Chur-Jen Chen

Adaptive audio watermarking via the optimization point of view on the wavelet-based entropy

This study aims to present an adaptive audio watermarking method using ideas of wavelet-based entropy (WBE). The method converts low-frequency coefficients of discrete wavelet transform (DWT) into the WBE domain, followed by the calculations of mean values of each audio as well as derivation of some essential properties of WBE. A characteristic curve relating the WBE and DWT coefficients is also presented. The foundation of the embedding process lies on the approximately invariant property demonstrated from the mean of each audio and the characteristic curve. Besides, the quality of the watermarked audio is optimized. In the detecting process, the watermark can be extracted using only values of the WBE. Finally, the performance of the proposed watermarking method is analyzed in terms of signal to noise ratio, mean opinion score and robustness. Experimental results confirm that the embedded data are robust to resist the common attacks like re-sampling, MP3 compression, low-pass filtering, and amplitude scaling.

Gronwall-Bellman-Type Integral Inequalities and Applications to BVPs

We establish some new nonlinear Gronwall-Bellman-Ou-Iang type integral inequalities with two variables. These inequalities generalize former results and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of differential equations. Example of applying these inequalities to derive the properties of BVPs is also given.

Iterative Approximation for a Boundary Value Problem Arising for the Electrical Potential on a Cylindrical Double Layer

Building on Banach’s contraction mapping principle, we give existence, uniqueness, and approximation theorems for a boundary value problem on an unbounded domain arising in the mathematical modelling of the electrical potential in a cylindrical double layer.

On Pečarić-Rajić-Dragomir-Type Inequalities in Normed Linear Spaces

We establish some generalizations of the recent Pečarić-Rajić-Dragomir-type inequalities by providing upper and lower bounds for the norm of a linear combination of elements in a normed linear space. Our results provide new estimates on inequalities of this type.

Integral Inequalities in Higher Dimensional Spaces

Integral inequalities play an important role in many different areas including differential equations, integral equations, variational calculus, etc. In this work, we present some new higher dimensional integral inequalities involving monotonic or convex functions in higher dimensional spaces. These are then applied to solve directly some Calculus of Variations problems for optimal solutions, effectively.

On Uryson Operators with Partial Integrals in Lebesgue Spaces with Mixed Norm

In this paper we consider some class of partial Uryson integral operators in spaces with mixed norm. We give some conditions for action, boundedness and continuity of those operators.