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

analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi ld m controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of nonlinear dynamic system containing fractional derivative ji zeng wang et al coiflets based method in the solution of nonlinear dynamic system containing fractional derivative in the fourth international conference on nonlinear mechanics icnm iv shanghai august 2002 pp 1304 1308 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with the exact solution a good agreement of the results is observed

bayesian single and double variable sampling plans for the weibull distribution with censoring the sampling inspection problem is one of the main research topics in quality control in this paper we employ bayesian decision theory to study single and double variable sampling plans for the weibull distribution with type ii censoring a general loss function which includes the sampling cost the time consuming cost the salvage value and the after sales cost is proposed to determine the bayes risk and the corresponding optimal sampling plan explicit expressions for the bayes risks for both single and double sampling plans are derived respectively numerical examples are given to illustrate the effectiveness of the proposed method comparisons between single and double sampling plans are made and sensitivity analysis is performed

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

variational iteration method and homotopy perturbation method for nonlinear evolution equations he s variational iteration and homotopy perturbation methods are applied to various evolution equations to assess the accuracy of the solutions we compare the results with the exact solutions revealing that both methods are capable of solving effectively a large number of nonlinear differential equations with high accuracy

variables sampling inspection scheme for resubmitted lots based on the process capability index cpk abstract this paper attempts to develop a sampling inspection scheme by variables based on process performance index for product acceptance determination which examines the situation where resampling is permitted on lots not accepted on original inspection the equations for plan parameters the required sample size and the corresponding critical value are derived based on the exact sampling distribution rather than an approximation approach hence the decisions made are more accurate and reliable moreover the efficiency of the proposed variables resubmitted sampling plan is evaluated and compared with the existing variables single sampling plan for illustrative purpose an example is presented to demonstrate the use of the derived results for making a decision on product acceptance determination

solitary wave solutions with non monotone shapes for the modified kawahara equation abstract the propagation of stationary solitary waves of the non linear modified kawahara equation is considered the asymptotic boundary conditions admit the trivial solution along with the solitary wave type solution which is a bifurcation problem the bifurcation is treated by reformulating the problem into a problem for identification of an unknown coefficient from over posed boundary data in which the trivial solution is excluded making use of the method of variational imbedding the inverse problem for the coefficient identification is reformulated as a higher order boundary value problem this approach to solving the fifth order modified kawahara equation is allowing identification of non trivial solutions the obtained boundary value problem is solved by means of an iterative difference scheme which is thoroughly validated new traveling wave solutions with monotone and non monotone shapes are obtained for different values of the problem parameters

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

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

a note on decision making method for product acceptance based on process capability indices cpk and cpmk abstract in this short note we prove that the derivation of the required sample size and critical acceptance value under the normality assumption of the quality characteristic proposed by wu c w aslam m jun c h 2012 variables sampling inspection scheme for resubmitted lots based on the process capability index c pk european journal of operational research 217 3 560 566 is inappropriate in fact it leads to a lower probability of acceptance than the one desired by the producer the same issue also occurs in the case of a variables single sampling plan described in a previous paper by pearn w l wu c w 2007 an effective decision making method for product acceptance omega 35 1 12 21 nevertheless a similar yet less severe inaccuracy is also noticed in wu c w pearn w l 2008 a variables sampling plan based on c pmk for product acceptance determination european journal of operational research 184 2 549 560

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

a linearly implicit conservative difference scheme for the generalized rosenau kawahara rlw equation this paper concerns the numerical study for the generalized rosenau kawahara rlw equation obtained by coupling the generalized rosenau rlw equation and the generalized rosenau kawahara equation we first derive the energy conservation law of the equation and then develop a three level linearly implicit difference scheme for solving the equation we prove that the proposed scheme is energy conserved unconditionally stable and second order accurate both in time and space variables finally numerical experiments are carried out to confirm the energy conservation the convergence rates of the scheme and effectiveness for long time simulation

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

polarized variation of hodge structures of calabi yau type and characteristic subvarieties over bounded symmetric domains in this paper we extend the construction of the canonical polarized variation of hodge structures over tube domain considered by gross math res lett 1 1 9 1994 to bounded symmetric domain and introduce a series of invariants of infinitesimal variation of hodge structures which we call characteristic subvarieties we prove that the characteristic subvariety of the canonical polarized variations of hodge structures over irreducible bounded symmetric domains are identified with the characteristic bundles defined by mok ann math 125 1 105 152 1987 we verified the generating property of gross for all irreducible bounded symmetric domains which was predicted in gross math res lett 1 1 9 1994

numerical comparison of methods for solving parabolic equations in this paper we apply a new decomposition scheme to solve the linear heat equation the approach is based on the choice of a suitable differential operator which may be ordinary or partial linear or nonlinear deterministic or stochastic it does not require discretization and consequently of massive computation in this scheme the solution is performed in the form of a convergent power series with easily computable components this paper is particularly concerned with the adomian decomposition method and the results obtained are compared to those obtained by a conventional finite difference method and the sinc method the numerical results demonstrate that the new method is relatively accurate and easily implemented

weakly non local solutions for capillary gravity waves fifth degree korteweg de vries equation hunter and scheurle have shown that capillary gravity water waves in the vicinity of bond number bo l 3 are consistently modelled by the korteweg de vries equation with the addition of a fifth derivative term this wave equation does not have strict soliton solutions for bo l 3 because the near solitons have oscillatory wings that extend indefinitely from the core of the wave however these solutions are arbitrarily small perturbations of solitary waves because the amplitude of the wings is exponentially small in the amplitude 6 of the core pomeau ramani and grammaticos have calculated the amplitude of the wings by applying matched asymptotics in the complex plane in the limit e 0 in this article we describe a mixed chebyshev radiation function pseudospectral method which is able to calculate the weakly non local solitons for all e we show that for fixed phase speed the solitons form a three parameter family because the linearized wave equation has three eigensolutions we also show that one may repeat the soliton with even spacing to create a three parameter of periodic solutions which we also compute because the amplitude of the wings is exponentially small these non local capillary gravity solitons are as interesting as the classical localized solitons that solve the korteweg de vries equation

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

exact and numerical soliton solutions of some nonlinear physical models we consider two types of variant water wave equations and the solitary wave solutions of them are constructed by using the adomian decomposition we also made a numerical comparison of the equations

analytical solution of a fractional diffusion equation by adomian decomposition method this paper presents an analytical solution of a fractional diffusion equation by adomian decomposition method by using an initial value the explicit solution of the equation has been presented in the closed form and then its numerical solution has been represented graphically the present method performs extremely well in terms of efficiency and simplicity

an explicit and numerical solutions of some fifth order kdv equation by decomposition method in this paper by considering the adomian decomposition method explicit and numerical solutions are calculated for a various fifth order korteweg de vries equations with initial condition the method does not need linearization or weak nonlinearity assumptions perturbation theory the decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self canceling noise terms where sum of components vanishes in the limit

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

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

design of progressively censored group sampling plans for weibull distributions an optimization problem optimization algorithms provides efficient solutions to many statistical problems essentially the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints usually related to the quality levels required by the producer and the consumer an optimal acceptance sampling plan is developed in this paper for the weibull distribution with unknown scale parameter the proposed plan combines grouping of items sudden death testing in each group and progressive group removals and its decision criterion is based on the uniformly most powerful life test a mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant the optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost excellent approximately optimal solutions are also provided in closed forms the sampling plan is considerably flexible and allows to save experimental time and cost in general our methodology achieves solutions that are quite robust to small variations in the weibull shape parameter a numerical example about a manufacturing process of gyroscopes is included for illustration

polarized mixed hodge structures and the local monodromy of a variation of hodge structure a variation of polarized hodge structures on the complement of a divisor with normal crossings gives rise locally on the divisor to a commuting set ni of nilpotent endomorphisms of the vector space underlying the variation the logarithms of the unipotent parts of the various picard lefschetz transformations these reflect properties of the singularities of the period map associated to the variation cf 5 7 9 and sect 3 for example a variation depending on a single parameter defines asymptotically a mixed hodge structure whose weight filtration is the monodromy weight filtration of the corresponding endomorphism n 9 11 this paper is mainly concerned with the properties of the set n arising in the several parameters case in particular theorem 3 3 asserts that all the elements in the open polyhedral cone c spanned over r by the n s determine the same monodromy weight filtration it also describes the relationship between this common filtration and those associated to the faces of the cone this statement was conjectured by deligne based on his analogous result 4 1 9 2 for the q cone associated to those variations which arise from families of polarized non singular algebraic varieties in w 1 we discuss some general properties of commuting sets of nilpotent endomorphisms and their associated filtrations section2 focuses on the case when each element in such set defines in the sense of 2 4 a polarized mixed hodge structure with a fixed hodge filtration f as is the case for the monodromy cone c of a variation these conditions imply cf 2 16 a generic uniqueness for the monodromy weight filtration we also consider those pola

analytical solution of the bagley torvik equation by adomian decomposition method abstract the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi d controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of bagley torvik equation r l bagley p j torvik on the appearance of the fractional derivative in the behavior of real materials asme j appl mech 51 1984 294 298 i podlubny fractional differential equations academic press san diego ca usa 1999 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with those available in the work of podlubny i podlubny fractional differential equations academic press san diego ca usa 1999 a good agreement of the results is observed

an explicit formula for the inverse of a pentadiagonal toeplitz matrix in this paper we mainly consider finding an explicit formula for the inverse of a pentadiagonal toeplitz matrix for that purpose we first factorize the modified form of a pentadiagonal toeplitz matrix by two tridiagonal toeplitz matrices and then use the sherman morrison woodbury inversion formula as a result an explicit inverse of a pentadiagonal toeplitz matrix is obtained under certain assumptions and numerical experiments are given to show the effectiveness of our results

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

sequential variable sampling plan for normal distribution abstract in this paper a sequential variable sampling plan is studied suppose that the quality of an item in a batch is measured by a normally distributed random variable with a known variance but the mean is unknown with a normal prior distribution then by using bayesian approach and considering a markov decision process the optimality equations for the minimum total expected cost are formulated we show that an optimal decision rule will have a control limit structure an algorithm for a sequence of optimal decisions is introduced then the statistical procedure for conducting the sequential sampling plan is presented

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

motives with exceptional galois groups and the inverse galois problem we construct motivic l adic representations of textup gal overline mathbb q mathbb q into exceptional groups of type e 7 e 8 and g 2 whose image is zariski dense this answers a question of serre the construction is uniform for these groups and is inspired by the langlands correspondence for function fields as an application we solve new cases of the inverse galois problem the finite simple groups e 8 mathbb f ell are galois groups over mathbb q for large enough primes l

series solution to the pochhammer chreeequation and comparison with exact solutions in this study a decomposition method for approximating the solution of the pochhammer chreeequation is implemented by using this scheme 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 solutions known for some special cases

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

application of modified decomposition method for the analytical solution of space fractional diffusion equation abstract spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow finance and others areas of application this paper presents the analytical solutions of the space fractional diffusion equations by modified decomposition method mdm by using initial conditions the explicit solutions of the equations have been presented in the closed form the decomposition series analytic solution of the problem is quickly obtained by observing the existence of the self cancelling noise phenomenon two examples the first one is one dimensional and the second one is two dimensional fractional diffusion equation are presented to show the application of the present technique the present method performs extremely well in terms of efficiency and simplicity

multi symplectic preissmann scheme for a high order wave equation of kdv type the high order wave equation of kdv type which describes many important physical phenomena has been investigated widely in last several decades here the new multi symplectic formulations for the high order wave equation of kdv type are presented and the associated local conservation laws are shown the multi symplectic discretization of each formulation is exemplified by the multi symplectic preissmann scheme the numerical experiments are given and the results verify the efficiency of the multi symplectic preissmann scheme

economic lot sampling inspection from defect counts with minimum conditional value at risk abstract expected cost functions are often minimized to determine optimal inspection schemes for lot acceptance purposes however minimum mean cost sampling plans usually have high probabilities of suffering great losses a risk management perspective based on minimizing the conditional value at risk cvar is proposed in order to avoid unacceptably large costs in essence the cvar associated with an inspection scheme is the expected cost of a given proportion of the most costly cases optimal defects per unit acceptance sampling plans with controlled producer and consumer risks for screening lots of incoming materials and outgoing products are determined by minimizing the cvar for a given risk aversion degree the decision criterion is based on the uniformly most powerful test the poisson distribution is used to model the number of nonconformities per sampled unit and the natural prior uncertainty on the defect rate is described by a truncated gamma distribution a computational algorithm is suggested to solve the underlying integer nonlinear programming problem practitioners can assume a restricted range for the defect rate and prior knowledge on may be updated using past performance of the inspection plan the developed methodology is applied to the manufacturing of paper for illustrative purposes

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

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

minimizing the area of a pareto confidence region abstract a constrained optimization problem is formulated and solved in order to determine the smallest confidence region for the parameters of the pareto distribution in a proposed family of sets the objective function is the area of the region whereas the constraints are related to the required confidence level explicit expressions for the area and confidence level of a given region are first deduced an efficient procedure based on minimizing the corresponding lagrangian function is then presented to solve the nonlinear programming problem the process is valid when some of the smallest and largest observations have been discarded or censored i e both single right or left and double censoring are allowed the optimal pareto confidence region is derived by simultaneously solving three four nonlinear equations in the right double censoring case in most practical situations newton s method with the balanced set as the starting point only needs a few iterations to find the global solution in general the reduction in area of the optimal pareto region with respect to the balanced set is considerable if the sample size n is small or moderately large which is usual in practice this reduction is sometimes impressive when n is quite small and the censoring degree is fairly high two numerical examples regarding component lifetimes and fire claims are included for illustrative and comparative purposes

existence of perturbed solitary wave solutions to a model equation for water waves abstract we prove the existence of travelling wave solutions to a fifth order partial differential equation which is a formal asymptotic approximation for water waves with surface tension these travelling waves are arbitrarily small perturbations of solitary waves but are not solitary waves themselves because they approach small amplitude oscillations for large values of the independent variable this result suggests that for bond numbers less than one third there are branches of travelling wave solutions to the water wave equations which are perturbations of supercritical elevation solitary waves and which bifurcate from froude number one and bond number one third

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

optimum attributes component test plans for k out of n f weibull systems using prior information abstract assuming that the proportion defective in a production process p is variable and the component lifetimes are weibull distributed integer nonlinear programming problems are formulated and solved in order to determine the optimum component inspection scheme by attributes for k out of n f system reliability demonstration using available prior knowledge a limited beta prior model is adopted to reflect the random fluctuations on p the required quantity of components to test and the permissible number of component failures up to a specified censoring time are found by solving a minimisation problem with nonlinear constraints which are related to the tolerable average producer and consumer risks first order taylor polynomials of the operating characteristic function are used to derive a quite accurate approximate solution lower and upper bounds are also deduced optimal solutions are usually robust to small variations in the weibull parameters and prior information existing technical knowledge and experience are shown to be of great practical value in designing optimal sampling plans for lot acceptance purposes the proposed approach generalises the classical viewpoint to those cases in which appreciable prior information on the fraction of defective systems exists and also allows the analyst to determine the acceptability of a k out of n f system before assembly and to limit the range of p moreover the practitioners may attain substantial savings in sample size and improved assessments of the true producer and consumer risks a 4 out of 5 f system of independent water pumps for cooling a reactor is considered to illustrate the suggested component test plans

necessary conditions for the appearance of noise terms in decomposition solutions series in this paper the phenomena of the noise terms that appear in the components of the series solution introduced by adomian and rach 1 will be examined extensively the phenomena is useful in demonstrating a fast convergence of the exact solution however the condition set by adomian and rach 1 in that these noise terms appear for every nonhomogeneous equation is not always true and the nonhomogeneity condition is not sufficient another necessary condition will be established in this study to ensure the appearance of noise terms in specific cases several differential and integral equations will be tested to confirm the newly developed condition

a systematic look at the gamma process capability indices abstract process capability indices pcis are widely used to measure whether an in control process conforms to manufacturing specifications the normal distribution is assumed in most traditional applications of pcis nevertheless it is not uncommon that some quality characteristics have skewed distributions in such cases the gamma distribution is an appropriate model and percentile based pcis for the gamma process have been studied in the literature in practical applications of pcis it is important to select an appropriate distribution between the normal and the gamma distributions based on historical data in this study we first construct a hypothesis test for model discrimination between the normal and the gamma distributions asymptotic distribution of the test statistic under the gamma process is derived we then consider statistical inference for the percentile based pcis under the gamma process the maximum likelihood method is used for point estimation and the method of generalized pivotal quantities is used for interval estimation we demonstrate the proposed methods by a practical example

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

variations of hodge structure and orbits in flag varieties abstract period domains the classifying spaces for pure polarized hodge structures and more generally mumford tate domains arise as open g r orbits in flag varieties g p we investigate hodge theoretic aspects of the geometry and representation theory associated with these flag varieties in particular we relate the griffiths yukawa coupling to the variety of lines on g p under a minimal homogeneous embedding construct a large class of polarized g r orbits in g p and compute the associated hodge theoretic boundary components an emphasis is placed throughout on adjoint flag varieties and the corresponding families of hodge structures of levels two and four

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

new exact solutions of space and time fractional modified kawahara equation abstract one of the important nonlinear evolution equations in mathematical physics is the modified kawahara equation in this work by utilizing an analytic method based on the jacobi elliptic functions a group of exact solutions of the fractional modified kawahara equation had been found the method can be applied to all of the time space and space time fractional equations four problems had also been given to demonstrate the application of the method and some solutions had been illustrated by the graphics

energy decay for the modified kawahara equation posed in a bounded domain abstract studied here is the eventual dissipation of solutions to initial boundary value problems for the modified kawahara equation with and without a localized damping term included it is shown that solutions of undamped problems posed on a bounded interval may not decay if the length of the interval is critical in contrast the energy associated to the locally damped problems is shown to be exponentially decreased independently of the interval length

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

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 numerical implementation of the decomposition method for the lienard equation in this study a kind of explicit exact and numerical solutions to the lienard equation is obtained and the applications of the results to this equation has been compared with their known theoretical solution this paper is particularly concerned with the adomian decomposition method and the numerical results demonstrate that the new method is relatively accurate and easily implemented