the three dimensional flow past a stretching sheet and the homotopy perturbation method an approximate analytical solution is obtained of the steady laminar three dimensional flow for an incompressible viscous fluid past a stretching sheet using the homotopy perturbation method hpm proposed by he the flow is governed by a boundary value problem bvp consisting of a pair of non linear differential equations the solution is simple yet highly accurate and compares favorably with the exact solutions obtained early in the literature the methodology presented in the paper is useful for solving the bvps consisting of more than one differential equation

the effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking stretching sheet the effects of variable viscosity and thermal conductivity on the flow and heat transfer in a laminar liquid film on a horizontal shrinking stretching sheet are analyzed the similarity transformation reduces the time independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations the resulting five parameter problem is solved by the homotopy perturbation method the results are presented graphically to interpret various physical parameters appearing in the problem

a convex log concave correlation inequality for gaussian measure and an application to abstract wiener spaces this paper deals with a generalization of a result due to brascamp and lieb which states that in the space of probabilities with log concave density with respect to a gaussian measure on open image in new window this gaussian measure is the one which has strongest moments we show that this theorem remains true if we replace x by a general convex function then we deduce a correlation inequality for convex functions quite better than the one already known finally we prove results concerning stochastic analysis on abstract wiener spaces through the notion of approximate limit

an elementary introduction to the homotopy perturbation method this paper is an elementary introduction to the concepts of the homotopy perturbation method particular attention is paid to giving an intuitive grasp for the solution procedure throughout the paper

onsager machlup functionals for non trace class spde s an onsager machlup functional limit is derived for a class of spde s whose principal part is not trace class both nondegenerate and degenerate limits are obtained and are illustrated by examples the proof uses fkg type inequalities

onsager machlup functional for the fractional brownian motion let x be the solution of the stochastic differential equation where b h is a fractional brownian motion with hurst parameter h in this paper we compute the onsager machlup functional of x for the supremum norm and holder norms of order with in the case and for holder norms of order with when

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

extended homotopy perturbation method and computation of flow past a stretching sheet we introduce an extended version of the homotopy perturbation method hpm for computing the steady flow of an incompressible viscous fluid past a radially stretching sheet in this version the independent variable is stretched by scaling it by a parameter that incorporates the homotopy parameter p the coefficients in the parameter are determined by requiring that the solutions obtained at each stage are free of secular terms it is shown that the totally analytical solution developed by applying the extended version leads to a convergent sequence of homotopy solutions the convergence of which can be accelerated by applying shanks transformation

the homotopy perturbation method and analytical solution of the problem of flow past a rotating disk analytical solutions have been obtained for the problem of steady laminar flow of a viscous incompressible fluid past a rotating disk using the homotopy perturbation method hpm the single parameter hpm is attempted first since it does not give adequately accurate results the extended hpm is invoked next in which the independent variable is scaled and the scale factor is expanded in a power series in p the homotopy parameter the coefficients in this power series are calculated by ensuring that the resulting solution is free of secular terms it is shown that the extended hpm solution converges to the true solution and that just eight terms in the perturbation expansion are sufficient to produce a highly accurate yet fully analytical solution

the analysis of categorical data from complex sample surveys chi squared tests for goodness of fit and independence in two way tables abstract the effect of stratification and clustering on the asymptotic distributions of standard pearson chi squared test statistics for goodness of fit simple hypothesis and independence in a two way contingency table denoted as x 2 and xi 2 respectively is investigated it is shown that both x 2 and xi 2 are asymptotically distributed as weighted sums of independent 1 2 random variables the weights are then related to the familiar design effects deffs used by survey samplers a simple correction to x 2 which requires only the knowledge of variance estimates or deffs for individual cells in the goodness of fit problem is proposed and empirical results on the performance of corrected x 2 provided empirical work on xi 2 indicated that the distortion of nominal significance level is substantially smaller with xi 2 than with x 2 some results under simple models for clustering are also given

reply to the comment on the three dimensional flow past a stretching sheet and the homotopy perturbation method by p d ariel computers and mathematics with applications 54 2007 920 925 by el mistikawy

an evaluation of model dependent and probability sampling inferences in sample surveys abstract in this paper we are concerned with inferences from a sample survey to a finite population we contrast inferences that are dependent on an assumed model with inferences based on the randomization induced by the sample selection plan randomization consistency for finite population estimators is defined and adopted as a requirement of probability sampling a numerical example is examined to illustrate the dangers in the use of model dependent estimators even when the model is apparently consonant with the sample data the paper concludes with a summary of principles that we believe should guide the practitioner of sample surveys of finite populations

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

onsager machlup functional for some smooth norms on wiener space in this paper we determine onsager machlup functionals for a variety of norms on wiener space which includes among others holder norms for every 0 1 2 as well as besov or sobolev type norms we basically require the knowledge of the small ball probabilities for the wiener measure and use versions of the norms which are rotationaly invariant on the range of the brownian paths a property of crucial importance in our approach

the onsager machlup functional for a class of anticipating processes consider the solution xt 0 t 1 of the equation x t x 0 w t mathop smallint limits 0 t b x s d s wherew wt 0 t 1 is ad dimensional wiener process b is a lipschitz function from d into d andx0 is ad dimensional functional of the wiener process

a simple perturbation approach to blasius equation in this paper we couple the iteration method with the perturbation method to solve the well known blasius equation the obtained approximate analytic solutions are valid for the whole solution domain comparison with howarth s numerical solution reveals that the proposed method is of high accuracy the first iteration step leads to 6 8 accuracy and the second iteration step yields the 0 73 accuracy of initial slop

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

soret and dufour effects on three dimensional oldroyd b fluid abstract in this article a realistic three dimensional magnetohydrodynamic flow of an oldroyd b fluid is studied after developing a convergent analytic scheme soret and dufour effects with mixed convection are taken into account the governing highly non linear partial differential equations are transformed into the system of ordinary differential equations using similarity transformations the resulting problems are computed by homotopy analysis method ham profiles of dimensionless velocities temperature and concentration are plotted and discussed for various emerging physical parameters numerical values of physical quantities of interest such as local nusselt number and local sherwood number are tabulated a comparative study with existing literature are found in an excellent agreement

estimation in survey sampling robustness and optimality abstract it is shown how the criteria of efficiency and robustness can be integrated fruitfully in a single optimality criterion within the framework of the unified theory godambe 1955 this is achieved by extending the scope of the usual model based estimation using appropriate sampling designs some situations of common occurrence in survey practice are discussed with a numerical study

comment on the three dimensional flow past a stretching sheet and the homotopy perturbation method by p d ariel computers and mathematics with applications 54 2007 920 925 in his application of the homotopy perturbation hp method to the problem of the three dimensional flow past a stretching sheet p d ariel the three dimensional flow past a stretching sheet and the homotopy perturbation method comput math appl 54 2007 920 925 encountered secular terms in the second order approximation which he could not avoid it is shown here that these secular terms can be removed by coordinate straining moreover the form of an hp solution which is free from secular terms at all levels of approximation and which can be determined recursively is indicated

on computation of the three dimensional flow past a stretching sheet abstract a non iterative numerical scheme is presented which computes the steady three dimensional flow of a viscous incompressible fluid past a stretching sheet in a single integration it also eliminates the possible error caused by taking the value of numerical infinity representing the unbounded domain of the flow as a finite number the solutions are developed in terms of a parameter k in the interval 0 1 from which the appropriate flow parameters can be readily obtained the scheme makes implicit use of infinite series of exponentials for velocity components along the sheet the issue of convergence of these series is also discussed

traces of random variables on wiener space and the onsager machlup functional abstract let f be a square integrable random variable on the classical wiener space and let us denote by f n the symmetric kernels appearing in its chaos expansion we give sufficient conditions for the unambiguous definition of f at the points of the cameron martin space we also give conditions for the existence of approximate limits in the sense of denjoy these results are first proved for multiple integrals i n f n before they are extended to the general random variables f the conditions are given in terms of the l p norms of the kernels f n the last section of the paper is devoted to an original application of our estimates to the proof of the existence of the onsager machlup functional for a nonanticipative stochastic differential equation of a special type

various topologies in the wiener space and levy s stochastic area in this paper we observe how levy s stochastic area looks when we see it through various topologies in the wiener space our theorem implies that it is quite natural from the viewpoint of topology to define a distinct skeleton of levy s stochastic areas w for each distinct topology in the wiener space or equivalently for each distinct abstract wiener space on which the wiener measure ands w are realized thus we cannot determine its intrinsic skeleton in the theory of abstract wiener spaces

remarks on the homotopy perturbation method for the peristaltic flow of jeffrey fluid with nano particles in an asymmetric channel in applied science the exact solution when available for any physical model is of great importance such exact solution not only leads to the correct physical interpretation but also very useful in validating the approximate analytical or numerical methods however the exact solution is not always available for the reason that many authors resort to the approximate solutions by using any of the analytical or the numerical methods to ensure the accuracy of these approximate solutions the convergence issue should be addressed otherwise such approximate solutions inevitably lead to incorrect interpretations for the considered model recently several peristaltic flow problems have been solved via the homotopy perturbation method which is an approximate analytical method one of these problems is selected in this paper to show that the solutions obtained by the homotopy perturbation method were inaccurate especially when compared with the exact solutions provided currently and also when compared with a well known accurate numerical method the comparisons reveal that great remarkable differences have been detected between the exact current results and those approximately obtained in the literatures for the temperature distribution and the nano particle concentration hence many similar problems that have been approximately solved by using the homotopy perturbation method should be re investigated by taking the convergence issue into consideration otherwise the published results were really incorrect

on the mortensen equation for maximum likelihood state estimation the main purpose of the paper is to formulate the maximum likelihood state estimation problem correctly for a continuous time nonlinear stochastic dynamical system by using the onsager machlup functional a modified likelihood is introduced the basic equation for the maximum likelihood state estimate is derived with the aid of a dynamic programming approach the numerical procedure for realizing the recursive filtering is also proposed with some numerical results

computational approach on three dimensional flow of couple stress fluid with convective boundary conditions abstract this investigation is concerned with the heat transfer analysis in a realistic three dimensional flow of a couple stress fluid convective boundary conditions have been adopted in the mathematical formulation keeping in view the physical consequences and detail examination of corresponding parameters the boundary layer analysis has been invoked for simplification of the highly nonlinear system of differential equations afterward the governing system of partial differential equations are transformed into coupled nonlinear ordinary differential equations by appropriate set of transformations the resulting system of differential equations are eventually solved for the series solutions employing ham technique effects of various embedding parameters on the flow and heat transfer are discussed it was found that couple stress parameter results in decay of velocity profile while the heat transfer rate increases by increasing biot number detailed comparison of the results are provided with already published data for limited cases the new findings are in excellent agreement with the existing literature finally the local nusselt number and other physical quantities are analyzed for various pertinent parameters

on the onsager machlup functional of diffusion processes around non c2 curves abstract the onsager machlup function namely the fictitious density of diffusions paths in function space is considered where the density is evaluated around non c2 curves thus extending earlier results the extension holds also for the case of diffusions evolving on a manifold

some exact equivalents for the brownian motion in holder norm some exact equivalents of small probabilities are given for the wiener measure on spaces of holder paths it turns out that most of them are easier to derive than their counterparts in the uniform norm because of a classical result of z ciesielski which makes the brownian motion on these spaces easy to handle in particular we study the equivalents of the probability of eb in a fixed ball ofb in a small ball and we give applications to the speed of clustering in strassen law

comparison of homotopy perturbation method and homotopy analysis method comparison of homotopy perturbation method hpm and homotopy analysis method is made revealing that the former is more powerful than the later furthermore the hpm is further developed in this paper by applying the modern perturbation methods