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

analytical methods for solving the time fractional swift hohenberg s h equation in this paper the most effective methods the homotopy perturbation method hpm and the differential transform method dtm are applied to obtain the approximate solutions of the nonlinear time fractional swift hohenberg s h equation the basic philosophy of these methods does not involve linearization weak nonlinearity assumptions or perturbation theory numerical solutions for various combinations of the parameters a eigenvalue parameter l length and a fractional index are obtained the solutions of the s h equation are useful for studies of shear thinning effects in non newtonian fluid flows at the end the solutions obtained are also presented graphically

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

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

normality of marsden weinstein reductions for representations of quivers we prove that the marsden weinstein reductions for the moment map associated to representations of a quiver are normal varieties we give an application to conjugacy classes of matrices

approximate analytical solutions of fractional benney lin equation by reduced differential transform method and the homotopy perturbation method in this paper the approximate analytical solutions of benney lin equation with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method rdtm and the homotopy perturbation method hpm rdtm technique does not require any discretization linearization or small perturbations and therefore it reduces significantly the numerical computation comparing the methodology rdtm with some known technique hpm shows that the present approach is effective and powerful the numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs the eight different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance

application of he s homotopy perturbation method for solving the cauchy reaction diffusion problem in this paper the solution of cauchy reaction diffusion problem is presented by means of the homotopy perturbation method reaction diffusion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields application of homotopy perturbation method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution

the application of homotopy perturbation method for mhd flows of ucm fluids above porous stretching sheets in this study by means of homotopy perturbation method hpm an approximate analytical solution of the magnetohydrodynamic mhd boundary layer flow of an upper convected maxwell ucm fluid over a porous stretching sheet is obtained the main feature of the hpm is that it deforms a difficult problem into a set of problems which are easier to solve hpm produces analytical expressions for the solution of nonlinear differential equations the obtained analytic solution is in the form of an infinite power series in this work the analytical solution obtained by using only two terms from hpm solution the results reveal that the proposed method is very effective and simple and can be applied to other nonlinear problems also it is shown that this method coincides with homotopy analysis method ham for the studied problem

hall current and mhd effects on heat transfer over an unsteady stretching permeable surface with thermal radiation the influence of hall current and thermal radiation on flow and heat transfer characteristics in a viscous fluid over an unsteady stretching permeable surface is studied in this paper the unsteadiness in the flow and temperature fields is because of the time dependent stretching velocity and surface temperature similarity transformations are used to convert the governing time dependent nonlinear boundary layer equations for momentum and thermal energy to a system of nonlinear ordinary differential equations these equations are solved numerically by applying shooting method using runge kutta fehlberg method and analytically by differential transform method with pade approximants dtm pade comparison of the numerical results and analytical solutions based on dtm pade approximant is made with the earlier published results the effects of the unsteadiness parameter thermal radiation hall effects suction injection parameter and non uniform heat source sink parameter on flow and heat transfer characteristics as well as on the local nusselt number are shown graphically

he s homotopy perturbation method for a boundary layer equation in unbounded domain by means of he s homotopy perturbation method hpm an approximate solution of a boundary layer equation in unbounded domain is obtained comparison is made between the obtained results and those in open literature the results show that the method is very effective and simple

new method based on the hpm and rkhsm for solving forced duffing equations with integral boundary conditions this paper investigates the forced duffing equation with integral boundary conditions its approximate solution is developed by combining the homotopy perturbation method hpm and the reproducing kernel hilbert space method rkhsm hpm is based on the use of the traditional perturbation method and the homotopy technique the hpm can reduce nonlinear problems to some linear problems and generate a rapid convergent series solution in most cases rkhsm is also an analytical technique which can solve powerfully linear boundary value problems therefore the forced duffing equation with integral boundary conditions can be solved using advantages of these two methods two numerical examples are presented to illustrate the strength of the method

approximate analytical solutions of nonlinear differential equations using the least squares homotopy perturbation method abstract in the present paper we introduce a new method to compute approximate analytical solutions for nonlinear differential equations called the least squares homotopy perturbation method the method is based on the well known homotopy perturbation method and its main feature is an accelerated convergence compared to the regular homotopy perturbation method the comparison with previous results emphasizes the high accuracy of the method

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

formality of dg algebras after kaledin abstract we provide proper foundations and proofs for the main results of kaledin 2007 ka the results include a flat base change for formality and behavior of formality in flat families of a and dg algebras

mhd flow and heat transfer analysis of fractional oldroyd b nanofluid between two coaxial cylinders abstract in previous study on the flow of fractional viscoelastic fluid between two coaxial cylinders due to the complexity of computation researchers commonly assume that the flow area is a rectangular pipe this paper studies two dimensional magnetohydrodynamic mhd flow and heat transfer of fractional oldroyd b nanofluid between two coaxial cylinders with variable pressure the boundary layer fractional cylindrical governing equations are firstly formulated and derived meanwhile the numerical solutions are obtained by using the newly developed finite difference method combined with l1 algorithm whose validity is confirmed by the comparison with the exact solution constructed results show that the fractional derivative parameters 1 and exponent parameter related to the wall temperature have significant effects on velocity and temperature fields specifically the velocity decreases with the augment of 1 but increases as rises up the temperature profiles intersect each other for different meanwhile increasing leads to an increase in temperature near the wall of inner tube but a decline near the outer cylinder which demonstrates increasing exponent parameter can enhance heat transfer

quasiaffine orbits of invariant subspaces for uniform jordan operators abstract we consider the problem of classification of invariant subspaces for the class of uniform jordan operators we show that given two invariant subspaces m 1 and m 2 of a uniform jordan operator t s s the subspace m 2 belongs to the quasiaffine orbit of m 1 if and only if the restrictions t m 1 and t m 2 are quasisimilar and the compression t m 2 can be injected in the compression t m 1 our result refines previous work on the subject by bercovici and smotzer

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

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

the global attractor of the viscous fornberg whitham equation abstract this paper aims to present a proof of the existence of the attractor for the one dimensional viscous fornberg whitham equation in this paper the global existence of solution to the viscous fornberg whitham equation in l 2 under the periodic boundary conditions is studied by using the time estimate of the fornberg whitham equation we get the compact and bounded absorbing set and the existence of the global attractor for the viscous fornberg whitham equation

magnetohydrodynamic flow of an oldroyd 6 constant fluid a study is made of the steady flow in an incompressible magnetohydrodynamic oldroyd 6 constant fluid by the motion of an infinite plate the analytical solution of the non linear problem is obtained by the homotopy analysis method the manner in which the various material parameters affect the structure of the velocity profile is delineated also a comparison of the present solution is made with the solution of an oldroyd 3 constant fluid

an improvement to homotopy perturbation method for solving system of linear equations in this paper we present an efficient numerical algorithm to find exact solutions for the system of linear equations based on homotopy perturbation method hpm a reliable modification is proposed and the modified method is employed to solve the system of linear equations the results are compared with those obtained by the original homotopy perturbation method two examples are given to illustrate the ability and reliability of the modified method the results reveal that the modified method is very simple and effective

on spectral tangential nevanlinna pick interpolation abstract in this paper we extend our work on spectral matricial nevanlinna pick interpolation from 4 to the tangential case as in 4 this will be deduced as a corollary of a spectral commutant lifting theorem which generalizes the corresponding result of 6

spectral lifting in banach algebras and interpolation in several variables let a be a unital banach algebra and let j be a closed two sided ideal of a we prove that if any invertible element of a j has an invertible lifting in a4 then the quotient homomorphism 1 a a4 j is a spectral interpolant this result is used to obtain a noncommutative multivariable analogue of the spectral commutant lifting theorem of bercovici foia and tannenbaum this yields spectral versions of sarason nevanlinna pick and caratheodory type interpolation for fn 3b 1c the wot closed algebra generated by the spatial tensor product of the noncommutative analytic toeplitz algebra f and b ac the algebra of bounded operators on a finite dimensional hilbert space kc a spectral tangential commutant lifting theorem in several variables is considered and used to obtain a spectral tangential version of the nevanlinna pick interpolation for f n03b kc in particular we obtain interpolation theorems for matrix valued bounded analytic functions on the open unit ball of cn in which one bounds the spectral radius of the interpolant and not the norm

homotopy perturbation method for fractional fornberg whitham equation this article presents the approximate analytical solutions to solve the nonlinear fornberg whitham equation with fractional time derivative by using initial values the explicit solutions of the equations are solved by using a reliable algorithm like homotopy perturbation method the fractional derivatives are taken in the caputo sense numerical results show that the hpm is easy to implement and accurate when applied to time fractional pdes

birational geometry of symplectic quotient singularities for a finite subgroup gamma subset mathrm sl 2 mathbb c and for n ge 1 we use variation of git quotient for nakajima quiver varieties to study the birational geometry of the hilbert scheme of n points on the minimal resolution s of the kleinian singularity mathbb c 2 gamma it is well known that x mathrm mathrm hilb n s is a projective crepant resolution of the symplectic singularity mathbb c 2n gamma n where gamma n gamma wr mathfrak s n is the wreath product we prove that every projective crepant resolution of mathbb c 2n gamma n can be realised as the fine moduli space of theta stable pi modules for a fixed dimension vector where pi is the framed preprojective algebra of gamma and theta is a choice of generic stability condition our approach uses the linearisation map from git to relate wall crossing in the space of theta stability conditions to birational transformations of x over mathbb c 2n gamma n as a corollary we describe completely the ample and movable cones of x over mathbb c 2n gamma n and show that the mori chamber decomposition of the movable cone is determined by an extended catalan hyperplane arrangement of the ade root system associated to gamma by the mckay correspondence in the appendix we show that morphisms of quiver varieties induced by variation of git quotient are semismall generalising a result of nakajima in the case where the quiver variety is smooth

the modified decomposition method and pade approximants for a boundary layer equation in unbounded domain the modified decomposition method is applied for analytic treatment of nonlinear differential equations that appear on boundary layers in fluid mechanics the modified method accelerates the rapid convergence of the series solution dramatically reduces the size of work the obtained series solution is combined with the diagonal pade approximants to handle the boundary condition at infinity

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

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method

asymptotology by homotopy perturbation method in the paper an heuristical example is given to illustrate the basic idea of the homotopy perturbation method so that homotopy perturbation method has made all that is necessary simple and all that is complex unnecessary

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

series solution of a nonlinear ode arising in magnetohydrodynamic by hpm pade technique in this study we investigate the magnetohydrodynamic mhd viscous flow due to a shrinking sheet by employing the homotopy perturbation method hpm and pade approximation the series solution of the governing nonlinear problem is developed generally the truncated series solution is adequate only in a small region when the exact solution is not reached we overcame this limitation by using the pade techniques which have the advantage in turning the polynomial approximation into a rational function are applied to the series solution to improve the accuracy and enlarge the convergence domain comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted

homotopy perturbation method for nonlinear mhd jeffery hamel problem the article solves the jeffery hamel flow using the homotopy perturbation method an explicit analytical solution is obtained and the effect of external magnetic field is studied comparison of the obtained result with the numerical one reveals validity of the used method

study of the effects of the reynolds number on circular porous slider via variational iteration algorithm ii abstract in this paper the problem of the porous slider where the fluid is injected through the porous bottom is considered the similarity transformation reduces the governing equations into coupled nonlinear ordinary differential equations the resulting equations are solved by using he s variational iteration algorithm ii the resulting series solution contains the well known reynolds number the influence of the reynolds number on the velocity field has been discussed graphically

stability for an abelian category abstract the main goal of the article is to give the definition of algebraic stability that would permit us to consider stability not only for algebraic vector bundles or torsion free coherent sheaves but for the abelian category of coherent sheaves or for whatever abelian category we present an axiomatic description of the algebraic stability on an abelian category and prove some general results then the stability for coherent sheaves on a projective variety is constructed which generalizes gieseker stability stabilities for graded modules and for quiver representations are also discussed the constructions could be used for other abelian categories as well

projectivity and birational geometry of bridgeland moduli spaces we construct a family of nef divisor classes on every moduli space of stable complexes in the sense of bridgeland this divisor class varies naturally with the bridgeland stability condition for a generic stability condition on a k3 surface we prove that this class is ample thereby generalizing a result of minamide yanagida and yoshioka our result also gives a systematic explanation of the relation between wall crossing for bridgeland stability and the minimal model program for the moduli space we give three applications of our method for classical moduli spaces of sheaves on a k3 surface 1 we obtain a region in the ample cone in the moduli space of gieseker stable sheaves only depending on the lattice of the k3 2 we determine the nef cone of the hilbert scheme of n points on a k3 surface of picard rank one when n is large compared to the genus 3 we verify the hassett tschinkel huybrechts sawon conjecture on the existence of a birational lagrangian fibration for the hilbert scheme in a new family of cases

singularities of moduli spaces of sheaves on k3 surfaces and nakajima quiver varieties abstract the aim of this paper is to study the singularities of certain moduli spaces of sheaves on k3 surfaces by means of nakajima quiver varieties the singularities in question arise from the choice of a non generic polarization with respect to which we consider stability and admit natural symplectic resolutions corresponding to choices of general polarizations for sheaves that are pure of dimension one we show that these moduli spaces are locally around a singular point isomorphic to a quiver variety and that via this isomorphism the natural symplectic resolutions correspond to variations of git quotients of the quiver variety

a new modified definition of caputo fabrizio fractional order derivative and their applications to the multi step homotopy analysis method mham abstract in this paper we present a new definition of fractional order derivative with a smooth kernel based on the caputo fabrizio fractional order operator which takes into account some problems related with the conventional caputo fabrizio factional order derivative definition the modified caputo fabrizio fractional order derivative here introduced presents some advantages when some approximated analytical methods are applied to solve non linear fractional differential equations we consider two approximated analytical methods to find analytical solutions for this novel operator the homotopy analysis method ham and the multi step homotopy analysis method mham the results obtained suggest that the introduction of the modified caputo fabrizio fractional order derivative can be applied in the future to many different scenarios in fractional dynamics

a spectral commutant lifting theorem 1991 american mathematical society first published in transactions of the american mathematical society vol 325 no 2 june 1991 by the american mathematical society

moduli spaces of stable sheaves on abelian surfaces in this paper we consider basic problems on moduli spaces of stable sheaves on abelian surfaces our main assumption is the primitivity of the associated mukai vector we determine the deformation types albanese maps bogomolov factors and their weight 2 hodge structures we also discuss the deformation types of moduli spaces of stable sheaves on k3 surfaces

a note on magnetohydrodynamic flow of a power law fluid over a stretching sheet this paper presents a numerical study of the flow of an electrically conducting power law fluid in the presence of a uniform transverse magnetic field this flow is governed by the non linear differential equationn f n 1 f f 2 2nn 1ff mf 0where a prime denotes differentiation with respect to the similarity variable h and n m are respectively the power law index and the magnetic parameter in this work the numerical solutions are obtained using a runge kutta algorithm for high order initial value problems

on moduli spaces of sheaves on k3 or abelian surfaces we investigate the moduli spaces of one and two dimensional sheaves on projective k3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability we can exclude the existence of new examples of projective irreducible symplectic manifolds lying birationally over components of the moduli spaces of one dimensional semistable sheaves on k3 surfaces and over components of many of the moduli spaces of two dimensional sheaves on k3 surfaces in particular of those for rank two sheaves

variational iteration method for unsteady flow of gas through a porous medium using he s polynomials and pade approximants in this paper we apply the variational iteration method using he s polynomials for finding the analytical solution of unsteady flow of gas through a porous medium the proposed method is an elegant combination of he s variational iteration and the homotopy perturbation methods the suggested algorithm is quite efficient and is practically well suited for use in such problems the proposed iterative scheme finds the solution without any discretization linearization or restrictive assumptions the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of the solution and to determine the initial slope a clear advantage of this technique over the decomposition method is that no calculation of adomian s polynomials is needed

the first integral method for some time fractional differential equations abstract in this paper the fractional derivatives in the sense of modified riemann liouville derivative and the first integral method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations the power of this manageable method is presented by applying it to several examples this approach can also be applied to other nonlinear fractional differential equations

comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations in this article the homotopy perturbation method proposed by j h he is adopted for solving linear fractional partial differential equations the fractional derivatives are described in the caputo sense comparison of the results obtained by the homotopy perturbation method with those obtained by the variational iteration method reveals that the present methods are very effective and convenient

singular symplectic moduli spaces moduli spaces of semistable sheaves on a k3 or abelian surface with respect to a general ample divisor are shown to be locally factorial with the exception of symmetric products of a k3 or abelian surface and the class of moduli spaces found by o grady consequently since singular moduli space that do not belong to these exceptional cases have singularities in codimension 4 they do no admit projective symplectic resolutions

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

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

convergence and error estimation of homotopy perturbation method for fredholm and volterra integral equations abstract in this paper an application of the homotopy perturbation method for solving fredholm and volterra integral equations of the second kind is presented discussed method consists in constructing the functional series sum of which determines the function giving the solution of considered problem conditions under which the constructed series is convergent are formulated and proved in the paper in general the composed series is rather fast convergent thanks to which calculation of few first terms ensures a very good approximation of the sought solution estimation of errors of approximate solution obtained by taking the partial sum of the series is also elaborated in the paper

on shifted jacobi spectral approximations for solving fractional differential equations in this paper a new formula of caputo fractional order derivatives of shifted jacobi polynomials of any degree in terms of shifted jacobi polynomials themselves is proved we discuss a direct solution technique for linear multi order fractional differential equations fdes subject to nonhomogeneous initial conditions using a shifted jacobi tau approximation a quadrature shifted jacobi tau q sjt approximation is introduced for the solution of linear multi order fdes with variable coefficients we also propose a shifted jacobi collocation technique for solving nonlinear multi order fractional initial value problems the advantages of using the proposed techniques are discussed and we compare them with other existing methods we investigate some illustrative examples of fdes including linear and nonlinear terms we demonstrate the high accuracy and the efficiency of the proposed techniques

homotopy perturbation method to obtain exact special solutions with solitary patterns for boussinesq like b m n equations with fully nonlinear dispersion in this paper we studied the boussinesq like equations with fully nonlinear dispersion b m n equations which exhibit solutions with solitary patterns new exact solitary solutions of the equations are found the two special cases b 2 2 and b 3 3 are chosen to illustrate the concrete scheme of the homotopy perturbation method in b m n equations the nonlinear equations b m n are addressed for two different cases namely when m n being odd and even integers general formulas for the solutions of b m n equations are established