reversible watermark using the difference expansion of a generalized integer transform a reversible watermarking algorithm with very high data hiding capacity has been developed for color images the algorithm allows the watermarking process to be reversed which restores the exact original image the algorithm hides several bits in the difference expansion of vectors of adjacent pixels the required general reversible integer transform and the necessary conditions to avoid underflow and overflow are derived for any vector of arbitrary length also the potential payload size that can be embedded into a host image is discussed and a feedback system for controlling this size is developed in addition to maximize the amount of data that can be hidden into an image the embedding algorithm can be applied recursively across the color components simulation results using spatial triplets spatial quads cross color triplets and cross color quads are presented and compared with the existing reversible watermarking algorithms these results indicate that the spatial quad based algorithm allows for hiding the largest payload at the highest signal to noise ratio

numerical solutions for systems of fractional differential equations by the decomposition method in this paper we use adomian decomposition method to solve systems of nonlinear fractional differential equations and a linear multi term fractional differential equation by reducing it to a system of fractional equations each of order at most unity we begin by showing how the decomposition method applies to a class of nonlinear fractional differential equations and give two examples to illustrate the efficiency of the method moreover we show how the method can be applied to a general linear multi term equation and solve several applied problems

an existence theorem for weak solutions for a class of elliptic partial differential systems in orlicz spaces abstract we prove the existence of a weak solution of the dirichlet problem for a class of elliptic partial differential systems in separable orlicz sobolev spaces

existence and uniqueness of weak solutions for a non uniformly parabolic equation in this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial boundary value problem of a non uniformly parabolic equation some well known parabolic equations are the special cases of this equation

hiding data in images by simple lsb substitution in this paper a data hiding scheme by simple lsb substitution is proposed by applying an optimal pixel adjustment process to the stego image obtained by the simple lsb substitution method the image quality of the stego image can be greatly improved with low extra computational complexity the worst case mean square error between the stego image and the cover image is derived experimental results show that the stego image is visually indistinguishable from the original cover image the obtained results also show a significant improvement with respect to a previous work

hiding secret data in images via predictive coding this paper presents a prediction based image hiding scheme that embeds secret data into compression codes during image compression this scheme employs a two stage structure a prediction stage and an entropy coding stage the secret data is embedded into the difference values of a given image after the prediction stage is performed according to the experimental results the image quality is better than jpeg jsteg and its improved scheme inform sci 141 1 2 2002 123 the average image quality of the stego images in the proposed scheme is greater than 50db when the hiding capacity is 1 bit per pixel whereas those values in jpeg jsteg and scheme in chang et al inform sci 141 1 2 2002 123 are 37 04 and 33 73db respectively the hiding capacity of the proposed scheme is 65 536 bits when the hiding capacity is 1 bit per pixel whereas it is 53 248 bits in scheme inform sci 141 1 2 2002 123 and less than 3000 bits in jpeg jsteg

reversible data hiding based on block median preservation this paper proposes a reversible data hiding scheme for gray level images it exploits the high correlation among image block pixels to produce a difference histogram secret data is embedded based on a multi level histogram shifting mechanism with reference to the integer median of each block the image blocks are divided into four categories due to four corresponding embedding strategies aiming at preserving the medians during data embedding in decoder the median pixels are retrieved first followed by the hidden data extraction and the host image can be accurately recovered via an inverse histogram shifting mechanism after removing the secret data from the marked image experimental results validate the effectiveness of our scheme and demonstrate that it outperforms several previous methods in terms of capacity and marked image s quality

numerical methods for the solution of partial differential equations of fractional order anomalous diffusion is a possible mechanism underlying plasma transport in magnetically confined plasmas to model this transport mechanism fractional order space derivative operators can be used here the numerical properties of partial differential equations of fractional order 1 2 are studied two numerical schemes an explicit and a semi implicit one are used in solving these equations two different discretization methods of the fractional derivative operator have also been used the accuracy and stability of these methods are investigated for several standard types of problems involving partial differential equations of fractional order

decomposition method for solving fractional riccati differential equations in this article we implement a relatively new analytical technique the adomian decomposition method for solving fractional riccati differential equations the fractional derivatives are described in the caputo sense in this scheme the solution takes the form of a convergent series with easily computable components the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of the solution the corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations some numerical examples are presented to illustrate the efficiency and reliability of the method

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

approximate solutions for boundary value problems of time fractional wave equation in this article we implement relatively a new analytical technique the adomian decomposition method for solving the boundary value problems of time fractional wave equation the fractional derivative is described in the caputo sense the decomposition method is used to construct analytical approximate solutions of time fractional wave equation subject to specified boundary conditions the solutions are calculated in the form of a convergent series with easily computable components some examples are given the results reveal that the adomian method is very effective and convenient

a second order accurate numerical method for the two dimensional fractional diffusion equation spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow finance and others in this paper we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation this numerical method combines the alternating directions implicit adi approach with a crank nicolson discretization and a richardson extrapolation to obtain an unconditionally stable second order accurate finite difference method the stability and the consistency of the method are established numerical solutions for an example super diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method

lossless data hiding for color images based on block truncation coding in this paper we present a novel reversible steganographic method which can reconstruct an original image effectively after extracting the embedded secret data the proposed reversible hiding method aims at btc block truncation coding compressed color images conventionally each block of a color image compressed by btc requires three bitmaps and three pairs of quantization levels for reconstruction in order to improve the compression rate a genetic algorithm ga is applied to find an approximate optimal common bitmap to replace the original three the secret data then are embedded in the common bitmap and the quantization levels of each block use the properties of side matching and the order of these quantization levels to achieve reversibility the experimental results demonstrate that the proposed method is practical for btc compressed color images and can embed more than three bits in each btc encoded block on average

legendre wavelets operational method for the numerical solutions of nonlinear volterra integro differential equations system in this paper legendre wavelet method is developed to approximate the solutions of system of nonlinear volterra integro differential equations the properties of legendre wavelets are first presented the properties of legendre wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved numerically by newton s method also the results obtained by present method have been compared with that of by b spline wavelet method illustrative examples have been discussed to demonstrate the validity and applicability of the present method

reversible data hiding for depth maps using the depth no synthesis error model when embedding hidden data in 3d images conventional reversible data hiding methods which are designed for 2d gray and color images can be applied to color and depth maps however directly applying these methods to depth maps may cause synthesis errors and lead to visual artifacts in the rendered virtual views two novel reversible data hiding methods based on the depth no synthesis error d nose model are proposed to embed hidden data in the depth maps of 3d images the proposed methods can preserve the quality of the rendered virtual view and achieve substantially higher embedding capacity experimental results show that the proposed methods achieve better performance than the existing state of the art methods in terms of both embedding capacity and the quality of the rendered virtual views

numerical solution of fractional pantograph differential equations by using generalized fractional order bernoulli wavelet in the current study new functions called generalized fractional order bernoulli wavelet functions gfbwfs based on the bernoulli wavelets are defined to obtain the numerical solution of fractional order pantograph differential equations in a large interval for the concept of fractional derivative we will use caputo sense by using riemann liouville fractional integral operator first the generalized fractional order bernoulli wavelets are constructed then these functions and their properties are employed to derive the gfbwfs operational matrices of fractional integration and pantograph the operational matrices of integral and pantograph are utilized to reduce the problem to a set of algebraic equations finally some examples are included for demonstrating the validity and applicability of our method

diffusion process modeling by using fractional order models this paper deals with a concept and description of a rc network as an electro analog model of diffusion process which enables to simulate heat dissipation under different initial and boundary conditions it is based on well known analogy between heat and electrical conduction in the paper are compared analytical solution together with numerical solution and experimentally measured data for the first time a fractional order model of diffusion process and its modeling via lumped rc network has been used simple examples of simulations measurements and their comparison are shown

analytical solution of a time fractional navier stokes equation by adomian decomposition method abstract the aim of the present analysis is to apply adomian decomposition method for the solution of a time fractional navier stokes equation in a tube by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

high capacity data hiding for error diffused block truncation coding block truncation coding btc is an efficient compression technique with extremely low computational complexity however the blocking and false contour effects are two major deficiencies in btc which cause severe perceptual artifacts the former scheme error diffused btc edbtc can significantly improve the above issues through the visual low pass compensation on the bitmap which thus widens its possible application market yet the corresponding security issue may limit its value in this paper a method namely complementary hiding edbtc is developed to cope the above issue this paper is managed by firstly discussing when a single watermark is embedded and then multiple watermarks are employed to test the limitation of the proposed scheme herein an adaptive external bias factor is employed to control the watermark embedding and this factor also affects the image quality and robustness simultaneously experimental results demonstrate that the proposed method only requires an extremely small external bias factor to carry watermarks which enables a high capacity scenario without significantly damaging image quality

block pulse operational matrix method for solving fractional partial differential equation in this paper we first introduce two dimensional block pulse functions and the block pulse operational matrices of the fractional order integration also the block pulse operational matrices of the fractional order differentiation are obtained then we present a computational method based on the above results for solving a class of fractional partial differential equations transforming the initial equation into a sylvester equation the error analysis of the method is given the method is computationally attractive and applications are demonstrated by some numerical examples moreover comparing the methodology with the known technique shows that our approach is more efficient and more convenient

operational matrix approach for the solution of partial integro differential equation in this paper an effective numerical method is introduced for the treatment of volterra singular partial integro differential equations they are based on the operational and almost operational matrix of integration and differentiation of 2d shifted legendre polynomials the methods convert the singular partial integro differential equation in to a system of algebraic equations convergence analysis and error estimates are derived for the proposed method illustrative examples are included to demonstrate the validity and applicability of the technique

distributed order calculus and equations of ultraslow diffusion abstract we consider equations of the form d u t x u t x f t x t 0 x r n where d is a distributed order derivative that is d t 0 1 d t d d is the caputo dzhrbashyan fractional derivative of order is a positive weight function the above equation is used in physical literature for modeling diffusion with a logarithmic growth of the mean square displacement in this work we develop a mathematical theory of such equations study the derivatives and integrals of distributed order

time domain wave equations for lossy media obeying a frequency power law for attenuation described by a slowly varying power law function of frequency 0 y classical lossy time domain wave equations exist only for the restricted cases where y 0 or y 2 for the frequently occurring practical situation in which attenuation is much smaller than the wave number a lossy dispersion characteristic is derived that has the desired attenuation general power law dependence in order to obtain the corresponding time domain lossy wave equation time domain loss operators similar in function to existing derivative operators are developed through the use of generalized functions three forms of lossy wave equations are found depending on whether y is an even or odd integer or a noninteger a time domain expression of causality analogous in function to the kramers kronig relations in the frequency domain is used to derive the causal wave equations final causal versions of the time domain wave equations are obtained even for the cases where y 1 which according to the paley wiener th

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

finding optimal least significant bit substitution in image hiding by dynamic programming strategy abstract the processing of simple least significant bit lsb substitution embeds the secret image in the least significant bits of the pixels in the host image this processing may degrade the host image quality so significantly that grabbers can detect that there is something going on in the image that interests them to overcome this drawback an exhaustive least significant bit substitution scheme was proposed by wang et al but it takes huge computation time wang et al then proposed another method that uses a genetic algorithm to search approximate optimal solutions and computation time is no longer so huge in this paper we shall use the dynamic programming strategy to get the optimal solution the experimental results will show that our method consumes less computation time and also gets the optimal solution

numerical approach to differential equations of fractional order in this paper the variational iteration method and the adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order the two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations in these schemes the solution takes the form of a convergent series with easily computable components this paper presents a numerical comparison between the two methods for solving systems of fractional differential equations numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order

application of legendre wavelets for solving fractional differential equations in this paper we develop a framework to obtain approximate numerical solutions to ordinary differential equations odes involving fractional order derivatives using legendre wavelet approximations the properties of legendre wavelets are first presented these properties are then utilized to reduce the fractional ordinary differential equations fodes to the solution of algebraic equations illustrative examples are included to demonstrate the validity and applicability of the technique results show that this technique can solve the linear and nonlinear fractional ordinary differential equations with negligible error compared to the exact solution

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

a new framework of lsb steganalysis of digital media we propose a general framework for the detection of the least significant bit lsb steganography using digital media files as cover objects the new framework exploits high order statistics of the samples it can compute a robust estimate of the length of a secret message hidden in the lsbs of samples for a large class of digital media contents such as image video and audio in which the underlying signals consist of correlated samples a case study on the lsb steganalysis of natural grey scale and color images and experimental results are reported

two dimensional wavelets collocation method for electromagnetic waves in dielectric media in this article we deal with a numerical wavelet collocation method nwcm using a technique based on two dimensional wavelets tdws approximation proposed for the fractional partial differential equations fpdes for electromagnetic waves in dielectric media ewdm by implementing the riemannliouville fractional derivative tdws approximation and its operational matrix along with collocation method are utilized to reduce fpdes firstly into weakly singular fractional partial integro differential equations fpides and then reduced weakly singular fpides into system of algebraic equation using legendre wavelet approximation lwa and chebyshev wavelet approximation cwa we investigated the convergence analysis and error analysis of the proposed problem finally some examples are included for demonstrating the efficiency of the proposed method via lwa and cwa respectively

an existence theorem for weak solutions for a class of elliptic partial differential systems in general orlicz sobolev spaces abstract i prove the existence of a weak solution for the dirichlet problem of a class of elliptic partial differential systems a i x x u x d u x b i x u x d u x 0 in general orlicz sobolev spaces w 0 1 l m r n where i 1 n 1 n u r n is a vector valued function and the summation convention is used throughout with i j running from 1 to n and running from 1 to n

two dimensional wavelets operational method for solving volterra weakly singular partial integro differential equations abstract in this article we discuss a method for finding an approximate solution of a class of two dimensional linear volterra weakly partial integro differential equations the operational matrices of integration differentiation and product are utilized to reduce the solution of the weakly partial integro differential equation to the linear algebraic system of equations furthermore some useful theorems are discussed to establish the convergence analysis of the proposed technique some numerical examples are solved by applying the presented scheme to show the effectiveness and applicability of the proposed scheme and also a comparison of error values between the two wavelets has been presented furthermore some figures are plotted to demonstrate the error analysis of the proposed scheme

a novel method for nonlinear fractional partial differential equations combination of dtm and generalized taylor s formula in this article a novel numerical method is proposed for nonlinear partial differential equations with space and time fractional derivatives this method is based on the two dimensional differential transform method dtm and generalized taylor s formula the fractional derivatives are considered in the caputo sense several illustrative examples are given to demonstrate the effectiveness of the present method results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order

image hiding by optimal lsb substitution and genetic algorithm in this paper we develop a novel method to embed important data in the host image so that the interceptors will not notice about the existence of the data the basic concept of the proposed method is by simple lsb substitution to prevent illicit access of data and increase the system performance the method of randomized process and the optimal lsb substitution are proposed the e ectiveness of the optimal lsb substitution in the worst case is proved we also develop a genetic algorithm to solve the problem of hiding important data in the rightmost k lsbs of the host image which may involve a huge computation time to nd the optimal result when k is large finally based on the concept of perceptual modeling an improved hiding technique is developed to obtain a high quality embedding result experimental results will reveal that the quality of the embedding result will not be seriously degraded and is near optimal by utilizing the proposed method 2001 pattern recognition society published by elsevier science ltd all rights reserved

an intelligent chaotic embedding approach to enhance stego image quality steganography s role in secret communication extends from concealing information to communication as one of several possible approaches to embed confidential information in digital images the least significant bit lsb technique has been widely used however maintaining the imperceptibility of the stego image is still a serious concern in this paper an adaptive random ar k bit embedding approach has been attempted to enhance the quality of stego images the original cover is divided into nonoverlapping blocks of equal size the encrypted confidential data are embedded in each block through four different random walks the best random walk which provides the minimum degradation for a particular block is identified and is fixed for that block the decision on the fixed random walk for each block is recorded and kept as the secret key the ar method has also been combined with the inverted pattern approach referred to as the adaptive random inverted pattern arip approach to further enhance the quality of the stego image the estimated peak signal to noise ratio psnr value for the arip method yields 1db enhancement

an operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro differential equations abstract in this article we introduce an operational matrix scheme based on two dimensional wavelets for the volterra weakly singular nonlinear partial integro differential equations by implementing two dimensional wavelets approximations and its operational matrices of integration and differentiation along with collocation points the weakly singular partial integro differential equations are reduced into the system of nonlinear algebraic equations moreover bernoulli wavelet approximation and legendre wavelet approximation have been used for inspecting the errors and convergence analysis of the given problems some numerical examples are included to establish the accuracy of the proposed scheme via bernoulli wavelet approximation and legendre wavelet approximation respectively additionally comparisons of error values between the two wavelets have been presented