computing the hilbert transform on the real line we introduce a new method for computing the hilbert transform on the real line it is a collocation method based on an expansion in rational eigenfunctions of the hilbert transform operator and implemented through the fast fourier transform an error analysis is given and convergence rates for some simple classes of functions are established numerical tests indicate that the method compares favorably with existing methods

calculating the hilbert transform on spaces with energy concentration convergence and divergence regions in many different applications it is important to determine the hilbert transform of a given function however it is generally impossible to calculate it in closed form therefore hilbert transform approximations are used this paper studies the convergence and divergence behavior of general classes of such approximation methods these classes are characterized by two very natural axioms and they include basically all known traditional numerical algorithms the convergence of these methods is investigated on a family of signal spaces of continuous functions with finite energy these spaces are parametrized by a number which measures the energy concentration in the low frequency components of the signal it is shown that stable methods only exist on signal spaces with a sufficient energy concentration and this paper gives some explicit examples of convergent methods on all other spaces in the family of signal spaces every sampling based hilbert transform approximation shows a blowup behavior of its peak value i e on these spaces every sampling based hilbert transform approximation diverges

fast planar oriented ripple search algorithm for hyperspace vq codebook this paper presents a fast codebook search method for improving the quantization complexity of full search vector quantization vq the proposed method is built on the planar voronoi diagram to label a ripple search domain then the appropriate codeword can easily be found just by searching the local region instead of global exploration in order to take a step further and obtain the close result full search vq would we equip the proposed method with a duplication mechanism that helps to bring down the possible quantizing distortion to its lowest level according to the experimental results the proposed method is indeed capable of providing better outcome at a faster quantization speed than the existing partial search methods moreover the proposed method only requires a little extra storage for duplication

a high payload frequency based reversible image hiding method to provide both a high payload capacity and a good stego image quality a high payload frequency based reversible image hiding hpfrih method was presented in this paper these performances can be achieved by transforming a cover image from the spatial domain into the frequency domain through haar digital wavelet transform hdwt method followed by an adaptive arithmetic coding method to encode the hdwt coefficients in a high frequency band the hpfrih method was used to conceal both the compressed data and the secret data in the high frequency band this simple method can completely reconstruct the cover image only from the stego image moreover experimental results showed that the hpfrih method offers both impressive hiding capacity and satisfied stego image quality

approximation of semigroups and related operator functions by resolvent series we consider the approximation of semigroups e tau a and of the functions varphi j tau a that appear in exponential integrators by resolvent series the interesting fact is that the resolvent series expresses the operator functions e tau a and varphi j tau a respectively in efficiently computable terms this is important for semigroups where the new approximation is different from well known approximations by rational functions as well as for the application of exponential integrators which are currently of high interest and which are usually studied in a semigroup setting on banach spaces the approximation of the operator functions varphi j tau a in a general strongly continuous semigroup setting has not been discussed in the literature so far but this is crucial for an application of these integrators with unbounded operators or bounded operators like discretization matrices with large norm and eigenvalues somewhere in the left half plane

overlap and channel errors in adaptive vector quantization for image coding adaptive vector quantization avq is a flexible adaptive single pass image compression method with fast decompression time for which practical compression achieved compares favorably with existing methods such as the jpeg standard and traditional trained vq in this paper we analyze its asymptotic performance for the lossless case and present variations to limit the effect of transmission errors on the decoding image

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

elliptic hypergeometry of supersymmetric dualities ii orthogonal groups knots and vortices we consider seiberg electric magnetic dualities for 4d mathcal n 1 sym theories with so n gauge group for all such known theories we construct superconformal indices scis in terms of elliptic hypergeometric integrals equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals in particular we describe a number of new elliptic beta integrals associated with the s confining theories with the spinor matter fields reductions of some dualities from sp 2n to so 2n or so 2n 1 gauge groups are described interrelation of scis and the witten anomaly is briefly discussed possible applications of the elliptic hypergeometric integrals to a two parameter deformation of 2d conformal field theory and related matrix models are indicated connections of the reduced scis with the state integrals of knot theory generalized agt duality for 3 3 d theories and a 2d vortex partition function are described

superconvergence of spectral collocation and p version methods in one dimensional problems superconvergence phenomenon of the legendre spectral collocation method and the p version finite element method is discussed under the one dimensional setting for a class of functions that satisfy a regularity condition m u k l cm k on a bounded domain it is demonstrated both theoretically and numerically that the optimal convergent rate is supergeometric furthermore at proper gaussian points or lobatto points the rate of convergence may gain one or two orders of the polynomial degree

joint coding and embedding techniques for multimedia images hiding data in digital images is a technique for secret data communication it involves embedding important data into a cover image in digital form with minimal perceptible degradation in this paper we first propose an improved data hiding method for side match vector quantization smvq compressed images which utilizes the codeword pairing procedure to modulate the index code of each image block in order to take it a step further and obtain a larger embedding capacity we remodel the first proposed method into a new one with the power of variable rate data embedding through the use of a multiple base notational system according to the experimental results the two proposed methods are indeed capable of providing a larger embedding capacity without causing noticeable distortions of stego images in comparison with previous methods moreover our methods also maintain a low compression bit rate without auxiliary data

computing the hilbert transform and its inverse we construct a new method for approximating hilbert transforms and their inverse throughout the complex plane both problems can be formulated as riemann hilbert problems via plemelj s lemma using this framework we re derive existing approaches for computing hilbert transforms over the real line and unit interval with the added benefit that we can compute the hilbert transform in the complex plane we then demonstrate the power of this approach by generalizing to the half line combining two half lines we can compute the hilbert transform of a more general class of functions on the real line than is possible with existing methods

elementary solutions for a model boltzmann equation in one dimension and the connection to grossly determined solutions abstract the fourier transformed version of the time dependent slip flow model boltzmann equation associated with the linearized bgk model is solved in order to determine the solution s asymptotics the ultimate goal of this paper is to demonstrate that there exists a robust set of solutions to this model boltzmann equation that possess a special property that was conjectured by truesdell and muncaster that solutions decay to a subclass of the solution set uniquely determined by the initial mass density of the gas called the grossly determined solutions first we determine the spectrum and eigendistributions of the associated homogeneous equation then using case s method of elementary solutions we find analytic time dependent solutions to the model boltzmann equation for initial data with a specialized compact support condition under the fourier transform in doing so we show that the spectrum separates the solutions into two distinct parts one that behaves as a set of transient solutions and the other limiting to a stable subclass of solutions thus we demonstrate that for gas flows with this specialized initial density condition in time all gas flows for the one dimensional model boltzmann equation act as grossly determined solutions

a new data hiding scheme for binary image authentication with small image distortion a new data hiding scheme for binary image authentication that has a small distortion of the cover image is proposed in this paper using the data embedding algorithm that is based on hamming codes the proposed scheme embeds authentication information into the cover image with flipping only a small number of pixels a special type of the pixels are selected and flipped by a new algorithm to minimize visual distortion this new algorithm is based on elssm edge line segment similarity measure randomly shuffling the bit order of the authentication information to be embedded the information can only be extracted by the designated receiver who has the symmetric key we employ two measurement metrics miss detection rates for the degree of security and psnr peak signal to noise ratio and elssm for the degree of the image distortion to demonstrate the feasibility of the proposed scheme using these metrics we analyze the proposed scheme and the previous schemes the analysis reveals that the proposed scheme requires less image distortion than the previous schemes whilst achieving the same level of the miss detection rate experimental results demonstrate that the proposed scheme is more resilient against recent steganalysis attacks than the previous schemes

a complete orthonormal system of functions in l 2 infty infty space a new complete orthonormal system of functions in the l 2 infty infty space is introduced the system consists of two sequences composed of odd and even functions respectively unlike hermite and laguerre sets of functions which behave exponentially at infinity the new system exhibits asymptoticbehavior x 1 for the odd sequence and x 2 for the even one formulae representing products derivatives etc in series in the system are developed a nonlinear differential equation with a requirement for summability of the square of its solutions instead of boundary conditions is solved the example displays most of the features of the new method important for essentially nonlinear problems

perceptually adaptive spread transform image watermarking scheme using hadamard transform the present paper proposes a digital image watermarking scheme using the characteristics of the human visual system hvs spread transform technique and statistical information measure spread transform st scheme is implemented using the transform coefficients of both the host and the watermark signal watermark embedding strength is adaptively adjusted using frequency sensitivity luminance contrast and entropy masking of hvs model the choice of hadamard transform as watermark embedding domain offers several advantages such as low loss in image information higher image fidelity greater reliability of watermark detection and higher data hiding capacity at high degree of compression performance of the proposed method is compared with a number of recently reported watermarking schemes based on spread spectrum ss and quantization index modulation qim

computations of the complex error function rational expansions for computing the complex error function w z e z 2 text erfc iz are presented these expansions have the following attractive properties 1 they can be evaluated using a polynomial evaluation routine such as homer s method 2 the polynomial coefficients can be computed once and for all by a single fast fourier transform fft and 3 high accuracy is achieved uniformly in the complex plane with only a small number of terms comparisons reveal that in some parts of the complex plane certain competitors may be more efficient however the difference in efficiency is never great and the new algorithms are simpler than existing ones a complete program takes eight lines of matlab code

self similar slip instability on interfaces with rate and state dependent friction we examine the development of a frictional instability with diverging sliding rate at the interface of elastic bodies in contact evolution of friction is determined by a slip rate and state depe

a generalization of the wiener rational basis functions on infinite intervals part ii numerical investigation in part i we introduced the generalized wiener rational basis functions and here in part ii we continue our investigation with numerical experiments wiener s generalized basis can utilize the fast fourier transform for integer values of the decay parameter s we outline two algorithms for doing so in addition the issue of galerkin representations for polynomial nonlinearities of expansions is addressed the wiener basis set is compared against domain truncation methods fourier and chebyshev polynomials hermite functions sinc interpolations and mapped chebyshev expansions and we show that for both exponentially and algebraically decaying functions the wiener approximation is as good as or superior to these alternatives in addition we carry out preliminary investigations regarding tuning of the decay parameter s numerical simulations of korteweg de vries type equations show the effectiveness of the wiener expansion we also explore the practical use of the wiener basis functions on the semi infinite interval which is compared against laguerre function methods and other jacobi polynomial mappings

computing zeros on a real interval through chebyshev expansion and polynomial rootfinding robust polynomial rootfinders can be exploited to compute the roots on a real interval of a nonpolynomial function f x by the following i expand f as a chebyshev polynomial series ii convert to a polynomial in ordinary series of powers form and iii apply the polynomial rootfinder complex valued roots and real roots outside the target interval are discarded the expansion is most efficiently done by adaptive chebyshev interpolation with n equal to a power of two where n is the degree of the truncated chebyshev series all previous evaluations of f can then be reused when n is increased adaption stops when n is sufficiently large so that further increases produce no significant change in the interpolant we describe two conversion strategies the convert to powers method uses multiplication by mildly ill conditioned matrices to create a polynomial of degree n the degree doubling strategy defines a polynomial of larger degree 2n but is very well conditioned the convert to powers method although faster restricts n to moderate values this can always be accomplished by subdividing the target interval both these strategies allow simultaneous approximation of many roots on an interval whether simple or multiple for nonpolynomial f x

a novel method for computing the hilbert transform with haar multiresolution approximation in this paper an algorithm for computing the hilbert transform based on the haar multiresolution approximation is proposed and the l 2 error is estimated experimental results show that it outperforms the library function hilbert in matlab the mathworks inc 1994 2007 finally it is applied to compute the instantaneous phase of signals approximately and is compared with three existing methods

a fourier hermite pseudospectral method for penetrative convection a fourier hermite pseudospectral method is developed to study numerically the three dimensional penetrative convection problem under the boussinesq approximation an s shaped temperature profile in the absence of motion is prescribed in the vertical direction all variables are expanded in terms of fourier hermite basis functions the hermite functions are scaled to adjust the length of the computational domain in the vertical a semi implicit scheme is used for time marching with the third order adam bashforth and crank nicholson scheme for the nonlinear and linear terms respectively an implementation of the numerical method on a parallel computer is also described numerical simulation results of resolution 643are presented for low to moderate rayleigh numbers with a prandtl number of unity the highly stable outer regions are seen to act as effective lids and all penetrative flow are contained within the computational box variances heat fluxes and their budgets are reported for several rayleigh numbers to demonstrate the efficacy of the numerical method

quantum 401 1401 1401 1algebras and macdonald polynomials we derive a quantum deformation of thew n algebra and its quantum miura transformation whose singular vectors realize the macdonald polynomials

the asymptotic chebyshev coefficients for functions with logarithmic endpoint singularities mappings and singular basis functions abstract when a function is singular at the ends of its expansion interval its chebyshev coefficients a n converge very poorly we analyze three numerical strategies for coping with such singularities of the form 1 x k log 1 x and in the process make some modest additions to the theory of chebyshev expansions the first two numerical methods are the convergence improving changes of coordinate x sin 2 y and x tanh ly 1 y 2 1 2 we derive the asymptotic chebyshev coefficients in the limit n for both mappings and for the original untransformed chebyshev series for the original function the asymptotic approximation for general k is augmented by the exact chebyshev coefficients for integer k numerical tests show that the sine mapping is excellent for k 1 increasing the rate of convergence to b n o 1 n 4 k 1 although the tanh transformation is guaranteed to be better for sufficiently large n we offer both theoretical and numerical evidence to explain why the sine mapping is usually better in practice sufficiently large n is usually huge instead of mapping one may use a third strategy supplementing the chebyshev polynomials with singular basis functions simple experiments show that this approach is also successful

asymptotic upper bounds for the coefficients in the chebyshev series expansion for a general order integral of a function the usual way to determine the asymptotic behavior of the chebyshev coefficients for a function is to apply the method of steepest descent to the integral representation of the coefficients however the procedure is usually laborious we prove an asymptotic upper bound on the chebyshev coefficients for the k th integral of a function the tightness of this upper bound is then analyzed for the case k 1 the first integral of a function it is shown that for geometrically converging chebyshev series the theorem gives the tightest upper bound possible as n for functions that are singular at the endpoints of the chebyshev interval x 1 the theorem is weakened two examples are given in the first example we apply the method of steepest descent to directly determine laboriously the asymptotic chebyshev coefficients for a function whose asymptotics have not been given previously in the literature a gaussian with a maximum at an endpoint of the expansion interval we then easily obtain the asymptotic behavior of its first integral the error function through the application of the theorem the second example shows the theorem is weakened for functions that are regular except at 1 we conjecture that it is only for this class of functions that the theorem gives a poor upper bound

a steganographic method based upon jpeg and particle swarm optimization algorithm in this paper a novel steganographic method based on jpeg and particle swarm optimization algorithm pso is proposed in order to improve the quality of stego images an optimal substitution matrix for transforming the secret messages is first derived by means of the pso algorithm the standard jpeg quantization table is also modified to contain more secret messages the transformed messages are then hidden in the dc to middle frequency components of the quantized dct coefficients of the cover image finally a jpeg file with secret messages is generated through jpeg entropy coding we compare our algorithm with chang et al s jpeg based steganographic algorithm the experimental results show that our proposed method has larger message capacity and better image quality than chang et al s in addition our method also has a high security level

the eigenvalues of hermite and rational spectral differentiation matrices we derive expressions for the eigenvalues of spectral differentiation matrices for unbounded domains in particular we consider galerkin and collocation methods based on hermite functions as well as rational functions a fourier series combined with a cotangent mapping we show that i first derivative matrices have purely imaginary eigenvalues and second derivative matrices have real and negative eigenvalues ii for the hermite method the eigenvalues are determined by the roots of the hermite polynomials and for the rational method they are determined by the laguerre polynomials and iii the hermite method has attractive stability properties in the sense of small condition numbers and spectral radii

elliptic genera of 2d mathcal n 2 gauge theories we compute the elliptic genera of general two dimensional mathcal n 2 2 and mathcal n 0 2 gauge theories we find that the elliptic genus is given by the sum of jeffrey kirwan residues of a meromorphic form representing the one loop determinant of fields on the moduli space of flat connections on t2 we give several examples illustrating our formula with both abelian and non abelian gauge groups and discuss some dualities for u k and su k theories this paper is a sequel to the authors previous paper benini et al lett math phys 104 465 493 2014

elliptic modular double and 4d partition functions we consider 4d supersymmetric special unitary gamma quiver gauge theories on compact manifolds which are t 2 fibrations over s 2 we show that their partition functions are correlators of vertex

image hiding scheme with modulus function and dynamic programming strategy on partitioned pixels in this paper we shall propose a novel image hiding scheme our new scheme classifies the host image pixels into two groups of pixels according to the pixel values for each group of pixels the corresponding secret pixel values go through an optimal substitution process and are transformed into other pixel values by following the dynamic programming strategy then we can embed the transformed pixel values in the host pixels by using the modulus functions and obtain the stego image extensive experimental results demonstrate that our new method is capable of offering better stego image quality than a number of well accepted schemes

the rate of convergence of fourier coefficients for entire functions of infinite order with application to the weideman cloot sinh mapping for pseudospectral computations on an infinite interval we analytically compute the asymptotic fourier coefficients for several classes of functions to answer two questions the numerical question is to explain the success of the weideman cloot algorithm for solving differential equations on an infinite interval their method combines fourier expansion with a change of coordinate using the hyperbolic sine function the sinh mapping transforms a simple function like exp z2 into an entire function of infinite order this raises the second analytical question what is the fourier rate of convergence for entire functions of an infinite order the answer is sometimes even slower than a geometric series in this case the fourier series converge only on the real axis even when the function u z being expanded is free of singularities except at infinity earlier analysis ignored stationary point contributions to the asymptotic fourier coefficients when u z had singularities off the real z axis but we show that sometimes these stationary point terms are more important than residues at the poles of u z

on exponential convergence of gegenbauer interpolation and spectral differentiation this paper is devoted to a rigorous analysis of exponential convergence of polynomial interpolation and spectral differentiation based on the gegenbauer gauss and gegenbauer gauss lobatto points when the underlying function is analytic on and within an ellipse sharp error estimates in the maximum norm are derived

infinite chiral symmetry in four dimensions we describe a new correspondence between four dimensional conformal field theories with extended supersymmetry and two dimensional chiral algebras the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four dimensional theory infinite chiral symmetry has far reaching consequences for the spectral data correlation functions and central charges of any four dimensional theory with mathcal n 2 superconformal symmetry

numerical and perturbative computations of solitary waves of the benjamin ono equation with higher order nonlinearity using christov rational basis functions computation of solitons of the cubically nonlinear benjamin ono equation is challenging first the equation contains the hilbert transform a nonlocal integral operator second its solitary waves decay only as o 1 x 2 to solve the integro differential equation for waves traveling at a phase speed c we introduced the artificial homotopy h u x x c u 1 d u 2 du 3 0 d 0 1 and solved it in two ways the first was continuation in the homotopy parameter d marching from the known benjamin ono soliton for d 0 to the cubically nonlinear soliton at d 1 the second strategy was to bypass continuation by numerically computing perturbation series in d and forming pade approximants to obtain a very accurate approximation at d 1 to further minimize computations we derived an elementary theorem to reduce the two parameter soliton family to a parameter free function the soliton symmetric about the origin with unit phase speed solitons for higher order benjamin ono equations are also computed and compared to their korteweg devries counterparts all computations applied the pseudospectral method with a basis of rational orthogonal functions invented by christov which are eigenfunctions of the hilbert transform

pseudospectral methods on a semi infinite interval with application to the hydrogen atom a comparison of the mapped fourier sine method with laguerre series and rational chebyshev expansions the fourier sine with mapping pseudospectral algorithm of fattal et al phys rev e 53 1996 1217 has been applied in several quantum physics problems here we compare it with pseudospectral methods using laguerre functions and rational chebyshev functions we show that laguerre and chebyshev expansions are better suited for solving problems in the interval r 0 for example the coulomb schrodinger equation than the fourier sinemapping scheme all three methods give similar accuracy for the hydrogen atom when the scaling parameter l is optimum but the laguerre and chebyshev methods are less sensitive to variations in l we introduce a new variant of rational chebyshev functions which has a more uniform spacing of grid points for large r and gives somewhat better results than the rational chebyshev functions of boyd j comp phys 70 1987 63

orthogonal rational functions on a semi infinite interval abstract by applying a mapping to the chebyshev polynomials we define a new spectral basis the rational chebyshev functions on the semi infinite interval denoted by tl n y continuing earlier work by the author and by grosch and orszag we show that these rational functions inherit most of the good numerical characteristics of the chebyshev polynomials orthogonality completeness exponential or infinite order convergence matrix sparsity for equations with polynomial coefficients and simplicity seven numerical examples illustrate their versatility the charney stability problem of meteorology for example is solved to show the feasibility of applying spectral methods to a semi infinite atmosphere for functions that are singular at both endpoints such as k 1 y one may combine rational chebyshev functions with a preliminary mapping to obtain a single exponentially convergent expansion on y 0 finally we successfully generalize the wkb method to obtain for the j 0 bessel function an amplitude phase approximation which is convergent rather than asymptotic and is accurate not merely for large y but for all y even the origin

a sinc quadrature subroutine for cauchy principal value integrals a subroutine is presented for the evaluation of cauchy principal value integrals based on a truncated sum of a sinc function series with the function evaluated at shifted sinc points the subroutine returns an approximation to the integral together with estimates of the relative and the absolute errors numerical results demonstrate that the new method works well on analytic functions with end point singularities

spectral methods using rational basis functions on an infinite interval by using the map y l cot t where l is a constant differential equations on the interval y can be transformed into t 0 and solved by an ordinary fourier series in this article earlier work by grosch and orszag j comput phys 25 273 1977 cain ferziger and reynolds j comput phys 56 272 1984 and boyd j comput phys 25 43 1982 57 454 1985 siam j numer anal 1987 is extended in several ways first the series of orthogonal rational functions converge on the exterior of bipolar coordinate surfaces in the complex y plane second galerkin s method will convert differential equations with polynomial or rational coefficients into banded matrix problems third with orthogonal rational functions it is possible to obtain exponential convergence even for u y that asymptote to a constant although this behavior would wreck alternatives such as hermite or sinc expansions fourth boundary conditions are usually natural rather than essential in the sense that the singularities of the differential equation will force the numerical solution to have the correct behavior at infinity even if no constraints are imposed on the basis functions fifth mapping a finite interval to an infinite one and then applying the rational chebyshev functions gives an exponentially convergent method for functions with bounded endpoint singularities these concepts are illustrated by five numerical examples

side match and overlap match vector quantizers for images a class of vector quantizers with memory that are known as finite state vector quantizers fsvqs in the image coding framework is investigated two fsvq designs namely side match vector quantizers smvqs and overlap match vector quantizers omvqs are introduced these designs take advantage of the 2 d spatial contiguity of pixel vectors as well as the high spatial correlation of pixels in typical gray level images smvq and omvq try to minimize the granular noise that causes visible pixel block boundaries in ordinary vq for 512 by 512 gray level images smvq and omvq can achieve communication quality reproduction at an average of 1 2 b pixel per image frame and acceptable quality reproduction because block boundaries are less visible the perceived improvement in quality over ordinary vq is even greater owing to the structure of smvq and omvq simple variable length noiseless codes can achieve as much as 60 bit rate reduction over fixed length noiseless codes

max plus algebra based wavelet transforms and their fpga implementation for image coding in the present paper we propose new image coding methods based on max plus algebra based wavelet transforms mp wavelets max plus algebra is an algebraic structure on the set of integers endowed with maximum minimum and standard addition as operations the proposed wavelet decomposition schemes are novel classes of morphological wavelets which in contrast to the existing approaches involve only integers and only max min and addition in their computation since they do not involve floating point calculations and multiplications mp wavelets have a very low computational complexity and they are suitable for efficient hardware implementation through image coding experiments using 10 000 images extracted from low resolution web crawled misc database the characteristics of the proposed mp wavelets are presented furthermore we show a computational complexity analysis to compare mp wavelets to one of the fastest wavelet transforms the conventional haar wavelet the applicability of mp wavelets in video coding is also confirmed by image coding experiments using residual frames finally the field programmable gate arrays fpga implementation of mp wavelets is presented to confirm suitability of mp wavelets for hardware implementation

adaptive data hiding for vector quantization images based on overlapping codeword clustering in this paper an overlapping codeword clustering based data hiding scheme is presented in this scheme a mapping table is designed to determine the overlapping codeword clustering and to indicate the index modification in the secret embedding the mapping table explores the relationship among the sub codebook s size the codeword s order and the embedding secret message to which the codeword overlapping in sub codebooks with different sizes is permitted in addition the secret embedding is also determined according to the mapping table the experimental results showed that the number of partitioned sub codebooks was increased significantly the average hiding capacity was about 30k bits while the average embedding distortion was about 1 2db in comparison to similar methods the proposed scheme provided a larger hiding capacity than others while preserving a similar stego image quality furthermore the proposed scheme offered a better proportion of hiding compared to image distortion

a method for the practical evaluation of the hilbert transform on the real line abstract we investigate a method for the numerical evaluation of the weighted hilbert transform over the entire real line exp x 2 f x x t 1 d x where the integral is taken in the cauchy principal value sense the method is based on a combination of two polynomial approximation processes in this way we obtain a procedure that is numerically stable and efficient the algorithm can be implemented in a fast way and existing well known software packages may be used from the point of view of theoretical error bounds the method is competitive generalizations to other approximation methods are also possible

objective picture quality scale pqs for image coding a new methodology for the determination of an objective metric for still image coding is reported this methodology is applied to obtain a picture quality scale pqs for the coding of achromatic images over the full range of image quality defined by the subjective mean opinion score mos this pqs takes into account the properties of visual perception for both global features and localized disturbances the pqs closely approximates the mos with a correlation coefficient of more than 0 92 as compared to 0 57 obtained using the conventional weighted mean square error wmse extensions and applications of the methodology and of the resulting metric are discussed

the elliptic gamma function and sl 3 z z3 abstract the elliptic gamma function is a generalization of the euler gamma function and is associated to an elliptic curve its trigonometric and rational degenerations are the jackson q gamma function and the euler gamma function respectively the elliptic gamma function appears in baxter s formula for the free energy of the eight vertex model and in the hypergeometric solutions of the elliptic qkzb equations in this paper the properties of this function are studied in particular we show that elliptic gamma functions are generalizations of automorphic forms of g sl 3 z z 3 associated to a non trivial class in h3 g z

a spectral method for unbounded domains a spectral method for an unbounded domain is presented rational basis functions which are algebraically mapped legendre functions are used for expansion in the radial direction of polar coordinates r or r z they satisfy the pole condition exactly at the coordinate singularity and their behavior asr is suitable for expanding smooth functions which decay algebraically or exponentially asr the method is not stiff when it is applied to initial value problems despite the presence of the coordinate singularity solenoidal vector fields are treated efficiently by the toroidal and poloidal decomposition which reduces the number of dependent variables from 3 to 2 examples include the computation of vortex dynamics in two and three dimensions

sharp error bounds for jacobi expansions and gegenbauer gauss quadrature of analytic functions this paper provides a rigorous and delicate analysis for exponential decay of jacobi polynomial expansions of analytic functions associated with the bernstein ellipse using an argument that can recover the best estimate for the chebyshev expansion we derive various new and sharp bounds of the expansion coefficients which are featured with explicit dependence of all related parameters and valid for degree n ge 1 we demonstrate the sharpness of the estimates by comparing with existing ones in particular the very recent results in siam j numer anal 50 2012 pp 1240 1263 we also extend this argument to estimate the gegenbauer gauss quadrature remainder of analytic functions which leads to some new tight bounds for quadrature errors

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