A Note on a Fourier Sine Transform

This is a compilation of definite integrals of the product of the hyperbolic cosecant function and polynomial raised to a general power. In this work, we used our contour integral method to derive a Fourier sine transform in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. A summary table of the results are produced for easy reading. A vast majority of the results are new.

Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers fluid through a micro-channel

In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

A HEVC Video Steganalysis Against DCT/DST-Based Steganography

The development of video steganography has put forward a higher demand for video steganalysis. This paper presents a novel steganalysis against discrete cosine/sine transform (DCT/DST)-based steganography for high efficiency video coding (HEVC) videos. The new steganalysis employs special frames extraction (SFE) and accordion unfolding (AU) transformation to target the latest DCT/DST domain HEVC video steganography algorithms by merging temporal and spatial correlation. In this article, the distortion process of DCT/DST-based HEVC steganography is firstly analyzed. Then, based on the analysis, two kinds of distortion, the intra-frame distortion and the inter-frame distortion, are mainly caused by DCT/DST-based steganography. Finally, to effectively detect these distortions, an innovative method of HEVC steganalysis is proposed, which gives a combination feature of SFE and a temporal to spatial transformation, AU. The experiment results show that the proposed steganalysis performs better than other methods.

Fast High-Order Difference Scheme for the Modified Anomalous Subdiffusion Equation Based on Fast Discrete Sine Transform

The modified anomalous subdiffusion equation plays an important role in the modeling of the processes that become less anomalous as time evolves. In this paper, we consider the efficient difference scheme for solving such time-fractional equation in two space dimensions. By using the modified L1 method and the compact difference operator with fast discrete sine transform technique, we develop a fast Crank-Nicolson compact difference scheme which is proved to be stable with the accuracy of O τ min 1 + α , 1 + β + h 4 . Here, α and β are the fractional orders which both range from 0 to 1, and τ and h are, respectively, the temporal and spatial stepsizes. We also consider the method of adding correction terms to efficiently deal with the nonsmooth problems. Numerical examples are provided to verify the effectiveness of the proposed scheme.

Regularity of the Transform of Laplace and the Transfom of Fourier

Regularity of the transform of Laplace in the opened area of 0 is proved with help of some methods of the transform of Fourier. The class of the transform of Laplace from the transform of Fourier is considered from some functions without a regularity in null. The functions are regular in the opened area of 0. It is proved, that the sine transform of Fourier from the cosine transform of Fourier is equal to the cosine transform from the sine transform of Fourier on the module.