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

some groups generated by transvection subgroups in the 1960 s j e mclaughlin lo 111 determined all irreducible finite dimensional linear groups generated by transvection subgroups a trans section of a k vector space v is linear map t cp x v t given by vt cp x 2 vqj y for all t e v where xe vand pe v are non zero and xcp 0 v is the dual space of v a k transvection subgroup t cp x consists of the identity and all r cp x where q and x range over the l dimensional subspaces spanned by cp and x respectively it is isomorphic to the additive group of k mclaughlin showed that the only such groups are the special linear and symplectic groups and in the case when k is f the field with two elements the orthogonal and symmetric groups it is our purpose to give a new proof of a result which includes mclaughlin s we discard the assumptions of finiteness of the dimension of v over k and also to some extent the irreducibility of the group while still obtaining a result which is recognizably like mclaughlin s our result for irreducible groups is the following unexplained terminol ogy will be defined after the statement of the theorem the more com plicated result under a weaker hypothesis is stated near the end of the introduction

pullbacks of prufer rings abstract in this paper we consider five extensions of the prufer domain notion to commutative rings with zero divisors and investigate their behavior in a special type of pullback called a conductor square that is for a pair of rings r t with non zero conductor of t into r we find necessary and sufficient conditions on the rings t t c and r c in order that r has one of the five prufer conditions

some remarks on prufer multiplication domains and class groups abstract let d be an integral domain with quotient field k and let x be an indeterminate over d also let t t be a defining family of quotient rings of d and suppose that is a finite type star operation on d induced by t we show that d is a p md respectively p v md if and only if c d f g c d f c d g respectively c d f g w c d f c d g w for all 0 f g k x a more general version of this result is given in the semistar operation setting we give a method for recognizing p v md s which are not p md s for a certain finite type star operation we study domains d for which the class group cl d equals the t class group cl t d for any finite type star operation and we indicate examples of p v md s d such that cl d cl t d we also compute cl v d for certain valuation domains d

generalized krull domains and the composite semigroup ring d e γ abstract let d e be an extension of integral domains be a nonzero torsion free additive grading monoid with quotient group g such that 0 set 0 and r d e in this paper we show that if g satisfies the ascending chain condition on cyclic subgroups then r is a generalized krull domain resp generalized unique factorization domain if and only if d e d is a generalized krull domain resp generalized unique factorization domain and is a generalized krull semigroup resp weakly factorial gcd semigroup

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

linear transvection groups and embedded polar spaces most classical groups arising from anti hermitian forms or pseudo quadratic forms contain so called isotropic transvections the isotropic transvection subgroups of these classical groups i e the subgroups generated by all isotropic transvections with a fixed axis form a class of abelian subgroups which is a class of abstract transvection groups in the sense of timmesfeld 24 in this paper we give a common characterization of all these classical groups with isotropic transvections as linear groups generated by a class of abstract transvection groups such that the elements of a are transvections

a multigrid homotopy method for nonlinear inverse problems abstract in the present contribution we develop a novel method combining the multigrid idea and the homotopy technique for nonlinear inverse problems in which the forward problems are modeled by some forms of partial differential equations the method first attempts to use the multigrid method to decompose the original inverse problem into a sequence of sub inverse problems which depend on the grid variables and are solved in proper order according to the grid size from the coarsest to the finest and then carries out the inversion on the coarsest grid by the homotopy method the strategy may give a rapidly and globally convergent method as a practical application this method is used to solve the nonlinear inverse problem of a nonlinear convection diffusion equation which is the saturation equation within the two phase porous media flow we demonstrate the effectiveness and merits of the multigrid homotopy method on two actual model problems

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

integral domains in which any two v coprime elements are comaximal domains in which the star operations d the trivial star operation and w coincide have received a good deal of attention recently these are exactly the domains d in which i d whenever i is a finitely generated ideal of d with iv d in this work we study what happens when finitely generated is replaced by two generated it turns out that these are precisely the domains in which d f where f is a certain star operation closely connected to but more complicated than the w operation

on the star class group of a pullback abstract for the domain r arising from the construction t m d we relate the star class groups of r to those of t and d more precisely let t be an integral domain m a nonzero maximal ideal of t d a proper subring of k t m t k the natural projection and let r 1 d for each star operation on r we define the star operation on d i e the projection of under and the star operation t on t i e the extension of to t then we show that under a mild hypothesis on the group of units of t if is a star operation of finite type then the sequence of canonical homomorphisms 0 cl d cl r cl t t 0 is split exact in particular when t r we deduce that the sequence 0 cl t d d cl t r r cl t r t t 0 is split exact the relation between t r t and t t and between cl t r t t and cl t t t is also investigated

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

almost bezout domains an integral domain r is said to be an almost bezout domain respectively almost gcd domain if for x y r 0 there exists an n with xn yn respectively xn yn v principal in this paper we continue the investigation of agcd domains begun by the second author and introduce the notion of an almost bezout domain we show that r is an almost bezout domain if and only if r the integral closure of r is a prufer domain with torsion class group and for every x r there exists an n with xsn r

cohen kaplansky domains integral domains with a finite number of irreducible elements we define an integral domain r to be a cohen kaplansky domain ck domain if every element of r is a finite product of irreducible elements and r has only finitely many nonassociate irreducible elements the purpose of this paper is to investigate ck domains many conditions equivalent to r being a ck domain are given for example r is a ck domain if and only if r is a one dimensional semi local domain and for each nonprincipal maximal ideal m of r rm is finite and rm is analytically irreducible or if and only if g r the group of divisibility of r is finitely generated and rank g r max r we show that a ck domain is a certain special type of composite or pullback of a subring of a finite homomorphic image of a semilocal pid noetherian domains with g r finitely generated are also investigated

maximal unipotent subgroups of finitary linear groups finitary linear groups have been in recent years the subject of intensiveinvestigations the structure of these groups has been studied and nowmuch is known about the locally solvable or locally nilpotent finitary lineargroups or about the locally finite ones a remarkable achievement is forinstance the classification of the simple locally finite finitary linear groups recently completed by j hall

prufer like conditions and pullbacks abstract this paper is a continuation of the investigation of some prufer like conditions such as almost prufer almost bezout and almost gcd begun by anderson zafrullah and anderson knopp lewin in the context of pullbacks

periodic simple groups of finitary linear transformations a group is locally finite if every finite subset generates a finite subgroup a group of linear transformations is finitary if each element minus the identity is an endomorphism of finite rank the classification and structure theory for locally finite simple groups splits naturally into two cases those groups that can be faithfully represented as groups of finitary linear transformations and those groups that are not finitary linear this paper completes the finitary case we classify up to isomorphism those infinite locally finite simple groups that are finitary linear but not linear

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

he s homotopy perturbation method for continuous population models for single and interacting species he s homotopy perturbation method is applied for obtaining approximate analytical solutions of continuous population models for single and interacting species in comparison with existing techniques this method is very straightforward and the solution procedure is very simple also it is highly effective in terms of accuracy and rapid convergence analytical and numerical studies are presented

extremal presentations for classical lie algebras abstract the long root elements in lie algebras of chevalley type have been well studied and can be characterized as extremal elements that is elements x such that the image of ad x 2 lies in the subspace spanned by x in this paper assuming an algebraically closed base field of characteristic not 2 we find presentations of the lie algebras of classical chevalley type by means of minimal sets of extremal generators the relations are described by simple graphs on the sets for example for c n the graph is a path of length 2n and for a n the graph is the triangle connected to a path of length n 3

almost gcd domains of finite t character abstract let d be an integral domain two nonzero elements x y d are v coprime if x y xy d is an almost gcd domain agcd domain if for every pair x y d there exists a natural number n n x y such that xn yn is principal we show that if x is a nonzero nonunit element of an almost gcd domain d then the set m m maximal t ideal x m is finite if and only if the set s x y d y nonunit y divides xn for some n does not contain an infinite sequence of mutually v coprime elements if and only if there exists an integer r such that every sequence of mutually v coprime elements of s x has length r one of the various consequences of this result is that a gcd domain d is a semilocal bezout domain if and only if d does not contain an infinite sequence of mutually v coprime nonunit elements then we study integrally closed agcd domains of finite t character of the type a xb x and we construct examples of nonintegrally closed agcd of finite t character by local algebra techniques

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

locally factorial integral domains following fossum 9 p 8 11 we define an integral domain r to be locally factorial if r r l f is factorial for each nonzero nonunit f e r for example any factorial integral domain or one dimensional quasilocal integral domain is locally factorial we show that a locally factorial integral domain r which is not quasilocal is a krull domain and r is factorial for each maximal ideal m of r we will be mainly interested in locally factorial krull domains in this case we can relate divisibility properties of r to group theoretic properties of cl r its divisor class group the first examples of dedekind domains which are locally factorial pid but not factorial pid are due to claborn 6 we know of no locally factorial krull domains which are neither factorial nor dedekind domains most of our results will be stated for arbitrary locally factorial krull domains and subintersections of krull domains however major emphasis will be towards dedekind domains in this case a factorial overring is just a pid and each overring is a subintersection in section 2 we prove several basic results about locally factorial integral domains and give several examples of locally factorial krull domains claborn s examples actually satisfy the stronger property that each proper overring of r is factorial pid in section 3 we study those krull domains each of whose proper overrings is factorial such an integral domain which is not quasilocal is necessarily a dedekind domain with cyclic divisor class 265

the w integral closure of integral domains abstract let d be an integral domain with quotient field k d the integral closure of d x an indeterminate over d and n v f d x a f v d let w be the operation on d defined by i w x k there is a finitely generated ideal a such that a 1 d and x a i and let d w u k u i w i w for some nonzero finitely generated ideal i of d then d w called the w integral closure of d is an integrally closed overring of d in this paper we show that d w d x n v k and d w x n v d x n v using this result we give several w integral closure analogs of the integral closure we also study the w integral closure of umt domains and strong mori domains