an application for a modified kdv equation by the decomposition method and finite element method a numerical solution to a modified korteweg de vries mkdv equation is obtained using a lumped galerkin method with quadratic b spline finite element method fem and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm classical problems concerning the development motion and interaction of solitons are used to validate the methods the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

a new approach for the application of adomian decomposition method for the solution of fractional space diffusion equation with insulated ends abstract this paper presents the new approach for the solution of the space fractional diffusion equation defined in finite domain by adomian decomposition method adm a typical example of special interest with fractional space derivative of order 1 2 is considered in the present analysis and solved by adm after expressing the initial condition as fourier series the explicit solution of the space fractional diffusion equation has been presented in the closed form and then the numerical solution has been represented graphically the behaviour of adomian solutions and the effects of different values of are shown graphically

on experimental results and explicit exact solutions for the generalized boussinesq type equation we implemented a decomposition method for approximating the solution of the generalized boussinesq type equation by using this scheme the explicit exact solution is calculated in the form of a convergent power series with easily computable components to illustrate the application of this method numerical results are derived by using the calculated components of the decomposition series the obtained results are found to be in good agreement with the exact solution

a model for the growth of a population exhibiting stage structure cannibalism and cooperation abstract a model of a stage structured population with fixed maturity time for the immature stage and interaction terms that may be interpreted as cooperation or cannibalism is proposed the existence and stability of the equilibrium set are discussed in the case of cannibalism it is shown by a numerical example how a hopf bifurcation could result in a stable periodic solution

new explicit exact solutions for the generalized coupled hirota satsuma kdv system in this paper we study the generalized coupled hirota satsuma kdv system by using the two new improved projective riccati equations method as a result many explicit exact solutions which contain new solitary wave solutions periodic wave solutions and combined formal solitary wave solutions and combined formal periodic wave solutions are obtained

stability criteria for a system involving two time delays a system of two autonomous ordinary differential equations with two discrete time delays is considered with a view to determining the stability of equilibria using the nyquist criterion on the characteristic equation estimates on the length of delays are given for which a system which is stable in the absence of delays remains stable conditions are also derived for there to be no change in stability even for unbounded delays the above mentioned criteria are applied to a system modeling competitive interacting populations and to a predator prey system

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

some new integrable nonlinear evolution equations and darboux transformation two classes of new nonlinear evolution equations are derived with the aid of a 4 4 matrix spectral problem with three potentials a darboux transformation for the first nontrivial nonlinear evolution equation is given based on the gauge transformation between the corresponding 4 4 matrix spectral problems as an application of the darboux transformation some explicit solutions of the nontrivially nonlinear evolution equation are obtained

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

solitary wave solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this letter based on the idea of adomian s decomposition method and with help of mathematica we obtain the exact solutions for compound kdv type and compound kdv burgers type equations with nonlinear terms of any order in this paper by considering the decomposition scheme we first obtain the exact solutions of these two equation for the initial conditions without using any classical transformations and then their numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions their remarkable accuracy is finally demonstrated in the study of some values p 1 of the compound kdv type and compound kdv burgers type equations

comparison of the solutions obtained by b spline fem and adm of kdv equation a numerical solution to a generalized korteweg de vries kdv equation is obtained using the galerkin method with quadratic b spline finite element method fem over which the nonlinear term is locally linearized and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

stability of a competition model with two stage structure a population model with stage structure which describes the competition of two species for space is considered the model is established under the assumptions that reproductive rates of two species are affected by competition and that the space occupied by one type of juveniles cannot be neglected estimates on the length of delays for which positive equilibrium of the model remains stable are given sufficient conditions are also derived that ensure global stability of positive equilibrium

multiple resolution segmentation of textured images a multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior in addition an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions both algorithms use a causal gaussian autoregressive model to describe the mean variance and spatial correlation of the image textures together the algorithms can be used to perform unsupervised texture segmentation the multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified this method results in accurate segmentations and requires significantly less computation than some previously known methods the field containing the classification of each pixel in the image is modeled as a markov random field segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint at each resolution the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks the unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the aic information criterion clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters concurrently the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached

stability and bifurcations of equilibria in a multiple delayed differential equation the influence of multiple negative delayed feedback loops on the stability of a single action mechanism are considered a characteristic equation for the linearized stability of the equilibrium is completely analyzed as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops the bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold in particular the nature of hopf and more degenerate higher codimension bifurcations are explicitly determined

solitary wave solutions for a generalized hirota satsuma coupled kdv equation the solitary wave solutions of a generalized hirota satsuma coupled kdv equation are obtained exactly by using the decomposition method the solutions were calculated in the form of a convergent power series with easily computable components a variety of initial value system is considered the convergence of the method as applied to the coupled kdv equation is illustrated numerically the present algorithm performs extremely well in terms of accuracy and simplicity

a analytic and numerical solution to a modified kawahara equation and a convergence analysis of the method abstract in this paper we present an adomian s decomposition method shortly adm for numerical approximation traveling wave solutions of the modified kawahara equation the numerical solutions are compared with the known analytical solutions we also prove the convergence of adomian decomposition method adm applied to the modified kawahara equation

text extraction and document image segmentation using matched wavelets and mrf model in this paper we have proposed a novel scheme for the extraction of textual areas of an image using globally matched wavelet filters a clustering based technique has been devised for estimating globally matched wavelet filters using a collection of groundtruth images we have extended our text extraction scheme for the segmentation of document images into text background and picture components which include graphics and continuous tone images multiple two class fisher classifiers have been used for this purpose we also exploit contextual information by using a markov random field formulation based pixel labeling scheme for refinement of the segmentation results experimental results have established effectiveness of our approach

a numerical solution of the coupled sine gordon equation using the modified decomposition method the modified decomposition method has been implemented for solving a coupled sine gordon equation we consider a system of coupled sine gordon equation which models one dimensional nonlinear wave processes in two component media by using an initial value system the numerical solutions of coupled sine gordon equation have been represented graphically

new exact jacobi elliptic functions solutions for the generalized coupled hirota satsuma kdv system abstract in this paper an generalized jacobi elliptic functions expansion method with computerized symbolic computation is used for constructing more new exact jacobi elliptic functions solutions of the generalized coupled hirota satsuma kdv system as a result eight families of new doubly periodic solutions are obtained by using this method some of these solutions are degenerated to solitary wave solutions and triangular functions solutions in the limit cases when the modulus of the jacobi elliptic functions m 1 or 0 which shows that the applied method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

stability of stage structured population models in order to model populations which go through distinct stages such as laboratory insect populations it is necessary to take the age structure of the population into account the oscillations which have frequently been observed in the sizes of such populations cannot be explained by a model which ignores the effects of age structure while it is feasible to use a fully age structured model of mckendrickkvon foerster type 3 or an analogous size structured model 4 it is generally impossible to derive qualitative information about the behavior of solutions of such models accordingly models have been proposed which subdivide the lifetime of an individual into two stages larvae and adults with different dynamics in each stage such models may be formulated as systems of differentialdifference equations and several different types of systems of differentialdifference equations to model different types of larval competition have been proposed in s our purpose is to analyze the stability properties of the various models proposed in s using the standard method of determining equilibria linearizing about an equilibrium and locating the roots of the corresponding characteristic equation by an equilibrium of a system of differential difference equations we mean simply a constant solution thus equilibria are found by setting the right side of each equation equal to zero assuming that each equation of the system has been solved for the derivatives of the unknown functions in cases where every constant is a solution of one of the equations in a system it is necessary to replace that equation by an integrated form which incorporates the initial data in order to solve for equilibria the linearization of a system about an equilibrium is obtained by using the deviations of the unknown functions from equilibrium as new variables expanding by taylor s theorem and retaining only the linear terms the

a decomposition method for finding solitary and periodic solutions for a coupled higher dimensional burgers equations in this paper we consider coupled higher dimensional burgers chdbur equations we find periodic solutions to chdbur equations using a modified adomian s decomposition method madm we find both exact and numerical solutions we compared the numerical solutions with corresponding analytical solutions we also show the effectiveness of the method

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation we find the explicit and numerical traveling wave solutions for a coupled kdv equation and a coupled mkdv equation by using the decomposition method with help of symbolic computation by using this method the solutions were calculated in the form of a convergent power series with easily computable components the convergence of the method as applied to the coupled kdv and mkdv equations is illustrated numerically

a new method for a generalized hirota satsuma coupled kdv equation abstract in this paper differential transform method dtm which is one of the approximate methods is implemented for solving the nonlinear hirota satsuma coupled kdv partial differential equation a variety of initial value system is considered and the convergence of the method as applied to the hirota satsuma coupled kdv equation is illustrated numerically the obtained results are presented and only few terms of the expansion are required to obtain the approximate solution which is found to be accurate and efficient numerical examples are illustrated the pertinent features of the proposed algorithm

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

lie group method for solving generalized hirota satsuma coupled korteweg de vries kdv equations method of lie group has been applied to study hirota satsuma coupled korteweg de vries kdv system of partial differential equations lie group method is applied to determine symmetry reductions of the nonlinear partial differential equations the resulting nonlinear ordinary differential equations are solved analytically and the obtained solutions are presented graphically

an application of the decompositionmethod for the two dimensional kdv burgers equation a relatively new decomposition method is presented to find the explicit and numerical solutions of the two dimensional korteweg de vries burgers equation tdkdvb for short for the initial conditions some numerical results are also given for this equation by using the decomposition method

on the numerical solution of the system of two dimensional burgers equations by the decomposition method adomian s decomposition method adm is proposed to approximate the numerical and analytical solutions of system two dimensional burgers equations stdbe with initial conditions the advantages of this work are the decomposition method reduces the computational work and improvement with regard to its accuracy and rapid convergence some examples are given to illustrate the performance of the method described

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

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

a numerical solution and an exact explicit solution of the nls equation we consider traveling wave solutions of the nonlinear schrodinger nls for short equation in this paper by considering the decomposition scheme we first obtain the exact solutions of the nls equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some initial values of the nls equation

exact and numerical traveling wave solutions of whitham broer kaup equations in this paper we find the explicit and numerical traveling wave solutions of whitham broer kaup for short wbk equations which contain blow up solutions and periodic solutions by using the decomposition method by using this method the solutions were calculated in the form of a convergent power series with easily computable components the convergence of the method as applied to the whitham broer kaup equations is illustrated numerically

text segmentation for mrc document compression the mixed raster content mrc standard itu t t 44 specifies a framework for document compression which can dramatically improve the compression quality tradeoff as compared to traditional lossy image compression algorithms the key to mrc compression is the separation of the document into foreground and background layers represented as a binary mask therefore the resulting quality and compression ratio of a mrc document encoder is highly dependent upon the segmentation algorithm used to compute the binary mask in this paper we propose a novel multiscale segmentation scheme for mrc document encoding based upon the sequential application of two algorithms the first algorithm cost optimized segmentation cos is a blockwise segmentation algorithm formulated in a global cost optimization framework the second algorithm connected component classification ccc refines the initial segmentation by classifying feature vectors of connected components using an markov random field mrf model the combined cos ccc segmentation algorithms are then incorporated into a multiscale framework in order to improve the segmentation accuracy of text with varying size in comparisons to state of the art commercial mrc products and selected segmentation algorithms in the literature we show that the new algorithm achieves greater accuracy of text detection but with a lower false detection rate of nontext features we also demonstrate that the proposed segmentation algorithm can improve the quality of decoded documents while simultaneously lowering the bit rate