Abstract-Due to the rapid development in digital communication through the international networks, data security has become an important problem in this field. Through different ways of hiding data in communications; steganography is used to hide the existence of the secret message. Steganography is a branch of hidden information's science, which tries to achieve an ideal security level in military and commercial usages, so that sending the invisible information will not be exposed or distinguished by the others. Steganography is implemented in different frequency and spatial domains. JSteg algorithm is one the first methods used for hiding data in frequency domain. In this algorithm; all of DCT coefficients are manipulated sequentially to hide secret data in the least significant bits of pixel values. In this way some characteristics of the cover image such as PSNR and histogram diagrams will be changed. These changes can be used later to diagnose the existence of the secret data behind the image and steganography will be failed. In this paper a new method for embedding data in the DCT coefficients is proposed. DCT values in this way will not be changed directly and for hiding reason the middle frequencies are replaced with each other. This algorithm has greater PSNR values and coefficient histogram of the steganograme is more similar to the original one. So this algorithm has higher robustness against the statistics attacks.

No abstract

We study the following nonlinear Robin boundary-value problem−Δp(x)u=λf(x,u)inΩ,|∇u|p(x)-2(∂u/∂v)+β(x)|u|p(x)−2u=0on∂Ω,whereΩ⊂ℝNis a bounded domain with smooth boundary∂Ω,∂u/∂vis the outer unit normal derivative on∂Ω,λ>0is a real number,pis a continuous function onΩ¯withinfx∈Ω¯p(x)>1,β∈L∞(∂Ω)withβ−:=infx∈∂Ωβ(x)>0, andf:Ω×ℝ→ℝis a continuous function. Using the variational method, under appropriate assumptions onf, we obtain results on existence and multiplicity of solutions.

The aim of this paper is to study the spectrum of the fourth order eigenvalue boundary value problem

In this paper, we investigate the existence of sign-changing solutions for the following class of fractional Kirchhoff type equations with potential ( 1 + b [ u ] α 2 ) ( ( - Δ x ) α u - Δ y u ) + V ( x , y ) u = f ( x , y , u ) , ( x , y ) ∈ ℝ N = ℝ n × ℝ m , \left( {1 + b\left[ u \right]_\alpha ^2} \right)\left( {{{\left( { - {\Delta _x}} \right)}^\alpha }u - {\Delta _y}u} \right) + V\left( {x,y} \right)u = f\left( {x,y,u} \right),\left( {x,y} \right) \in {\mathbb{R}^N} = {\mathbb{R}^n} \times {\mathbb{R}^m}, where [ u ] α = ( ∫ ℝ N ( | ( - Δ x ) α 2 u | 2 + | ∇ y u | 2 ) d x d y ) 1 2 {\left[ u \right]_\alpha } = {\left( {\int {_{{\mathbb{R}^N}}\left( {{{\left| {{{\left( { - {\Delta _x}} \right)}^{{\alpha \over 2}}}u} \right|}^2} + {{\left| {{\nabla _y}u} \right|}^2}} \right)dxdy} } \right)^{{1 \over 2}}} . Based on variational approach and a variant of the quantitative strain lemma, for each b > 0, we show the existence of a least energy nodal solution ub . In addition, a convergence property of ub as b → 0 is established.