al., 2003)). We give inequalities f...

In this paper, a digital image watermarking technique combining Discrete Wavelet Transform (DWT) and Discrete Fractional Fourier Transform (DFRFT) has been investigated. This is a non-blind watermarking technique that exploits multi-resolution sub-band decomposition property of DWT and applies DFRFT on selected sub-bands in DWT-transformed image. The performance of this algorithm under various ...

In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on $L2$-$1_\sigma$ formula and exponential-sum-approximation technique. The evaluation method can achieve accuracy further reduce computational cost acting memory for VO derivative. This algorithm applied construct relevant temporal spatial fourth-order s...

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

The integrity of descending white matter pathways, measured by fractional anisotropy from DW-MRI, is a key prognostic indicator of motor recovery after stroke. Barriers to translation of fractional anisotropy measures into routine clinical practice include the time required for manually delineating volumes of interest (VOIs), and inter-examiner variability in this process. This study investigat...

In this article, we give an integral representation of the resolvent kernel on H-type groups, then derive Kaplan's fundamental solution groups. Also obtain Green for fractional powers its sub-Laplacian.