block based progressive visual secret sharing block based progressive visual secret sharing bpvss is an encryption technique that utilizes the human visual system to recover a secret image the recovery method is based on building up different image blocks step by step in the last few years several research projects have been devoted to the study of bpvss however they have some common drawbacks their dispatching matrices are chaotically designed by adding some redundant 0 1s in order to maintain the size as a fixed value which makes the methods hard to be implemented in addition the pixel expansion ratio grows faster when the number of participants increases and the visual quality of the restored image is quite poor in this paper we propose a non expanded block based progressive visual secret sharing scheme with noise like and meaningful shares respectively experimental results demonstrate the feasibility of this scheme our design has several advantages over other related methods 1 the model is concise easy to implement and the number of participants need not be restricted 2 with noise like shares the contrast of the restored image is 50 which means that the hidden message can be clearly recognized by the naked eye 3 when transparencies are transferred from noise like patterns into a meaningful cover image the contrast in the shares and the restored image is 25 which is still superior to that obtained in other studies 4 our scheme is more suitable for grayscale and color secret images and 5 the size of the transparencies is the same as that of the secret image

metastability of the cahn hilliard equation in one space dimension abstract we establish metastability of the one dimensional cahn hilliard equation for initial data that is order one in energy and order one in h 1 away from a point on the so called slow manifold with n well separated layers specifically we show that for such initial data on a system of lengthscale there are three phases of evolution 1 the solution is drawn after a time of order 2 into an algebraically small neighborhood of the n layer branch of the slow manifold 2 the solution is drawn after a time of order 3 into an exponentially small neighborhood of the n layer branch of the slow manifold 3 the solution is trapped for an exponentially long time exponentially close to the n layer branch of the slow manifold the timescale in phase 3 is obtained with the sharp constant in the exponential

slow motion manifolds far from the attractor in multistable reaction diffusion equations abstract we consider a scalar reaction diffusion equation with multistable nonlinearity with a particular symmetry by reduction to a family of transmission problems in r and by contraction arguments a manifold close to an invariant manifold formed by functions exhibiting a pattern of transition layers is constructed an approximation for the associated vector field is also provided this shows that the motion on those manifolds is exponentially slow as in the well known case of the bistable equation however in opposition to the bistable case some of these manifolds are far from the attractor since these manifolds correspond to metastable patterns this shows the importance of the transient motion toward the attractor and the importance of these manifolds in organizing that motion it is also shown that by a suitable perturbation we can obtain new equilibria on those manifolds

jordanian deformation of sl 2 as a contraction of its drinfeld jimbo deformation we introduce a contraction procedure for obtaining the jordanian deformation of sl 2 from its drinfeld jimbo deformation to be specific we obtain slh 2 its differential geometry and its star product from their q deformed counterparts we also present a transformation of the generators of uq sl 2 which in a limit yield the generators of uh sl 2

on the security of a visual cryptography scheme for color images hou visual cryptography for color images pattern recognition 36 2003 1619 1629 proposed a four share visual cryptography scheme for color images the scheme splits a dithered eight color secret image into four shares the black mask and other three shares it was claimed that without knowing the black mask no information about the secret image can be obtained even if all the other three shares are known in this paper we show that this may be true for a few specific two color secret images only in all other cases however security cannot be guaranteed we show that an attacker can compromise a randomly chosen two color secret image from any two of the other three shares with probability 47 by completely recovering the shape and pattern of the secret image the advantage will increase to 67 if all the three shares are known if the secret image has three or four colors we show that the attacker can compromise it with probability 47 and 835 respectively finally we show that our technique can be extended to compromising secret images with more than four colors

visual multiple secret sharing based upon turning and flipping the secret sharing schemes in conventional visual cryptography are capable of sharing one secret image into a set of random transparencies called shares in the form of rectangles which reveal the secret image to the human visual system when they are superimposed recently visual secret sharing schemes involving multiple secrets have attracted much attention by adopting rotations on one of the two encoded circle shares more than two secrets could be shared yet the encoding and decoding processes of circle shares need more sophisticated mechanisms than those of rectangular or square ones in this paper we explore the possibilities of visual multiple secret sharing using simply two rectangular or square shares specifically we define some operations onto a transparency based upon turning over or flipping around then we propose visual cryptographic schemes that are able to encode two or four secrets into two rectangular shares and up to eight secrets into two square shares such that the secrets cannot be obtained from any single share whereas they are revealed by stacking the two shares under various combinations of turning or flipping operations the proposed schemes which solidly elaborate the relationship between the encoded shares and the shared secrets broaden the research scope and enrich the flexibility and applicability of visual cryptography or image encryption theoretically and practically

on general construction for extended visual cryptography schemes numerous visual cryptography schemes vcss have been proposed to protect a secret image with share images most vcss use random looking shares to code a single binary secret image some schemes are designed for color secret images droste s new results on visual cryptography in advances in cryptology crypto 96 lecture notes in computer science vol 1109 springer berlin 1996 pp 401 415 n n vcs is introduced for multiple binary secret images extended vcs evcs by ateniese et al extended capabilities for visual cryptography theoretical computer science 250 2001 143 161 for binary secret image uses meaningful innocent looking shares in this paper we start with a more concise derivation of matrix extension in the ecvs model this is implemented by concatenating an extended matrix to each basis matrix we then present a general construction method for single or multiple binary grayscale color secret images using matrix extension utilizing meaningful shares the result k n visual secret sharing schemes are more general than most existing schemes in terms of the secret share image types using our matrix extension algorithm any existing vcs with random looking shares can be easily modified to utilize meaningful shares the effectiveness of our schemes is demonstrated by real examples

sharing a verifiable secret image using two shadows in this paper we propose a novel 2 2 verifiable secret sharing vss scheme which not only protects a secret image but also allows users to verify the restored secret image in the revealing and verifying phase for all binary grayscale and color images error diffusion and image clustering techniques are adopted to achieve our objective experimental results and discussions show that the proposed scheme with its smaller shadow size and lower computational complexity obviously outperforms previous vss schemes designed either with or without the cheating prevention mechanism moreover the use of a halftone logo gives an efficient solution to verifying whether the restored secret image is correct by using a halftone logo

adaptive localized replay an efficient integration scheme for accurate simulation of coarsening dynamical systems coarsening dynamical systems cds of ordinary differential equations odes have as a defining feature the presence of discontinuities in the governing equations due to the removal of vanishing elements from the system simple commonly used integration strategies for odes neglect these discontinuities resulting in large errors in contrast available methods to resolve discontinuities exhibit total running times that scale like o n 2 as the number of elements n the resulting need to choose between either speed or accuracy frustrates attempts to gather well converged statistical data from large ensembles of elements a common goal in studies of coarsening in this work we introduce a numerical scheme called adaptive localized replay alr which overcomes this dilemma provided the underlying system has sparse neighbor dependence by analyzing the system after each timestep and then selectively re simulating only those small parts of the system that were affected by discontinuities we attain high order accuracy while maintaining running times of o n using a reference implementation of our algorithm applied to a sample problem from the field of faceted surface evolution we obtain convergence and runtime results for the alr method which compares favorably with existing methods

quantum lobachevsky planes we classify all sl 2 r covariant poisson structures on the lobachevsky plane with respect to all multiplicative poisson structures on sl 2 r and describe quantizations for all these poisson structures

metastable patterns for the cahn hilliard equation part ii layer dynamics and slow invariant manifold abstract in this paper we study the dynamics of the 1 dimensional cahn hilliard equation u t 2 u xx w u xx in a finite interval in a neighborhood of an equilibrium with n 1 transition layers where is a small parameter and w is a double well energy density function with equal minima the lower bound of the layer motion speed is given explictly and the layer motion directions are described precisely if a solution of the cahn hilliard equation starts outside a neighborhood of the equilibrium of size o ln 1 it is proved that there is an n dimensional unstable invariant manifold which is a smooth graph over the approximate manifold constructed in j differential equations 111 1994 421 457 with its global lipschitz constant exponentially small and this unstable invariant manifold attracts solutions exponentially fast uniformly in

colored visual cryptography scheme based on additive color mixing a t n visual cryptography scheme vcs encodes a secret image into n shadow images shadows distributed among n participants when any qualified set of at least t participants stack their shadows the secret image can be visually revealed the first vcs proposed by naor and shamir was only designed for encrypting a black and white secret image subsequently some colored vcss cvcss for sharing colored images were proposed to enhance the applicability in cvcss we usually use several color subpixels to represent a secret pixel where the number of subpixels is referred to as the pixel expansion generally the cvcs requires a larger pixel expansion to produce more colors however this expansion will increase the shadow size we therefore study the additive color mixing in a probabilistic way and propose a new cvcs whose pixel expansion is fixed and improves on the previous cvcss at the price of reducing the contrast quality to certain level

duality for exotic bialgebras in the classification of hietarinta three triangular 4 4 r matrices lead via the frt formalism to matrix bialgebras which are not deformations of the trivial one in this paper we find the bialgebras which are in duality with these three exotic matrix bialgebras we note that the l t duality of frt is not sufficient for the construction of the bialgebras in duality we find also the quantum planes corresponding to these bialgebras both by the wess zumino r matrix method and by manin s method

slow dynamics for the cahn hilliard equation in higher space dimensions the motion of bubbles it is known that the van der waals cahn hilliard w c h dynamics can be approximated by a quasi static stefan problem with surface tension it turns out that the stefan problem has a manifold of equilibria equal in dimension to that of the domain any sphere of fixed radius with interface contained in the domain is an equilibrium indistinguishable from the point of view of the perimeter functional we resolve this degeneracy by showing that at the w c h level this manifold is replaced by a quasi invariant stable manifold on which the typical solution preserves its bubble like shape until it reaches the boundary moreover we show that the bubble moves superslowly we also obtain an equation that determines those special spheres that correspond to equilibria at the w c h level our work establishes the phenomenon of superslow motion in higher space dimensions in the class of single interface solutions

two parametric extension of h deformation of gr 1 1 the two parametric quantum deformation of the algebra of coordinate functions on the supergroup gl 1 1 via a contraction of glp q 1 1 is presented related differential calculus on the quantum superplane is introduced

metastability and stability of patterns in a convolution model for phase transitions where e is a small positive parameter and f is bistable having only three zeros 1 a 1 and is balanced i e r 1 1 f u du 1 4 0 see fig 1 for a typical initial datum j which crosses a several times at the beginning the solution evolves as if the diffusion term euxx were not there and in the time scale o ej n ej the solution gets close to 1 or 1 in intervals separated by thin layers of thickness at the order of o ej n ej 17 28 at this moment a spatial pattern is generated it persists on a time scale o ece but is eventually destroyed typically u x t 1 u x t 1 uniformly for x on 1 20 1 as t 1 it is possible that u x t converges to a or a nonconstant steady state as t 1 but this is an unlikely event because all these steady states are unstable 16 27 research supported in part by the national science foundation and bor leqsf

slow motion in higher order systems and g convergence in one space dimension the slow motion in higher order systems and convergence in one space dimension was studied some of the theorems and computations that support and proves the stability of the equations are presented

color visual cryptography schemes for black and white secret images in this paper we propose the use of colors to improve visual cryptography schemes for black and white secret images the resulting model is called colored black and white visual cryptography cbw vc model using this new model we exploit colors to obtain schemes to share bw this is a direct consequence of the definition of contrast which distinguishes only black and non black pixels we discuss an alternative measure of contrast that takes into account the distance between colors we conjecture that also with this definition of contrast there exist schemes that use only full intensity colors and achieve optimal contrast

surface critical exponents for models of polymer collapse and adsorption the universality of the theta and theta points the surface critical exponents are estimated both in ordinary and in special regimes from exact series expansions of up to 28 terms for a model of the theta point they are found to be in agreement with those derived for the theta point confirming the conjecture that the theta and theta points lie in the same universality class some essential features of the phase diagram for a self interacting self avoiding polymer in solution are also calculated to a higher degree of accuracy than previously obtained

a new approach to image sharing with high security threshold structure image sharing is an attractive research subject in computer image techniques and in the information security field this article presents a novel scheme of image sharing with a t n high security threshold structure the scheme can encode secret images into n shadow images in such a way that all the shadow images are in a perfect and ideal t n threshold structure while each shadow image has its own visual content assigned at random the most common method to implement image sharing is based on interpolation polynomial over the field fp 0 1 2 m p 1 shamir 1979 in this article the authors present a new approach to image sharing and its computation based on algebraic geometry code over the pixel value field gf 2m

the three dimensional euclidean quantum group e 3 q and its r matrix a contraction procedure starting from so 4 q is used to determine the quantum analog e 3 q of the three dimensional euclidean group and the structure of its representations a detailed analysis of the contraction of the r matrix is then performed and its explicit expression has been found the classical limit of r is shown to produce an integrable dynamical system by means of the r matrix the pseudogroup of the noncommutative representative functions is considered it will finally be shown that a further contraction made on e 3 q produces the two dimensional galilei quantum group and this in turn can be used to give a new realization of e 3 q and e 2 1 q

dispersive and friction induced stabilization of the cahn hilliard inverse cascade we discuss the stabilization of the inverse cascade in the large scale instability of the kolmogorov flow described by the complete cahn hilliard equation with inclusion of effect large scale friction and deformation radius the friction and the values halting the inverse cascade at the various possible intermediate states are calculated by means of singular perturbation techniques and compared to the values resulting from numerical simulation of the complete cahn hilliard equation the excellent agreement validates the theory our main result is that the critical values of friction or halting the inverse cascade scale exponentially as a function of the jet separation in the final flow contrary to previous theories and phenomenological approach 2002 elsevier science b v all rights reserved pacs 47 10 g 92 60 ek 47 27 i 47 27 ak 47 35 i

h deformation of gr 2 the h deformation of functions on the grassmann matrix group gr 2 is presented via a contraction of as an interesting point we have seen that in the case of the h deformation both r matrices of and are the same

a novel secret image sharing scheme in color images using small shadow images over the past several years secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on in addition to traditional cryptography because smaller shadows can speed up the transmission of a secret color image in this paper we combine chang and wu s gradual search algorithm for a single bitmap btc gsbtc and shamir s k n threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random like image that prevents leakage of information about the secret color image furthermore the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image and the presented scheme also achieves on average an npcr 0 414 and auci 32 78 thus with our scheme one pixel difference could cause a significant difference in the corresponding shadows therefore the security of the presented scheme is also confirmed

classification of quantum group structures on the group gl 2 all quantum group structures on the group gl 2 are classified in addition to the known quantum groups glqp 2 and glhh 2 there exists one exceptional new quantum group glhq 2

quantumsu 2 ande 2 groups contraction procedure in 3 it was shown in the framework of deformed enveloping algebras that quantumsu 2 ande 2 groups are related by the contraction procedure we consider the same problem on thec level as a result we find a number of formulae coupling the comultiplications in quantumsu 2 ande 2 in particular we show that the comultiplications in both groups are implemented by partial isometries an unexpected feature of quantume 2 is discovered and the corresponding strange behavior of quantumsu 2 is described

extended color visual cryptography for black and white secret image recently de prisco and de santis introduced a k n colored black and white visual cryptography scheme cbw vcs which adopts colored pixels in shadow images to share a black and white secret image only k or more participants can reconstruct the secret image by combining their shadow images it seems that no one study k n cbw vcs with the extended ability revealing meaningful shadow images denoted as cbw extended vcs cbw evcs in this paper we extend the conventional evcs i e bw evcs to the cbw evcs this paper has two main contributions i we construct k n cwb evcss ii all constructions are proven to satisfy security contrast and cover image conditions we propose the k n colored black and white extended visual cryptography scheme cbw evcs our k n cbw evcs has the extended ability revealing meaningful shadow images we extend the conditions of k n cwb evcs to those of k n cwb evcs we prove that our constructions satisfy security contrast and cover image conditions

a discussion on the relationship between probabilistic visual cryptography and random grid abstract in a k n visual cryptography scheme vcs the dealer encodes the secret into n shadow images each pixel of the secret image is expanded into m sub pixels in each share in a k n vcs the secret can be visually reconstructed when k or more shares are available the reconstruction process employs the human visual system and no computations are required to solve the pixel expansion problem of vcss probabilistic vcss are directly converted from vcss with no pixel expansion another well known secret image sharing scheme random grid rg is also provided with this novel stacking to see property compared with vcs the most appealing benefit of rg is that there is no pixel expansion in this paper we use the probabilistic vcs without pixel expansion to study the construction and performance of rg this paper has two main results i we show that each step of the share generation process in all existing 2 2 rg 2 n rg n n rg k n rg incremental rg can be mapped to a corresponding step in pvcss and their shadow images between pvcs and rg are perfectly indistinguishable and the reconstructed images are the same also include our 2 n rg ii from the quality of reconstructed image pixel expansion recognized region size and image types to be considered for evaluating pvcss and rgs we point out that rg and pvcs have no difference other than the terminology furthermore rgs is a subset of pvcss

two parameter nonstandard deformation of 2 2 matrices we introduce a two parameter deformation of 2 2 matrices without imposing any condition on the matrices and give the universal r matrix of the nonstandard quantum group which satisfies the quantum yang baxter relation although in the standard two parameter deformation the quantum determinant is not central in the nonstandard case it is central we note that the quantum group thus obtained is related to the quantum supergroup glp q 1 1 by a transformation

spinodal decomposition for the cahn hilliard equation in higher dimensions part i probability and wavelength estimate this paper is the first in a series of two papers addressing the phenomenon of spinodal decomposition for the cahn hilliard equation where is a bounded domain with sufficiently smooth boundary and f is cubic like for example f u u u3 we will present the main ideas of our approach and explain in what way our method differs from known results in one space dimension due to grant 26 furthermore we derive certain probability and wavelength estimates the probability estimate is needed to understand why in a neighborhood of a homogeneous equilibrium u0 of the cahn hilliard equation with mass in the spinodal region a strongly unstable manifold has dominating effects this is demonstrated for the linearized equation but will be essential for the nonlinear setting in the second paper 37 as well moreover we introduce the notion of a characteristic wavelength for the strongly unstable directions

contraction of the gr s quantum group to its nonstandard analog and corresponding colored quantum groups the quantum group gr s provides a realization of the two parameter quantum glp q 2 which is known to be related to the two parameter nonstandard glh h 2 group via the contraction method we apply the contraction procedure to gr s and obtain a new jordanian quantum group gm k furthermore we provide a realization of glh h 2 in terms of gm k the contraction procedure is then extended to the colored quantum group glr 2 to yield a new jordanian quantum group glm 2 both gr s and gm k are then generalized to their colored versions which in turn provide similar realizations of glr 2 and glm 2

the quantum group glh 2 among all quantum group structures on the space mat 2 of 2 by 2 matrices how many have a central quantum determinant so that one can define quantum sl 2 out of quantum gl 2 up to isomorphism there are two such structures glq 2 and glh 2 the former is well known the latter is described in this letter

differential geometry of glp q 1 1 we introduce a construction of the differential calculus on the quantum supergroup glp q 1 1 we obtain two differential calculi respectively associated with the left and the right cartan maurer one forms we also obtain the quantum superalgebra of glp q 1 1 although all of the structures we obtain are derived without an r matrix they nevertheless can be expressed using an r matrix

poisson lie structures on infinite dimensional jet groups and quantum groups related to them we study the problem of classifying all poisson lie structures on the group g of formal diffeomorphisms of the real line r1 which leave the origin fixed as well as the extended group of diffeomorphisms g0 g whose action on r1 does not necessarily fix the origin a complete local classification of all poisson lie structures on the groups g and g0 is given this includes a classification of all lie bialgebra structures on the lie algebra g of g which we prove to be all of the coboundary type and a classification of all lie bialgebra strucutures on the lie algebra g0 the witt algebra of g0 which also turned out to be all of the coboundary type a large class of poisson structures on the space v of densities on the real line is found such that v becomes a homogeneous poisson space under the action of the poisson lie group g we construct a series of quantum semigroups whose quasiclassical limits are finite dimensional poisson lie quotient groups of g and g0

sharing multiple secrets in visual cryptography the secret sharing schemes in conventional visual cryptography are characterized by encoding one shared secret into a set of random transparencies which reveal the secret to the human visual system when they are superimposed in this paper we propose a visual secret sharing scheme that encodes a set of x 2 secrets into two circle shares such that none of any single share leaks the secrets and the x secrets can be obtained one by one by stacking the first share and the rotated second shares with x different rotation angles this is the first true result that discusses the sharing ability in visual cryptography up to any general number of multiple secrets in two circle shares

differential geometry of glh 1 1 we construct a differential calculus on the quantum supergroup glh 1 1 and obtain the h deformed superalgebra of glh 1 1

coarsening dynamics of the one dimensional cahn hilliard model the dynamics of one dimensional cahn hilliard model is studied the stationary and particle type solutions the bubbles are perused as a function of initial conditions boundary conditions and system size we characterize the bubble solutions which are involved in the coarsening dynamics and establish the bifurcation scenarios of the system a set of ordinary differential equation permits us to describe the coarsening dynamics in very good agreement with numerical simulations we also compare these dynamics with the bubble dynamics deduced from the classical kink interaction computation where our model seems to be more appropriated in the case of two bubbles we deduce analytical expressions for the bubble s position and the bubble s width besides a simple description of the ulterior dynamics is presented

deformed minkowski spaces classification and properties using general but simple covariance arguments we classify the quantum minkowski spaces for dimensionless deformation parameters this requires a previous analysis of the associated lorentz groups which reproduces a previous classification by woronowicz and zakrzewski as a consequence of the unified analysis presented we give the commutation properties the deformed and central length element and the metric tensor for the different spacetime algebras

probabilistic visual secret sharing schemes for grey scale images and color images visual secret sharing vss scheme is an encryption technique that utilizes the human visual system in recovering the secret image and does not require any cryptographic computation pixel expansion has been a major issue of vss schemes a number of probabilistic vss schemes with minimum pixel expansion have been proposed for binary secret images this paper presents a general probabilistic k n vss scheme for grey scale images and another scheme for color images with our schemes the pixel expansion can be set to a user defined value when this value is 1 there is no pixel expansion at all the quality of reconstructed secret images measured by average contrast or average relative difference is equivalent to the contrast of existing deterministic vss schemes previous probabilistic vss schemes for black and white images can be viewed as special cases in the schemes proposed here

a multiple level visual secret sharing scheme without image size expansion in traditional vss schemes the size of the share image is substantially expanded since each pixel of the secret image is mapped onto a block consisting of several pixels in addition the quality of the reconstructed secret image is normally degraded in contrast especially for halftone images this study proposes a vss scheme that maps a block in a secret image onto one corresponding equal sized block in each share image without image size expansion two types of techniques including histogram width equalization and histogram depth equalization are proposed to generate the corresponding share blocks containing multiple levels rather than two levels based on the density of black pixels on the blocks for a secret block in the former technique the gray scale image histogram is obtained by uniformly splitting the range of the pixel gray levels in the secret image while in the latter the buckets are created so that the area of each bucket is roughly constant by containing approximately the same number of pixels the proposed schemes significantly improve the quality of the reconstructed secret image compared to several previous investigations

efficient visual secret sharing scheme for color images a k out of n visual secret sharing scheme vsss resolves the visual variant of the k out of n secret sharing problem where only k or more out of n participants can reveal the secret by human visual system without any cryptographic computation the best pixel expansion of the general k out of n vsss for c colored images was cxm by yang and laih new colored visual secret sharing schemes des codes cryptogr 24 2000 325 335 where m is the pixel expansion of an existing binary k out of n vsss regarding the c colored n out of n scheme the best pixel expansion is c 1 2 n 1 c 2 and c c 1 2 n 2 c when n is odd and even respectively by blundo et al improved schemes for visual cryptography des codes cryptogr 24 2001 255 278 in this paper we propose a new c colored k out of n vsss by using a pixel expansion of log 2c xm that is more efficient than ever

image encryption by multiple random grids in this paper we first give a formal definition to the visual cryptograms of n 2 random grids vcrg n for encrypting an image specifically a set of vcrg n with respect to image p consists of n random grids printed on transparencies such that only when the n transparencies are superimposed altogether can p be recognized by human vision without any computing device while any group of less than n transparencies obtains no information about p then we design novel vcrg n encryption schemes for binary gray level and color images validate the correctness by formal proofs and demonstrate the feasibility by computer simulations our schemes do not require any extra pixel expansion neither any encoding basis matrix which are necessary and inevitable in the approaches of conventional visual cryptography these attractive advantages make our schemes more informative in theoretical interests and much applicable in practical applications

secret image sharing based on cellular automata and steganography recently lin and tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 and yang et al improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 proposed secret image sharing schemes combining steganography and authentication based on shamir s polynomials the schemes divide a secret image into some shadows which are then embedded in cover images in order to produce stego images for distributing among participants to achieve better authentication ability chang et al sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 proposed in 2008 an improved scheme which enhances the visual quality of the stego images as well and the probability of successful verification for a fake stego block is 1 16 in this paper we employ linear cellular automata digital signatures and hash functions to propose a novel t n threshold image sharing scheme with steganographic properties in which a double authentication mechanism is introduced which can detect tampering with probability 255 256 employing cellular automata instead of shamir s polynomials not only improves computational complexity from o nlog 2n to o n but obviates the need to modify pixels of cover images unnecessarily compared to previous methods c lin w tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 c yang t chen k yu c wang improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 c chang y hsieh c lin sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 we use fewer number of bits in each pixel of cover images for embedding data so that a better visual quality is guaranteed we further present some experimental results

on combined standard nonstandard or hybrid q h deformations combined q h deformations proposed by kupershmidt and ballesteros herranz parashar are studied in each case a transformation is shown to lead to an equivalent standard q deformation we briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric p q deformations to nonhybrid but biparametric nonstandard g h ones finally a case of hybrid q h deformation is recalled related to the superalgebra gl 1 1

representations and clebsch gordan coefficients for the jordanian quantum algebra representation theory for the jordanian quantum algebra is developed closed form expressions are given for the action of the generators of on the basis vectors of finite dimensional irreducible representations it is shown how representation theory of has a close connection to the combinatorial identities involving summation formulae a general formula is obtained for the clebsch gordan coefficients of these clebsch gordan coefficients are shown to coincide with those of su 2 for but for they are in general a non zero monomial in

generalization of the h deformation to higher dimensions we construct glh 3 from glq 3 by a singular map we show that there exist two singular maps which map glq 3 to new quantum groups we also construct their r matrices and will show that although the maps are singular their r matrices are not then we generalize these singular maps to the case gl n and for cn series

dynamics as a mechanism preventing the formation of finer and finer microstructure we study the dynamics of pattern formation in the one dimensional partial differential equation u u w u x x u xxt u 0 text u u x t text x in 0 1 text t 0 proposed recently by ball holmes james pego swart bhjps as a mathematical cartoon for the dynamic formation of microstructures observed in various crystalline solids here w is a double well potential like 1 4 ux 2 1 2 what makes this equation interesting and unusual is that it possesses as a lyapunov function a free energy consisting of kinetic energy plus a nonconvex elastic energy but no interfacial energy contribution which does not attain a minimum but favours the formation of finer and finer phase mixtures e u u t int limits 0 1 frac u t 2 2 w u x frac u 2 2 dx our analysis of the dynamics confirms the following surprising and striking difference between statics and dynamics conjectured in bhjps on the basis of numerical simulations of swart holmes sh while minimizing the above energy predicts infinitely fine patterns mathematically weak but not strong convergence of all minimizing sequences unvn of e u v in the sobolev space w1p 0 1 l2 0 1 solutions to the evolution equation of ball et al typically develop patterns of small but finite length scale mathematically strong convergence in w1p 0 1 l2 0 1 of all solutions u t ut t with low initial energy as time t

image encryption by random grids a random grid in this paper is a transparency comprising a two dimensional array of pixels that are either transparent or opaque determined in a totally random way we design algorithms by using random grids to accomplish the encryption of the secret gray level and color images in such a way that neither of the two encrypted shares alone leaks the information of the secret image whereas the secret can be seen when these two shares are superimposed the decryption process is done by our visual system and no computation is required as compared to the approaches in visual cryptography our algorithms do not need the basis matrices to encode the shares so that the problem of pixel expansion exists no more that is the sizes of the secret image and the encrypted shares are the same

two parameter deformation of grassmann matrix group and supergroup the two parameter quantum deformations of 2 2 grassmann matrices gr 2 and supermatrices gr 1 1 are presented gr 2 whose matrix elements are all grassmannian variables is called the superdual of the general linear group gl 2 and gr 1 1 whose diagonal matrix elements are grassmannian variables is called the superdual of the supergroup gl 1 1 whose nondiagonal elements are grassmannian noncentral dual superdeterminant for grassmann supermatrices belonging to grp q 1 1 is constructed as with the 2 2 quantum matrices the relations satisfied by the matrix elements of the grassmann matrices and supermatrices are expressed in terms of an r matrix the properties of the nth power of a grassmann supermatrix are given as an appendix

representation functions for jordanian quantum group slh 2 and jacobi polynomials the explicit expressions of the representation functions d functions for jordanian quantum group slh 2 are obtained by combination of tensor operator technique and drinfeld twist it is shown that the d functions can be expressed in terms of jacobi polynomials as the undeformed d functions can some of the important properties of the d functions for slh 2 such as wigner s product law recurrence relations and rtt type relations are also presented

inhomogeneous quantum groups related to two dimensional quantum planes we propose a simple and compact method for deriving quantum groups acting on manin s q and h planes using this method we classify all the rigid motions of the two dimensional quantum planes requiring that these inhomogenous transformations preserve differential structure of the quantum plane we obtain two distinct inhomogenous quantum groups for the q plane and one previously unknown inhomogenous quantum group for the h plane iglh h 2

the keller segel model with logistic sensitivity function and small diffusivity the keller segel model is the classical model for chemotaxis of cell populations it consists of a drift diffusion equation for the cell density coupled to an equation for the chemoattractant here a variant of this model is studied in one dimensional position space where the chemotactic drift is turned off for a limiting cell density by a logistic term and where the chemoattractant density solves an elliptic equation modeling a quasi stationary balance of reaction and diffusion with production of the chemoattractant by the cells the case of small cell diffusivity is studied by asymptotic and numerical methods on a time scale characteristic for the convective effects convergence of solutions to weak entropy solutions of the limiting nonlinear hyperbolic conservation law is proven numerical and analytic evidence indicates that solutions of this problem converge to irregular patterns of cell aggregates separated by entropic shocks from vacuum regions as time tends to infinity close to each of these p

jordanian quantum algebra h sl n via contraction method and mapping using a contraction procedure developed earlier we construct in the first part of the present paper the jordanian quantum hopf algebra h sl 3 which has a remarkably simple coalgebraic structure and contains the jordanian algebra h sl 2 obtained by ohn as a hopf subalgebra a nonlinear map between the quantum h sl 3 and the classical sl 3 algebras is then established and the universal h matrix of the h sl 3 algebra is given in the second part we give the higher dimensional jordanian algebras h sl n for all n the universal h matrix of the h sl n algebra is also given

reduce shadow size in aspect ratio invariant visual secret sharing schemes using a square block wise operation an aspect ratio invariant visual secret sharing arivss scheme is a perfectly secure method for sharing secret images due to the nature of the vss encryption each secret pixel is expanded to m sub pixels in each of the generated shares the advantage of arivss is that the aspect ratio of the recovered secret image is fixed and thus there is no loss of information when the shape of the secret image is our information for example a secret image of a circle is compromised to an ellipse if m does not have a square value two arivss schemes based on processing one and four pixel blocks respectively were previously proposed in this paper we have generalized the square block wise approach to further reduce pixel expansion

irreducible decomposition for tensor product representations of jordanian quantum algebras tensor products of irreducible representations of the jordanian quantum algebras and are considered for both the highest weight finite dimensional representations of and the lowest weight infinite dimensional ones of it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding lie algebras

duality for the jordanian matrix quantum group we find the hopf algebra dual to the jordanian matrix quantum group as an algebra it depends only on the sum of the two parameters and is split into two subalgebras with three generators and with one generator the subalgebra is a central hopf subalgebra of the subalgebra is not a hopf subalgebra and its co algebra structure depends on both parameters we discuss also two one parameter special cases g h and g h the subalgebra is a hopf algebra and coincides with the algebra introduced by ohn as the dual of the subalgebra is isomorphic to u sl 2 as an algebra but has a nontrivial co algebra structure and again is not a hopf subalgebra of

sharing secrets in stego images with authentication recently lin and tsai and yang et al proposed secret image sharing schemes with steganography and authentication which divide a secret image into the shadows and embed the produced shadows in the cover images to form the stego images so as to be transmitted to authorized recipients securely in addition these schemes also involve their authentication mechanisms to verify the integrity of the stego images such that the secret image can be restored correctly unfortunately these schemes still have two shortcomings one is that the weak authentication cannot well protect the integrity of the stego images so the secret image cannot be recovered completely the other shortcoming is that the visual quality of the stego images is not good enough to overcome such drawbacks in this paper we propose a novel secret image sharing scheme combining steganography and authentication based on chinese remainder theorem crt the proposed scheme not only improves the authentication ability but also enhances the visual quality of the stego images the experimental results show that the proposed scheme is superior to the previously existing methods

quantum jordanian twist the quantum deformation of the jordanian twist q for the standard quantum borel algebra uq b is constructed it gives the family uq b of quantum algebras depending on parameters and h in a generic point these algebras represent the hybrid standard nonstandard quantization the quantum jordanian twist can be applied to the standard quantization of any kac moody algebra the corresponding classical r matrix is a linear combination of the drinfeld jimbo and the jordanian ones the two parametric families of hopf algebras obtained here are smooth and for the limit values of the parameters the standard and nonstandard quantizations are recovered the twisting element q also has correlated limits in particular when q tends to unity it acquires the canonical form of the jordanian twist to illustrate the properties of the quantum jordanian twist we construct the hybrid quantizations for u sl 2 and for the corresponding affine algebra the universal quantum matrix and its defining representation are presented