root exclusion from complex polydomains and some of its applications abstract a solution to an open research problem related to testing root exclusion of a real n dimensional polynomial n 1 from a subspace of n defined as a cartesian product n times of c c is given in this paper the solution is presented in two theorems which have application to several research problems related to robust relative multidimensional stability among them are the testing of robust relative stability of linear differential systems the testing of robust relative stability of linear delay differential systems and a complementary test for a robust stabilization algorithm several examples are presented to illustrate some of these applications

on the stability and instability of n dimensional discrete systems n 1 the applicability of sufficient conditions for stability and for instability of multidimensional discrete systems is extended the approach is based on interpreting in the transform domain an extension which has been previously proposed only for one dimensional systems and had been based on time domain considerations

the ngp stability of runge kutta methods for systems of neutral delay differential equations this paper deals with the stability analysis of implicit runge kutta methods for the numerical solutions of the systems of neutral delay differential equations we focus on the behavior of such methods with respect to the linear test equations where tau 0 l m and n are d times d complex matrices we show that an implicit runge kutta method is ngp stable if and only if it is a stable

another simplification in multidimensional stability tests the main computational burden of checking stability of a multidimensional system is to check whether a multivariable polynomial has zeros on the distinguished boundary of a certain region of analyticity a transformation is performed yielding an expression which has zeros on the distinguished boundary if and only if the original polynomial has such zeros in some cases especially where a linear dependence of certain auxiliary variables defined in the text can be presented in terms of nonnegative integers the transformed expression is considerably simpler and its test is easier to perform than the original one examples are provided

n dimensional stability margins computation and a variable transformation stability margins for n dimensional n geq 2 linear discrete causal systems are defined following a definition suggested recently in the literature for n 2 these can serve as a measure in some sense for the tendency of a stable n d system to become unstable also presented is a new procedure for the computation of these stability margins which is explicitly formulated the computational complexity is equivalent to that of solving for one indeterminate a set of n 1 real equations in n 1 real indeterminates also an n dimensional expansion of a known variable transformation which preserves the core condition of stability is presented and used to considerably simplify n dimensional stability tests and stability margins computations for a class of special cases numerical examples are also provided

approximating the solution of nonlinear hammerstein fuzzy integral equations abstract in this paper we prove the convergence of the method of successive approximations used to approximate the solution of nonlinear hammerstein fuzzy integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration this numerical stability is proved and finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

on the one leg θ methods for solving nonlinear neutral functional differential equations abstract this paper discusses the one leg methods for the numerical solution of nonlinear neutral functional differential equations with pantograph delay y t f t y t y pt y pt t 0 0 p 1 y 0 y in recent years the numerical techniques for the solution to this kind of equations have been developed by numerous authors who have mainly considered the linear system instead in the present paper we study the nonlinear case the first step integration of above systems on 0 t 0 by one leg methods is analyzed it is proved that the numerical solution preserves the contractivity property for some t0 on the quasi geometric mesh the numerical stability of one leg methods for above systems is investigated some sufficient conditions for global stability and asymptotic stability are established two numerical examples are also included

regular solutions of the shabat equation the shabat equationf t q2f qt f2 t q2f2 qt t r where andqare parameters is the simplest self similar reduction of the so called dressing chain for constructing and analyzing exactly solvable schrodinger equations it is so relevant to the study of theq oscillator algebra in quantum mechanics the main objective of this paper is to investigate whether the shabat equation has a nontrivial global solutionf t c1 r that is normalizable in the sense that the corresponding potentialu t f2 t f t 1 q2 is in the function space l1 r and whether in the case 1 q2 0 it has a global solutionf t c1 r that is regular in the sense thatf t 1 q2 o t 2 andf t o t 3 ast

local shannon entropy measure with statistical tests for image randomness in this paper we propose a new image randomness measure using shannon entropy over local image blocks the proposed local shannon entropy measure overcomes several weaknesses of the conventional global shannon entropy measure including unfair randomness comparisons between images of different sizes failure to discern image randomness before and after image shuffling and possible inaccurate scores for synthesized images statistical tests pertinent to this new measure are also derived this new measure is therefore both quantitative and qualitative the parameters in the local shannon entropy measure are further optimized for a better capture of local image randomness the estimated statistics and observed distribution from 50 000 experiments match the theoretical ones finally two examples are given applying the proposed measure to image randomness among shuffled images and encrypted images both examples show that the proposed method is more effective and more accurate than the global shannon entropy measure

design of image cipher using block based scrambling and image filtering an image cipher using block based scrambling and image filtering ic bsif is introduced it is the first time that image filtering is used to do encryption ic bsif uses the well known substitution permutation network and strictly follows the principles of confusion and diffusion the block based scrambling is to fast separate neighboring pixels to different rows and columns and thus can sufficiently weaken the strong correlation between adjacent pixels ic bsif can encrypt different kinds of images into noise like ones and security evaluations demonstrate that it can achieve better performance than some state of the art encryption schemes the operation of image filtering is widely used to deblur digital images however using inappropriate masks it can also blur images motivated by this concept this paper introduces an image cipher using block based scrambling and image filtering ic bsif to the best of our knowledge this is the first time that image filtering has been used for image encryption ic bsif uses the well known substitution permutation network and strictly follows the concepts of confusion and diffusion the block based scrambling is able to separate neighboring pixels to different rows and columns and thus can efficiently weaken the strong correlations between adjacent pixels using randomly generated masks by the secret key the image filtering can spread little change of plain images to the entire pixels of cipher images simulation results show that ic bsif can encrypt different kinds of images into noise like ones and security evaluations demonstrate that it can achieve better performance than several state of the art encryption schemes

new error estimate in the iterative numerical method for nonlinear fuzzy hammerstein fredholm integral equations in this paper we obtain the error estimation of the iterative method based on quadrature formula to solve nonlinear fuzzy fredholm integral equations of the second kind given in fuzzy sets syst 245 2014 1 17 in terms of uniform and partial modulus of continuity moreover we extend in the context of using the modulus of continuity the notion of numerical stability of the solution with respect to the first iteration

strong convergence of the semi implicit euler method for nonlinear stochastic volterra integral equations with constant delay abstract this paper is mainly concerned with the strong convergence analysis of the semi implicit euler method for nonlinear stochastic volterra integral equations svies with constant delay the solvability and the boundedness of the numerical solution are established it is proved that the strong convergence order of the semi implicit euler method is 0 5 under lipschitz conditions moreover the strong superconvergence order is 1 0 if further the kernel of the stochastic term satisfies 0 0 the theoretical results are illustrated by extensive numerical examples

error estimation in the approximation of the solution of nonlinear fuzzy fredholm integral equations using a fixed point technique the sequence of successive approximations and a recent quadrature formula for fuzzy number valued functions it is constructed a numerical method for the solution of nonlinear fuzzy fredholm integral equations moreover the error estimate of the method and a criterion to stop the corresponding algorithm are given

a chaos based symmetric image encryption scheme using a bit level permutation in recent years a variety of chaos based digital image encryption algorithms have been suggested most of these algorithms implement permutations and diffusions at the pixel level by considering the pixel as the smallest atomic element of an image in fact a permutation at the bit level not only changes the position of the pixel but also alters its value here we propose an image cryptosystem employing the arnold cat map for bit level permutation and the logistic map for diffusion simulations have been carried out and analyzed in detail demonstrating the superior security and high efficiency of our cryptosystem

iterated collocation methods for volterra integral equations with delay arguments in this paper we give a complete analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for volterra integral equations with constant delay this analysis includes continuous collocation based volterra runge kutta methods as well as iterated collocation methods and their discretizations

discretized stability and error growth of the nonautonomous pantograph equation this paper is concerned with the stability properties of runge kutta methods for the pantograph equation a functional differential equation with a proportional delay the focus is on nonautonomous equations both linear and nonlinear cases are considered sufficient and necessary conditions for the asymptotic stability of the numerical solution of general neutral pantograph equations are given an upper bound for the error growth is investigated for algebraically stable methods applied to nonneutral equations finally some stability results are extended to the case of a more general class of equations

on the t method for delay differential equations with infinite lag abstract this paper discusses the method for the numerical solution of delay differential equations with infinite lag our analysis is based on the test equation y t ay t by t where a b c and 0 1 in order to solve the storage problem involved in studying the long time behaviour of the solution we use a grid with increased stepsizes monotonicity uniform boundedness asymptotic stability algebraic decay and global discretisation error of the numerical solution are investigated

numerical analysis of a high order method for nonlinear delay integral equations abstract in this paper we introduce a new class of multistep collocation method mcm for solving the non linear volterra functional integral equations vfies including two types of linear and non linear lag functions we divide the definition domain into several subintervals according to the primary discontinuous points associated with the delay function in each subinterval where the solution is smooth enough we can apply mcm to approximate the solution convergence analysis of the method for both types is also analyzed and illustrative five examples are provided to confirm the applicability of this method

2d sine logistic modulation map for image encryption because of the excellent properties of unpredictability ergodicity and sensitivity to their parameters and initial values chaotic maps are widely used in security applications in this paper we introduce a new two dimensional sine logistic modulation map 2d slmm which is derived from the logistic and sine maps compared with existing chaotic maps it has the wider chaotic range better ergodicity hyperchaotic property and relatively low implementation cost to investigate its applications we propose a chaotic magic transform cmt to efficiently change the image pixel positions combining 2d slmm with cmt we further introduce a new image encryption algorithm simulation results and security analysis demonstrate that the proposed algorithm is able to protect images with low time complexity and a high security level as well as to resist various attacks

analytic solutions to a class of nonlinear infinite delay differential equations abstract the infinite delay differential equations iddes are studied and the analytic solution of a class of nonlinear iddes is presented based on the characteristics of the reproducing kernel space w 2 0 besides the exact solution is represented in the form of series it is proved that the n term approximation u n x converges to the exact solution u x of the iddes moreover the approximate error of u n x is monotone decreasing the results of experiments showed that the proposed method in this paper is computationally efficient

recent advances in the numerical analysis of volterra functional differential equations with variable delays the numerical analysis of volterra functional integro differential equations with vanishing delays has to overcome a number of challenges that are not encountered when solving classical delay differential equations with non vanishing delays in this paper i shall describe recent results in the analysis of optimal global and local superconvergence orders in collocation methods for such evolutionary problems following a brief survey of results for equations containing volterra integral operators with non vanishing delays the discussion will focus on pantograph type volterra integro differential equations with linear and nonlinear vanishing delays the paper concludes with a section on open problems these include the asymptotic stability of collocation solutions u h on uniform meshes for pantograph type functional equations and the analysis of collocation methods for pantograph type functional equations with advanced arguments

r k formulae applied to volterra equations with delay abstract we consider convergence and stability of a class of runge kutta formulae applied to a class of volterra integral equations with fixed delay although derived from standard runge kutta tableau the formulae differ from those applied to classical volterra integral equations consideration of the formulae is prompted by the search for highly stable formulae which have acceptable orders of convergence the theory and numerical results presented establish the existence of acceptable runge kutta formulae

optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays in this paper we analyze the optimal convergence properties of collocation approximations to solutions of volterra integral equations of the second kind with vanishing variable delays the focus of the analysis is on the superconvergence of the iterated collocation approximation corresponding to collocation in the space of discontinuous piecewise polynomials of degree m 1 geq 0 we show that on uniform meshes the iterated collocation solution possesses the global superconvergence order m 1 and that the solution s order of local superconvergence at the nodes of the underlying mesh cannot exceed m 2 in sharp contrast to problems with nonvanishing delays moreover the optimal order p ast m 2 can be attained only under suitable assumptions this result also resolves a conjecture of 1997 regarding the attainable order of local superconvergence for volterra integral equations containing a proportional delay qt with q in 0 1

natural continuous extensions of runge kutta methods the present paper develops a theory of natural continuous extensions nces for the discrete approximate solution of an ode given by a runge kutta process these nces are defined in such a way that the continuous solutions furnished by the one step collocation methods are included

on the stability of runge kutta methods for delay integral equations we present a class of runge kutta methods for the numerical solution of a class of delay integral equations dies described by two different kernels and with a fixed delay the stability properties of these methods are investigated with respect to a test equation with linear kernels depending on complex parameters the results are then applied to collocation methods in particular we obtain that any collocation method for dies resulting from ana stable collocation method for odes with a stepsize which is submultiple of the delay preserves the asymptotic stability properties of the analytic solutions

a super attainable order in collocation methods for differential equations with proportional delay abstract we are concerned with the pantograph differential equation y t ay t by qt f t t 0 y 0 y 0 with proportional delay qt 0 q 1 in the literatures it is known that if we choose some proper m collocation points for m 2 then collocation leads to a superconvergence result of order p 2 m 1 at the first mesh point t h in this paper in such collocation solution to the above equation we show that there are cases for some 0 q 1 such that the attainable order at the first mesh point t h becomes a super attainable order just o h 2 m 2 numerical experiments of such 0 q 1 are also presented

2d sudoku associated bijections for image scrambling sudoku refers to a two dimensional 2d number placement puzzle with simple constraints that there are no repeated digits in each row each column or each block motivated by this sudoku configuration we introduce a number of sudoku associated matrix element representations besides the conventional representation using matrix row column pair specifically they are representations via sudoku matrix row digit pair digit row pair column digit pair digit column pair block digit pair and digit block pair this means we can secretly represent matrix elements via a sudoku matrix and furthermore develop new sudoku associated 2d parametric bijections to demonstrate the effectiveness and randomness of bijections we introduce a simple but effective sudoku associated image scrambler only using 2d sudoku associated bijections for image scrambling without bandwidth expansion simulations and comparisons demonstrate that the proposed method outperforms several state of the art methods

spline collocation methods for nonlinear volterra integral equations with unknown delay in this paper we introduce and study polynomial spline collocation methods for systems of volterra integral equations with unknown lower integral limit arising in mathematical economics their discretization leads to implicit runge kutta type methods the global convergence and local superconvergence properties of these methods are proved and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation

collocation and continuous implicit runge kutta methods for a class of delay volterra integral equations abstract in this paper we present an analysis of the global convergence properties of certain piecewise polynomial collocation methods for a class of volterra integral equations with constant delay this analysis also encompasses continuous implicit m stage volterra runge kutta methods based on collocation techniques

stability invariance of discrete and continuous multidimensional systems under some variable tranformations a variable transformation for stability tests of multidimensional discrete systems which was previously shown to retain a nonvanishing property of a multivariable polynomial on the distinguished boundary of the multidimensional unit ball is shown here to retain this property in the entire multidimensional unit ball also a new variable transformation is presented for stability tests of multidimensional continuous systems and is shown to retain the nonvanishing property on the finite part of the distinguished boundary of the right half hyperplane the multidimensional finite imaginary axis applying this new transformation some necessary conditions are derived for the nonvanishing of multivariable quadratic form polynomials on the finite multidimensional imaginary axis also explicit necessary and sufficient conditions are derived for this case where the dimensionality is two

h stability of linear θ method with general variable stepsize for system of pantograph equations with two delay terms this paper deals with h stability of the linear q method with a general variable stepsize for the system of pantograph equations with two delay terms a sufficient condition such that the system of pantograph equations is asymptotically stable is derived furthermore when the linear q method with a general variable stepsize is applied to this system it is shown that the linear q method is h stable if and only if 1 2 q 1

superconvergence in collocation methods for volterra integral equations with vanishing delays in this paper we investigate the optimal global and local convergence orders of the iterated collocation solutions for second kind volterra integral equations with vanishing delays on quasi geometric meshes it turns out that the classical global convergence results still hold under certain regularity conditions of the given functions in particular it is shown that the optimal local superconvergence order p 2 m can be attained if collocation is at the m gauss legendre points which contrasts with collocations both on uniform meshes and on geometric meshes numerical experiments are performed to confirm our theoretical results

stability analysis of theta methods for neutral functional differential equations this paper deals with the subject of numerical stability for the neutral functional differential equation y t ay t by qt cy pt qquad t 0 it is proved that numerical solutions generated by theta methods are convergent if c b if and only if theta geq 1 2 and that the one leg theta method is lambda stable if theta 1 we also find out that inappropriate stepsize causes spurious solution in the marginal case where rm re a 0 and a b

quantum cryptographic algorithm for color images using quantum fourier transform and double random phase encoding abstract a novel encryption decryption method for color images is proposed in which quantum fourier transform qft and double random phase encoding drpe techniques have been used the encryption process can be realized by performing two secret random phase encoding operations respectively in the input and the qft planes because all quantum operations are invertible the decryption process is the inverse of the encryption process supported by detailed numerical simulation and theoretical analysis the method has clarified its robustness security and computational complexity over its classical counterpart and it opens the door for introducing color image encryption into quantum scenarios

numerical stability of higher order derivative methods for the pantograph equation abstract dealing with numerical stability of higher order derivative methods with variable stepsize is the purpose of this paper for pantograph equations a new way to compute this kind of equation is provided and a sufficient condition for the numerical stability of high order derivative forms is given some numerical examples are presented to confirm our theoretical analysis

secure public key encryption scheme without random oracles since the first practical and secure public key encryption scheme without random oracles proposed by cramer and shoup in 1998 cramer shoup s scheme and its variants remained the only practical and secure public key encryption scheme without random oracles until 2004 in 2004 canetti et al proposed a generic transformation from a selective identity based encryption scheme to a public key encryption by adding a one time strongly signature scheme since then some transformation techniques from a selective identity based encryption scheme to a public key encryption have been proposed to enhance the computational efficiency for example boneh katz s construction and boyen mei waters scheme these transformations have either traded off the publicly verifiable properties or tightness of security reduction in 2007 zhang proposed another generic transformation by adding chameleon hash functions in this paper we introduce another technique from the boneh boyen s selective identity based encryption scheme to a public key encryption which is publicly verifiable and is slightly more efficient than zhang s transformation the proposed public key encryption scheme is based on the decisional bilinear diffie hellman assumption and the target collision resistant hash functions

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

numerical solutions of volterra integral equations with a solution dependent delay on demontre l existence et l unicite des solutions pour l equation ainsi qu une limitation a priori de la solution on definit une solution numerique et on demontre que la solution numerique converge vers la solution de l equation integrale

application of simpson quadrature rule and iterative method for solving nonlinear fuzzy delay integral equations abstract in this study firstly we present an iterative method by using simpson quadrature formula for solving nonlinear fuzzy delay integral equations in addition the convergence analysis of the proposed method is investigated also we prove numerical stability analysis of the method by means of choosing the perturbation in the first iteration finally numerical examples to illustrate applicability of this method are presented

iterated collocation methods and their discretizations for volterra integral equations it is known that the numerical solution of volterra integral equations of the second kind by polynomial spline collocation at the gauss legendre points does not lead to local superconvergence at the knots of the approximating function in the present paper we show that iterated collocation approximation restores optimal local superconvergence at the knots but does not yield global superconvergence on the entire interval of integration in contrast to fredholm integral equations with smooth kernels we also analyze the discretized versions obtained by suitable numerical quadrature of the collocation and iterated collocation methods

unconditionally stable compact theta schemes for solving the linear and semi linear fourth order diffusion equations abstract this paper is concerned with numerical methods for solving a class of fourth order diffusion equations combining the compact difference operator in space discretization and the linear method in time the compact theta scheme for the linear problem is first proposed by virtue of the fourier method the suggested scheme is shown to be unconditionally stable and convergent in the discrete l2 norm for any 1 2 1 and then this idea is generalized to the semi linear case the corresponding compact theta scheme is constructed and analyzed in detail numerical experiments corresponding to the linear and semi linear situations are carried out to support our theoretical statements

high order collocation methods for nonlinear delay integral equation abstract the classical collocation methods based on piecewise polynomials have been studied for delay volterra integral equations of the second kind in brunner 2004 these collocation methods have uniform order m for any choice of the collocation parameters and can achieve local superconvergence in the grid points by choosing the suitable collocation parameters in this paper with the aim of increasing the order of classical collocation methods we use a general class of multistep methods based on hermite collocation methods and prove that this numerical method has uniform order 2 m 2 r for r previous time steps and m collocation points some numerical examples are given to show the validity of the presented method and to confirm our theoretical results

circular inter intra pixels bit level permutation and chaos based image encryption the new image encryption architecture presented in this paper employs a novel circular inter intra pixels bit level permutation strategy this strategy aims to reduce redundancies implied by the fridrich s structure the newly proposed scheme was subject to extensive security analyses including statistical and differential analysis and information entropy calculation these highlight a desirable security level provided by the insurance of the coveted confusion and diffusion factors

image encryption to protect image contents most existing encryption algorithms are designed to transform an original image into a texture like or noise like image which is however an obvious visual sign indicating the presence of an encrypted image and thus results in a significantly large number of attacks to address this problem this paper proposes a new image encryption concept to transform an original image into a visually meaningful encrypted one as an example of the implementation of this concept we introduce an image encryption system simulation results and security analysis demonstrate excellent encryption performance of the proposed concept and system

stability of θ methods for delay integro differential equations stability of methods for delay integro differential equations dides is studied on the basis of the linear equation du dt u t u t k t t u d where k are complex numbers and is a constant delay it is shown that every a stable method possesses a similar stability property to p stability i e the method preserves the delay independent stability of the exact solution under the condition that k is real and h is an integer where h is a step size it is also shown that the method does not possess the same property if h is not an integer as a result no method can possess a similar stability property to gp stability with respect to dides

a generalization of rudin s multivariable stability theorem rudin s n variable stability theorem requires testing in addition to a multidimensional condition on the distinguished boundary a single one variable condition a generalization of rudin s theorem is presented in this paper in which the single variable condition is replaced with n single variable conditions where 1 leq n leq n at one s choice the tradeoff is between simpler and a smaller number of single variable conditions the special case n 1 reduces to the original rudin theorem other special cases reduce to some well known stability theorems either with 1 or with n single variable conditions an example is provided where choosing n neq 1 n is advantageous from the computational point of view

a convertible multi authenticated encryption scheme for group communications recently wu et al proposed a convertible multi authenticated encryption cmae scheme which allows a signing group with multiple signers to generate a multi authenticated ciphertext signature on the chosen message so that only a designated verifier can recover and verify the message in case of later dispute the verifier can convert the multi authenticated ciphertext signature into an ordinary one that can be verified by anyone in this study a cmae scheme for group communications is proposed this is presented by first reviewing the concepts of group oriented encryption schemes and the merits of wu et al s scheme this shows that not only can a multi authenticated ciphertext signature be generated by a signing group but also the message can be recovered and verified by a verifying group with multiple verifiers the security of the proposed scheme is based solely on the ddh problem which provides higher security confidence than using the cdh problem in wu et al s cmae scheme

numerical solutions of the nonlinear fuzzy hammerstein volterra delay integral equations in this paper an iterative numerical method that solves nonlinear fuzzy hammerstein volterra integral equations with constant delay is developed by using the error estimates a practical stopping criterion of the algorithm is obtained the convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples the study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology

personalized information encryption using ecg signals with chaotic functions the development of efficient data encryption to ensure high security of information transmission has long been a popular research subject because electrocardiogram ecg signals vary from person to person and can be used as a new tool for biometric recognition this study introduces an individual feature of ecg with chaotic henon and logistic maps for personalized cryptography this study also develops an encryption algorithm based on the chaos theory to generate initial keys for chaotic logistic and henon maps the proposed personalized encryption system uses a convenient handheld device to collect ecg signals from the user high quality randomness in ecg signals results in a widely expanded key space making it an ideal key generator for personalized data encryption the experiments reported in this study demonstrate the use of this approach in encrypting texts and images and applied of the proposed approach to secure communications

stability margin of two dimensional continuous systems the margin of stability of two dimensional 2 d continuous systems is considered in particular the definition of the stability margins for a 2 d discrete system is extended to a 2 d continuous one two methods to compute the stability margin of 2 d continuous systems are presented illustrative examples are provided

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

signcryption from randomness recoverable public key encryption we propose a new generic construction for signcryption and show that it is secure under the security models which are comparable to the security against adaptive chosen ciphertext attacks for public key encryption and the existential unforgeability against chosen message attacks for signature in particular the security models also capture the notion of insider security the generic construction relies on the existence of a special class of efficient public key encryption schemes which allow the encryption randomness to be recovered during decryption we also propose two efficient instantiations for the generic construction and show that one of them has less message expansion and yields smaller ciphertext when compared with all the existing signcryption schemes

simplifications in multidimensional stability margin computations previously published algorithms for the computation of multidimensional stability margins of discrete systems require a stability test of these systems before starting the computational algorithm in this correspondence it is shown that the multidimensional stability test may be replaced by single dimensional tests for one kind of stability margin and can be omitted completely for the second kind of stability margin

numerical solution of linear fredholm fuzzy integral equations of the second kind by adomian method using parametric form of fuzzy numbers we convert a linear fuzzy fredholm integral equation of the second kind to a linear system of integral equations of the second kind in crisp case we use adomian method and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy fredholm integral equation of the second kind we apply the method to some examples

a symmetric image encryption algorithm based on mixed linear nonlinear coupled map lattice abstract we propose a new image encryption algorithm based on the spatiotemporal chaos of the mixed linear nonlinear coupled map lattices this spatiotemporal chaotic system has more outstanding cryptography features in dynamics than the logistic map or the system of coupled map lattices does in the proposed image encryption we employ the strategy of bit level pixel permutation which enables the lower bit planes and higher bit planes of pixels permute mutually without any extra storage space simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed algorithm

zero sets of multiparameter functions and stability of multidimensional systems new theorems which can be used to find the zero set of a multiparameter rational function of a complex variable where the distinguished boundary of the parameters closed domain of definition is composed of piecewise smooth jordan arcs or curves are stated and proved the results are used to derive a new simplified procedure for a multi dimensional stability test presented for the continuous analog case as well as for the discrete digital case now proofs to huang s and strintzis theorems on multidimensional stability are also provided as an application of the theorems on zero sets

stability of runge kutta methods for the generalized pantograph equation this paper deals with stability properties of runge kutta rk methods applied to a non autonomous delay differential equation dde with a constant delay which is obtained from the so called generalized pantograph equation an autonomous dde with a variable delay by a change of the independent variable it is shown that in the case where the rk matrix is regular stability properties of the rk method for the dde are derived from those for a difference equation which are examined by similar techniques to those in the case of autonomous ddes with a constant delay as a result it is shown that some rk methods based on classical quadrature have a superior stability property with respect to the generalized pantograph equation stability of algebraically stable natural rk methods is also considered

the stability of modified runge kutta methods for the pantograph equation in the present paper the modified runge kutta method is constructed and it is proved that the modified runge kutta method preserves the order of accuracy of the original one the necessary and sufficient conditions under which the modified runge kutta methods with the variable mesh are asymptotically stable are given as a result the 0 methods with 1 2 1 the odd stage gauss legendre methods and the even stage lobatto iiia and iiib methods are asymptotically stable some experiments are given

on the numerical stability of volterra integral equations with delay argument abstract stability properties of numerical methods for volterra integral equations with delay arguments are considered some suitable definitions for the stability of the numerical methods are included and also plots of the stability regions for particular cases are included

stability of one leg θ methods for nonlinear neutral differential equations with proportional delay the stability properties of one leg q methods for nonlinear neutral differential equations with proportional delay is investigated in recent years the stability of one leg q methods for this class of equations on a quasi geometric mesh is investigated instead in the present paper the focus is on stability of one leg q methods for the neutral differential equations with constant delay obtained by applying the approach of transformation to the proportional delay equations some sufficient conditions for global stability and asymptotic stability are established two numerical examples are also included

positive solutions of nonlinear integral equations arising in infectious diseases on considere l equation integrale non lineaire x t t t f s x s ds on utilise la theorie d indice du point fixe et la technique monotone pour etablir trois theoremes sur les solutions le premier affirme l existence de deux solutions non negatives non triviales de periode les deux autres concernent l existence et l unicite des solutions positives non triviales sous certaines conditions

h stability of runge kutta methods with general variable stepsize for pantograph equation this paper deals with h stability of runge kutta methods with variable stepsize for pantograph equations it is shown that the runge kutta methods with a regular matrix a are h stable if and only if the modulus of stability function at infinity is less than 1 furthermore the same conclusion can be obtained if the runge kutta methods are stiffly accurate

on neutral functional differential equations with proportional delays abstract in this paper we develop a comprehensive theory on the well posedness of the initial value problem for the neutral functional differential equation y t ay t i 1 b i y q i t i 1 c i y p i t t 0 y 0 y 0 and the asymptotic behaviour of its solutions we prove that the existence and uniqueness of solutions depend mainly on the coefficientsci i 1 2 and on the smoothness of functions in the solution space as far as the asymptotic behaviour of analytic solutions is concerned thecihave little effect we prove that if re a 0 then the solutiony t either grows exponentially or is polynomial the most interesting result is that if re a 0 anda 0 then the asymptotic behaviour of the solution depends mainly on the characteristic equation a i 1 b i q i 0 these results can be generalized to systems of equations finally we present some examples to illustrate the change of asymptotic behaviour in response to the variation of some parameters the main idea used in this paper is to express the solution in either dirichlet or dirichlet taylor series form

compression unimpaired batch image encryption combining vector quantization and index compression as the network bandwidth has grown rapidly it has become common to share a large number of still images via the internet by means of batch transmission unfortunately most existing methods encrypt only a single image so there is room for improvement in our ability to send batches of images at one time a complete reconstruction of the methods is sometimes necessary especially when considering performance criteria this paper presents a novel batch image encryption algorithm that combines vector quantization vq and additional index compression process to benefit from their computational efficiency and low transmission bandwidth without affecting the original compression rate the experimental results show the performance of this new scheme in terms of compression rate and computational cost

stability of the radau ia and lobatto iiic methods for neutral delay differential system abstract numerical stability is considered for several runge kutta methods to systems of neutral delay differential equations the linear stability analysis is adopted to the system adapted with the equistage interpolation process as well as the continuous extension the runge kutta methods are shown to have the numerical stability similar to the analytical asymptotic stability with arbitrary stepsize when certain assumptions hold for the logarithmic matrix norm on the coefficient matrices of the ndde system

stability of a class of runge kutta methods for a family of pantograph equations of neutral type this paper deals with the stability of runge kutta methods for a class of neutral infinite delay differential equations with different proportional delays under suitable conditions the asymptotic stability of some runge kutta methods with variable stepsize are considered by the stability function at infinity it is proved that the even stage gauss legendre methods are not asymptotically stable but the radau ia methods radau iia methods and lobatto iiic methods are all asymptotically stable furthermore some numerical experiments are given to demonstrate the main conclusions