In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of s...In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.展开更多
In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear...In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear differential operator with unbounded coefficients has a bounded inverse in the scalar case.展开更多
As an effective way to securely transfer secret images,secret image sharing(SIS)has been a noteworthy area of research.Basically in a SIS scheme,a secret image is shared via shadows and could be reconstructed by havin...As an effective way to securely transfer secret images,secret image sharing(SIS)has been a noteworthy area of research.Basically in a SIS scheme,a secret image is shared via shadows and could be reconstructed by having the required number of them.A major downside of this method is its noise-like shadows,which draw the malicious users'attention.In order to overcome this problem,SIS schemes with meaningful shadows are introduced in which the shadows are first hidden in innocent-looking cover images and then shared.In most of these schemes,the cover image cannot be recovered without distortion,which makes them useless in case of utilising critical cover images such as military or medical images.Also,embedding the secret data in Least significant bits of the cover image,in many of these schemes,makes them very fragile to steganlysis.A reversible IWT-based SIS scheme using Rook polynomial and Hamming code with authentication is proposed.In order to make the scheme robust to steganalysis,the shadow image is embedded in coefficients of Integer wavelet transform of the cover image.Using Rook polynomial makes the scheme more secure and moreover makes authentication very easy and with no need to share private key to participants.Also,utilising Hamming code lets us embed data with much less required modifications on the cover image which results in high-quality stego images.展开更多
An alternative method of solving Lagrange＇s first-order partial differential equation of the form（a1x ＋b1y＋C1z）p＋ （a2x ＋b2y＋c2z）q =a3x ＋b3y＋c3z,where p = Эz/Эx, q = Эz/Эy and ai, bi, ci （i = 1,2,3） a...An alternative method of solving Lagrange＇s first-order partial differential equation of the form（a1x ＋b1y＋C1z）p＋ （a2x ＋b2y＋c2z）q =a3x ＋b3y＋c3z,where p = Эz/Эx, q = Эz/Эy and ai, bi, ci （i = 1,2,3） are all real numbers has been presented here.展开更多
The author proposes an alternative way of using fixed point theory to get the existence for semilinear equations.As an example,a nonlocal ordinary differential equation is considered.The idea is to solve homogeneous e...The author proposes an alternative way of using fixed point theory to get the existence for semilinear equations.As an example,a nonlocal ordinary differential equation is considered.The idea is to solve homogeneous equations in the linearization.One feature of this method is that it does not need the equation to have special structures,for instance,variational structures,maximum principle,etc.Roughly speaking,the existence comes from good properties of the suitably linearized equation.The idea may have wider application.展开更多
文摘In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.
文摘In this paper we estimate the solutions of homogeneous linear system of differential equations with unbounded coefficients on the real line R. We also give a necessary and sufficient condition in order that the linear differential operator with unbounded coefficients has a bounded inverse in the scalar case.
基金Iran National Science Foundation,Grant/Award Number:99009224。
文摘As an effective way to securely transfer secret images,secret image sharing(SIS)has been a noteworthy area of research.Basically in a SIS scheme,a secret image is shared via shadows and could be reconstructed by having the required number of them.A major downside of this method is its noise-like shadows,which draw the malicious users'attention.In order to overcome this problem,SIS schemes with meaningful shadows are introduced in which the shadows are first hidden in innocent-looking cover images and then shared.In most of these schemes,the cover image cannot be recovered without distortion,which makes them useless in case of utilising critical cover images such as military or medical images.Also,embedding the secret data in Least significant bits of the cover image,in many of these schemes,makes them very fragile to steganlysis.A reversible IWT-based SIS scheme using Rook polynomial and Hamming code with authentication is proposed.In order to make the scheme robust to steganalysis,the shadow image is embedded in coefficients of Integer wavelet transform of the cover image.Using Rook polynomial makes the scheme more secure and moreover makes authentication very easy and with no need to share private key to participants.Also,utilising Hamming code lets us embed data with much less required modifications on the cover image which results in high-quality stego images.
文摘An alternative method of solving Lagrange＇s first-order partial differential equation of the form（a1x ＋b1y＋C1z）p＋ （a2x ＋b2y＋c2z）q =a3x ＋b3y＋c3z,where p = Эz/Эx, q = Эz/Эy and ai, bi, ci （i = 1,2,3） are all real numbers has been presented here.
文摘The author proposes an alternative way of using fixed point theory to get the existence for semilinear equations.As an example,a nonlocal ordinary differential equation is considered.The idea is to solve homogeneous equations in the linearization.One feature of this method is that it does not need the equation to have special structures,for instance,variational structures,maximum principle,etc.Roughly speaking,the existence comes from good properties of the suitably linearized equation.The idea may have wider application.
