entropy and data compression schemes some new ways of defining the entropy of a process by observing a single typical output sequence as well as a new kind of shannon mcmillan breiman theorem are presented this provides a new and conceptually very simple ways of estimating the entropy of an ergodic stationary source as well as new insight into the workings of such well known data compression schemes as the lempel ziv algorithm

he s variational iteration method for treating nonlinear singular boundary value problems this paper applies he s variational iteration method for solving nonlinear singular boundary value problems the solution process is illustrated and various physically relevant results are obtained comparison of the obtained results with exact solutions shows that the method used is an effective and highly promising method for treating various classes of both linear and nonlinear singular boundary value problems

numerical method for non linear wave and diffusion equations by the variational iteration method this paper applies he s variational iteration to the wave equations in an infinite one dimensional medium and some non linear diffusion equations a suitable choice of an initial solution can lead to the needed exact solution by a few iterations copyright 2007 john wiley sons ltd

variational iteration method for the time fractional fornberg whitham equation this paper presents the approximate analytical solutions to solve the nonlinear fornberg whitham equation with fractional time derivative by using initial values explicit solutions of the equations are solved by using a reliable algorithm like the variational iteration method the fractional derivatives are taken in the caputo sense the present method performs extremely well in terms of efficiency and simplicity numerical results for different particular cases of a are presented graphically

solution of a system of nonlinear equations by adomian decomposition method in this paper the adomian decomposition method is applied to solve a system of nonlinear equations convergence of the method is proved and some examples are presented to illustrate the method

adomian decomposition a tool for solving a system of fractional differential equations abstract adomian decomposition method has been employed to obtain solutions of a system of fractional differential equations convergence of the method has been discussed with some illustrative examples in particular for the initial value problem d 1 y 1 d n y n t a y 1 y n t y i 0 c i i 1 n where a a i j is a real square matrix the solution turns out to be y x e 1 n 1 x 1 a 1 x n a n y 0 where e 1 n 1 denotes multivariate mittag leffler function defined for matrix arguments and a i is the matrix having ith row as a i 1 a i n and all other entries are zero fractional oscillation and bagley torvik equations are solved as illustrative examples

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

new iterative technique for solving nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the nonlinear equations in this paper a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique the convergence of the proposed methods is proved it is shown that the new family contains several well known iterative methods as special case for the implementation and performance of the new methods a nonlinear equation arising in the population model and another one arising in the motion of a particle on inclined plane is solved

resolving view sensitivity with surface locality if a three dimensional 3d object is defined under a coordinate system that depends on viewing direction its representation changes when the view changes it is regarded as view sensitivity in object recognition as an approach of solving the problem this paper introduces an object modeling method that provides view insensitive 3d representation surface locality is investiated to define localized surfaces so that 3d objects can be described independently of viewing directions with their boundary surfaces and topological relations the stability of this method is analysed and tested with range images

revised adomian decomposition method for solving a system of nonlinear equations a modification of adomian decomposition method is suggested and used for solving a system of nonlinear equations which yields a series solution with accelerated convergence illustrative examples have been presented to demonstrate the method and the results obtained are compared with those derived from the standard adomian decomposition method

new iterative method application to partial differential equations abstract in the present article we implement the new iterative method nim proposed by daftardar gejji and jafari v daftardar gejji h jafari an iterative method for solving non linear functional equations j math anal appl 316 2006 753 763 to solve linear nonlinear partial differential equations of integer and fractional order the results obtained are compared with those obtained by other iterative methods such as adomian decomposition homotopy perturbation and variational iteration methods

solution of a system of volterra integral equations of the first kind by adomian method in this article we consider linear and non linear systems of integral equations of the first kind the problem of existence and uniqueness are considered the adomian decomposition method is being used to solve these linear and non linear systems of volterra integral equations of the first kind some examples are prepared to show the efficiency and simplicity of the method

new approach for the fornbergwhitham type equations this paper applies the reproducing kernel hilbert space method to the solutions of three types of fornbergwhitham equations original modified and time fractional comparison with adomian decomposition method homotopy analysis method and the variational iteration method shows the validity and applicability of the technique

numerical method for solving fractional coupled burgers equations in this paper we use the fractional variational iteration method fvim to solve a time and space fractional coupled burgers equations some numerical examples are presented to show the efficiency of considered method a comparison of the proposed method is made with the exact solution adomain decomposition method adm generalized differential transformation method gdtm and homotopy perturbation method hpm

solution of the system of ordinary differential equations by adomian decomposition method in this article we use adomian decomposition method which is a well known method for solving functional equations now a days to solve systems of differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one theoretical considerations are being discussed and convergence of the method for theses systems is addressed some examples are presented to show the ability of the method for linear and non linear systems of differential equations

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

high accuracy power series solutions with arbitrarily large radius of convergence for the fractional nonlinear schrodinger type equations fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories nonlinearity and fractional derivatives these effective descriptions thus appear commonly in physical and mathematical modeling we present a new series method providing systematic controlled accuracy for solutions of fractional nonlinear differential equations including the fractional nonlinear schrodinger equation and the fractional nonlinear diffusion equation the method relies on spatially iterative use of power series expansions our approach permits an arbitrarily large radius of convergence and thus solves the typical divergence problem endemic to power series approaches in the specific case of the fractional nonlinear schrodinger equation we find fractional generalizations of cnoidal waves of jacobi elliptic functions as well as a fractional bright soliton for the fractional nonlinear diffusion equation we find the combination of fractional and nonlinear effects results in a more strongly localized solution which nevertheless still exhibits power law tails albeit at a much lower density

solving the breaking soliton equation by he s variational method he s variational method is applied to obtain the soliton solutions of the breaking soliton equation where the semi inverse method is applied to establish a needed variational functional

classification of travelling waves in the fornberg whitham equation abstract in this paper the fornberg whitham fw equation is investigated by using the improved qualitative method which combines characteristics of several methods to solve equations we classify all travelling wave solutions of this equation in specified regions of the parametric space besides already known solutions such as peaked and kink like wave solutions this equation also admits looped and cusped wave solutions especially some composite waves including fractal like waves and stumpons what is more interesting is that we give the limit behavior of all periodic solutions as the parameters trend to some special values

an iterative method with quartic convergence for solving nonlinear equations in this study a new two step and three step iterative methods are derived for solving nonlinear equations it is shown that the three step iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

a new predictor corrector method for fractional differential equations we present a new predictor corrector method to solve non linear fractional differential equations involving caputo derivative the proposed method is compared with the fractional adams method numerous illustrative examples discussed here demonstrate that the new method is more accurate and time efficient a detailed error analysis given points to the higher accuracy of the new method furthermore the proposed method when applied to fractional analog of chaotic system introduced by bhalekar and daftardar gejji unravels the underlying rich dynamics of the system

a new family of predictor corrector methods for solving fractional differential equations abstract in the present paper we propose a new family of six predictor corrector methods to solve non linear fractional differential equations fdes of the form d y t f t y t 0 1 where d denotes the th order caputo derivative and perform the stability and error analysis further we extend these methods for solving systems of fdes the proposed methods have higher order accuracy and their execution time is drastically reduced as compared to existing methods such as fractional adams method fam and new predictor corrector method npcm they require only 10 of the time taken by fam and 20 of the npcm further these methods converge for very small values of when fam and npcm fail we illustrate the applicability of the proposed methods by solving a variety of examples and some chaotic systems

extreme value laws in dynamical systems for non smooth observations we prove the equivalence between the existence of a non trivial hitting time statistics law and extreme value laws in the case of dynamical systems with measures which are not absolutely continuous with respect to lebesgue this is a counterpart to the result of the authors in the absolutely continuous case moreover we prove an equivalent result for returns to dynamically defined cylinders this allows us to show that we have extreme value laws for various dynamical systems with equilibrium states with good mixing properties in order to achieve these goals we tailor our observables to the form of the measure at hand

correlation decay and recurrence asymptotics for some robust nonuniformly hyperbolic maps we study a robust class of multidimensional non uniformly hyperbolic transformations considered by oliveira and viana ergod theory dyn syst 28 501 533 2008 for an open class of holder continuous potentials with small variation we show that the unique equilibrium state has exponential decay of correlations and that the distribution of hitting times is asymptotically exponential furthermore using that the equilibrium states satisfy a weak gibbs property we also prove log normal fluctuations of the return times around their average

numerical treatment of stochastic models used in statistical systems and financial markets in this paper by means of the variational iteration method numerical solutions are computed for some stochastic models without any linearization or weak assumptions two stochastic models the fokker planck equation for non equilibrium statistical systems and the black scholes model for pricing stock options are solved numerically in this approach the solution is found in the form of a convergent series with easily computed components the behavior of the approximate solutions is shown graphically

travelling wave solutions of the fornberg whitham equation zhou and tian j b zhou l x tian a type of bounded travelling wave solutions for the fornberg whitham equation j math anal appl 346 2008 255 261 successfully found a type of bounded travelling wave solutions of the fornberg whitham equation in this paper we improve the previous result by using the phase portrait analytical technology moreover some smooth periodic wave smooth solitary wave periodic cusp wave and loop soliton solutions are given and the numerical simulation is made the results show that our theoretical analysis agrees with the numerical simulation

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

toward a new analytical method for solving nonlinear fractional differential equations abstract the variational iteration method is widely used in approximate calculation the main difficulty of the method is to identify the lagrange multiplier for differential equations of fractional order especially of high order where the procedure is complex and merely approximate it is shown in this paper that the application of the variational iteration method to nonlinear fractional differential equations leads to inaccurate approximations to completely overcome the demerit we propose a new analytical method requiring no lagrange multiplier to solve nonlinear fractional differential equations where the solution procedure becomes easier more effective and straightforward the validity and reliability of this method is tested by its application in various nonlinear fractional differential equations and the obtained results reveal that the proposed method is more accurate and efficient

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

an efficient method for solving systems of fractional integro differential equations in this study a decomposition method for approximating the solution of systems of fractional integro differential equations is implemented the fractional derivative is considered in the caputo sense the approximate solutions are calculated in the form of a convergent series with easily computable components numerical results show that this approach is easy to implement and accurate when applied to integro differential equations

explicit peakon and solitary wave solutions for the modified fornberg whitham equation in this paper the modified fornberg whitham equation is studied by using the bifurcation theory and the method of phase portraits analysis in some parametric conditions some peakons and solitary waves are found and their exact parametric representations in explicit form are obtained

an abstraction based approach to 3 d pose determination from range images an abstraction based paradigm that makes explicit the process of imposing assumptions on data is discussed the units of abstraction are models in which levels of abstraction are determined by the degree of assumption necessary for their application a general to specific refinement process provides a mechanism to proceed gracefully through the abstraction hierarchy this strategy was applied to the recognition and pose determination of objects comprising simple and compound cylindrical and planar surfaces in dense range data a method of computing reliable gaussian and mean curvature sign map descriptors from the polynomial approximations of surfaces is demonstrated a means for determining the pose of constructed geometric forms whose algebraic surface descriptions are nonlinear in terms of their orienting parameters is developed it is shown that biquadratic surfaces are suitable companion linear forms for cylinder approximation and parameter estimation the estimates provide the initial parametric approximations necessary for a nonlinear regression stage to fine tune the estimates by fitting the actual nonlinear form to the data

solving systems of fractional differential equations using differential transform method this paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method the fractional derivatives are described in the caputo sense the application of differential transform method developed for differential equations of integer order is extended to derive approximate analytical solutions of systems of fractional differential equations the solutions of our model equations are calculated in the form of convergent series with easily computable components some examples are solved as illustrations using symbolic computation the numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations the method introduces a promising tool for solving many linear and nonlinear fractional differential equations

some numerical methods for solving nonlinear equations by using decomposition technique in this paper we use the system of coupled equations involving an auxiliary function together with decomposition technique to suggest and analyze some new classes of iterative methods for solving nonlinear equations these new methods include the halley method and its variant forms as special cases various numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

a new iterative technique for a fractional model of nonlinear zakharov kuznetsov equations via sumudu transform abstract the main objective of this paper is to suggest a new computational technique namely new iterative sumudu transform method nistm to solve numerically nonlinear time fractional zakharov kuznetsov fzk equation in two dimensions we implemented the proposed technique on two test examples plotted the solution and compared the absolute error with the variational iterative technique vim and homotopy perturbation transform method hptm

three step iterative methods for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

efficient method for solving a system of nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations by using decomposition technique in conjunction with the coupled system of equations we develop new iterative method for solving a system of nonlinear equations which has better efficiency index we prove the fifth order convergence of the proposed method we provide the comparison of efficiency index with some other well known methods for the implementation and performance of the new method we solve the kinematic synthesis problem for steering chandrasekhar integral equation and combustion problem for a temperature of 3000 c and compare the results with some existing methods

differentiability of thermodynamical quantities in non uniformly expanding dynamics abstract in this paper we study the ergodic theory of a robust non uniformly expanding maps where no markov assumption is required we prove that the topological pressure is differentiable as a function of the dynamics and analytic with respect to the potential moreover we not only prove the continuity of the equilibrium states and their metric entropy as well as the differentiability of the maximal entropy measure and extremal lyapunov exponents with respect to the dynamics we also prove a local large deviations principle and central limit theorem and show that the rate function mean and variance vary continuously with respect to observables potentials and dynamics finally we show that the correlation function associated to the maximal entropy measure is differentiable with respect to the dynamics and it is c 1 convergent to zero in addition precise formulas for the derivatives of thermodynamical quantities are given

an analytical approach to the fornberg whitham type equations by using the variational iteration method in this paper he s variational iteration method vim is applied to solve the fornberg whitham type equations the vim provides fast converged approximate solutions to nonlinear equations without linearization discretization perturbation or the adomian polynomials this makes the method attractive and reliable for solving the fornberg whitham type equations numerical examples related to two initial value problems are presented to show the efficiency of the vim

iterative methods with fourth order convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 m aslam noor new iterative schemes for nonlinear equations appl math comput in press and noor and noor m aslam noor k inayat noor some iterative schemes for nonlinear equations appl math comput in press we show that this new iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

the homotopy analysis method for solving the fornberg whitham equation and comparison with adomian s decomposition method in this work an analytical technique namely the homotopy analysis method ham is applied to obtain an approximate analytical solution of the fornberg whitham equation a comparison is made between the ham results and the adomian s decomposition method adm and the homotopy perturbation method hpm the results reveal that ham is very simple and effective the ham contains the auxiliary parameter h which provides us with a simple way to adjust and control the convergence region of solution series

the distribution of the first return time for rational maps we obtain exponential error estimates for the approximation of the zeroth return time to the poisson distribution for rational maps which might have critical points within the julia set

a new finite difference predictor corrector method for fractional differential equations abstract we present a new finite difference predictor corrector method l1 pcm to solve nonlinear fractional differential equations fdes along with its error and stability analysis the method is further extended for systems of fdes the proposed method is applied to fractional version of chaotic system introduced by bhalekar and daftardar gejji to explore its rich dynamics the proposed method is accurate time efficient and performs well even for very small values of the order of the derivatives

polyhedral object recognition using hough space features abstract we propose a new technique for three dimensional 3 d polyhedral object recognition on the basis of a single two dimensional 2 d view of a 3 d scene the binary gradient image of the captured scene is converted into the hough space domain the cluster patterns originating from straight line features of the image are explored by reasoning in hough space this yields an attributed graph representation of the object to be recognized which is compared to similar representations of cad designed wire frame model objects by means of a new attributed subgraph isomorphism algorithm simulation experiments illustrate this promising new approach

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

new recurrence algorithms for the nonclassic adomian polynomials in this article we present new algorithms for the nonclassic adomian polynomials which are valuable for solving a wide range of nonlinear functional equations by the adomian decomposition method and introduce their symbolic implementation in mathematica beginning with rach s new definition of the adomian polynomials we derive the explicit expression for each class of the adomian polynomials e g a email protected k 1 mf k u 0 z m k for the class ii iii and iv adomian polynomials where the z m k are called the reduced polynomials these expressions provide a basis for developing improved algorithmic approaches by introducing the index vectors the recurrence algorithms for the reduced polynomials are suitably deduced which naturally lead to new recurrence algorithms for the class ii and class iii adomian polynomials mathematica programs generating these classes of adomian polynomials are subsequently presented computation shows that for computer generation of the class iii adomian polynomials the new algorithm reduces the running times compared with the definitional formula we also consider the number of summands of these classes of adomian polynomials and obtain the corresponding formulas finally we demonstrate the versatility of the four classes of adomian polynomials with several examples which include the nonlinearity of the form f t u explicitly depending on the argument t

he s fractional derivative a powerful tool to fractional fornberg whitham equation abstract in this paper fractional fornberg whitham equation is studied in a fractal process based on he s fractional derivative the fractional complex transform is used to convert the studied fractional equation into an ordinary differential equation and gejji jafari iteration method is used to solve the equation

higher order iterative schemes for nonlinear equations using decomposition technique in this paper we suggest and analyze some unique recurrence relations which can generate different classes of iterative methods for solving nonlinear equations using the system of coupled equations together with decomposition technique by using an auxiliary function various numerical examples are given to illustrate the efficiency and performance of the newly suggested methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

a numerical investigation of time fractional modified fornberg whitham equation for analyzing the behavior of water waves in this paper a new wavelet method based on the hermite wavelet expansion together with operational matrices of fractional integration and derivative of wavelet functions is proposed to solve time fractional modified fornberg whitham mfw equation the approximate solutions of time fractional modified fornberg whitham equation which are obtained by hermite wavelet method are compared with the exact solutions as well as the solutions obtained by optimal homotopy asymptotic method oham the present numerical scheme is quite simple effective and expedient for obtaining numerical solution of fractional modified fornberg whitham equation

variational iteration method for twelfth order boundary value problems in this paper he s variational iteration method is applied to solve twelfth order boundary value problems the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the variational iteration method is of high accuracy more convenient and efficient for solving high order boundary value problems

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

picard iteration algorithm combined with gauss seidel technique for initial value problems abstract in this paper we introduce and implement a relatively new improvement for the well known picard s method for studying linear and nonlinear systems of ordinary differential equations in this method the solution takes the form of a rapidly convergent series with easily computable components a mathematica computer algebra system mathematica 5 1 is used to introduce a code which generates the series different illustrative examples have been considered as well as different comparison criterion between the proposed method and modern reliable and conventional methods the deeply mathematical roots of the method fixed point theorem and the correspondence with the theory of algebraic systems makes it is very interesting theoretical considerations are being discussed and convergence of the method is addressed other extensions and applications for further work are mentioned

new iterative technique for solving a system of nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations in this paper a new family of iterative methods for solving a system of nonlinear equations is developed by using a new decomposition technique the convergence of the new methods is proved efficiency index of the proposed methods is discussed and compared with some other well known methods the upper bounds of the error and the radius of convergence of the methods are also found for the implementation and performance of the new methods the combustion problem streering problem and van der pol equation are solved and the results are compared with some existing methods several new iterative methods are derived from the general iterative scheme using the ideas and techniques of this paper one may be able to suggest and investigate a wide class of iterative methods for solving the system of nonlinear equations this is another direction of future research

an iterative method with cubic convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of this new method new method can be viewed as an improvement of the previously known iterative methods

statistics of close visits to the indifferent fixed point of an interval map we study a dynamical system defined by a map of the interval 0 1 which has 0 as an indifferent fixed point but is otherwise expanding we prove that the sequence of successive entrance times in a small neighborhood 0 a converges in law when suitably normalized to a homogeneous poisson point process

chaos in fractional order financial delay system abstract chaotic dynamics of the fractional order financial system involving time delay is studied the numerical simulations are done using the new predictor corrector method proposed by daftardar gejji et al and by modified fractional adams method fam the results obtained using new predictor corrector method are matching with fam it is observed that the new predictor corrector method is more time efficient than the fam

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

an iterative method for solving nonlinear functional equations an iterative method for solving nonlinear functional equations viz nonlinear volterra integral equations algebraic equations and systems of ordinary differential equation nonlinear algebraic equations and fractional differential equations has been discussed

variational iteration method for nonlinear age structured population models this paper investigates nonlinear age structured population models the numerical solutions are obtained by using the variational iteration method and are of high accuracy two numerical examples are presented to illustrate the strength of the method

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

the modified decomposition method for solving nonlinear algebraic equations in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of nonlinear algebraic equations the conditions of the convergence which depend on the coefficients of the equation are found the truncation error of the method is obtained special cases of the nonlinear algebraic equation are solved using the modified algorithm the presented work shows that the modified approach gives improvements over existing techniques

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

solving a system of nonlinear fractional differential equations using adomian decomposition adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations dxiyi x ni x y1 yn yi k 0 cki 0 k i 1 i n and dxi denotes caputo fractional derivative some examples are solved as illustrations using symbolic computation

an analytical approach to the dynamic analysis of a rotating electric machine this study presents an analytical approach to the dynamic problem encountered by a rotating electric machine supported by nonlinear bearings with damping properties subjected to a forcing excitation caused by an unbalanced force and a parametric excitation caused by an axial thrust the method employed in this analytical study is the optimal variational iteration method ovim which proves to be very effective and accurate in solving nonlinear problems the results are presented in the form of a time displacement response the results obtained from numerical simulations are in very good agreement with the approximate analytical results obtained through the proposed method

statistics of return times a general framework and new applications in this paper we provide general estimates for the errors between the distribution of the first and more generally the k th return time suitably rescaled and the poisson law for measurable dynamical systems in the case that the system exhibits strong mixing properties these bounds are explicitly expressed in terms of the speed of mixing using these approximations the poisson law is finally proved to hold for a large class of non hyperbolic systems on the interval

a new approach for solving a system of fractional partial differential equations in this paper we propose a new method for solving systems of linear and nonlinear fractional partial differential equations this method is a combination of the laplace transform method and the iterative method and here after called the iterative laplace transform method this method gives solutions without any discretization and restrictive assumptions the method is free from round off errors and as a result the numerical computations are reduced the fractional derivative is described in the caputo sense finally numerical examples are presented to illustrate the preciseness and effectiveness of the new technique

new ideas for decomposing nonlinearities in differential equations abstract in this paper we consider the decomposition for the nonlinearity in a differential equation for the solution by decomposition by analyzing and transforming the taylor expansion of the nonlinearity about the initial solution component the decomposition of the nonlinearity is converted to the partitions of the solution sets for a class of diophantine equations this conversion simplifies the discussion and presents a new idea for decompositions we enumerate five types of partitions and their corresponding decomposition polynomials each of the last four types contains infinitely many kinds of decomposition polynomials in the form of finite sums in types 2 3 and 4 there is a parameter q and each value of q corresponds to a class of decomposition polynomials in type 5 each positive integer sequence c j satisfying 1 c 1 c 2 and j c j for j 2 3 corresponds to a class of decomposition polynomials four classes of the adomian polynomials r rach a new definition of the adomian polynomials kybernetes 37 2008 910 955 are derived as particular cases

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

a note on three step iterative method for nonlinear equations abstract noor and noor m a noor k i noor three step iterative methods for nonlinear equations appl math comput 183 2006 322 327 proposed a three step iterative method for solving nonlinear equations and they showed that the method has third order convergence in this paper we propose a new three step iterative method for solving nonlinear equations which is a significant improvement of the method proposed by noor and noor it is shown that this iterative method has fourth order convergence not third order convergence some numerical experiments are given to illustrate the performance of the three step iterative method

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation

a type of bounded traveling wave solutions for the fornberg whitham equation abstract in this paper by using bifurcation method we successfully find the fornberg whitham equation u t u x x t u x u u x x x u u x 3 u x u x x has a type of traveling wave solutions called kink like wave solutions and antikink like wave solutions they are defined on some semifinal bounded domains and possess properties of kink waves and anti kink waves their implicit expressions are obtained for some concrete data the graphs of the implicit functions are displayed and the numerical simulation is made the results show that our theoretical analysis agrees with the numerical simulation

a reliable algorithm for obtaining positive solutions for nonlinear boundary value problems abstract in this paper we propose an algorithm for solving the nonlinear two point boundary value problem that has at least one positive solution 1 6 for in a compatible interval our method stems mainly from combining the decomposition series solution obtained by adomian decomposition method with pade approximates the validity of the approach is verified through illustrative numerical examples