homotopy of unitaries in simple c algebras with tracial rank one let 0 be a positive number is there a number 0 satisfying the following given any pair of unitaries u and v in a unital simple c algebra a with v 0 in k1 a for which uv vu there is a continuous path of unitaries v t t 0 1 a such that v 0 v v 1 1and uv t v t u for allt 0 1 an answer is given to this question when a is assumed to be a unital simple c algebra with tracial rank no more than one let c be a unital separable amenable simple c algebra with tracial rank no more than one which also satisfies the uct suppose that c a is a unital monomorphism and suppose that v a is a unitary with v 0 in k1 a such that v almost commutes with it is shown that there is a continuous path of unitaries v t t 0 1 in a with v 0 v and v 1 1 such that the entire path v t almost commutes with provided that an induced bott map vanishes other versions of the so called basic homotopy lemma are also presented

minimal dynamical systems on the product of the cantor set and the circle we prove that a crossed product algebra arising from a minimal dynamical system on the product of the cantor set and the circle has real rank zero if and only if the set of invariant measures of the system come from the associated cantor minimal system in the case that cocycles take values in the rotation group it is also shown that this condition implies tracial rank zero and in particular the crossed product algebra is isomorphic to a unital simple at algebra of real rank zero under the same assumption we show that two systems are approximately k conjugate if and only if there exists a sequence of isomorphisms between two associated crossed products which approximately maps open image in new window

on tracial approximation let c be a class of unital c algebras the class tac of c algebras which can be tracially approximated in the egorov like sense first considered by lin by the c algebras in c is studied lin considered the case that c consists of finite dimensional c algebras or the tensor products of such with c 0 1 in particular the question is considered whether for any simple separable a tac there is a c algebra b which is a simple inductive limit of certain basic homogeneous c algebras together with c algebras in c such that the elliott invariant of a is isomorphic to the elliott invariant of b an interesting case of this question is answered in the final part of the paper the question is also considered which properties of c algebras are inherited by tracial approximation results of this kind are obtained which are used in the proof of the main theorem of the paper and also in the proof of the classification theorem of the second author given in z niu a classification of tracially approximately splitting tree algebra in preparation and z niu a classification of certain tracially approximately subhomogeneous c algebras phd thesis university of toronto 2005 which also uses the main result of the present paper

the klein gordon equation of generalized hulthen potential in complex quantum mechanics we have investigated the reality of exact bound states of complex and or pt symmetric non hermitian exponential type generalized hulthen potential the klein gordon equation has been solved by using the nikiforov uvarov method which is based on solving the second order linear differential equations by reduction to a generalized equation of hypergeometric type in many cases of interest negative and positive energy states have been discussed for different types of complex potentials

abelian mathrm c ast subalgebras of mathrm c ast algebras of real rank zero and inductive limit mathrm c ast algebras

nonnuclear subalgebras of af algebras we show that any non type i separable unital af algebra b can be modeled from inside by a nonnuclear c algebra and from outside by a nonexact c algebra more precisely there exist unital separable quasidiagonal c algebras a b c of real rank zero stable rank one such that a is nonnuclear c is nonexact and both a and c are asymptotically homotopy equivalent to b in particular a b and c have the same ordered k theory groups hence isomorphic ideal lattices and a and b have affinely homeomorphic trace spaces

staggered grids hybrid dual spectral element method for second order elliptic problems application to high order time splitting methods for navier stokes equations abstract this paper is a presentation of a mixed spectral element method based on staggered grids strategy used for the discretization of second order elliptic problems set under hybrid dual formulation a numerical analysis is performed proving the expected optimality and some numerical tests are described to confirm the predicted convergence rates the second part deals with a high order time splitting spectral scheme for the simulation of unsteady incompressible navier stokes flows we show how to use such a solver as a filtering tool to obtain divergence free discrete velocity some computational examples are reported which quantify the improvements induced by such a filter we have observed a strengthening of the stability and of the accuracy

extensions of c x by simple c algebras of real rank zero let ext c x a be the set of unitarily equivalence classes of essential c algebra exten sions of the following form 0 a e c x 0 where a is a nonunital separable simple c algebra of real rank zero stable rank one with unique normalized trace and x is a finite cw complex we show that there is a bijection ext c x a kk c x m a a where m a is the multiplier algebra of a in particular we determine when an extension is actually splitting we also in a more general setting give a condition when an essential extension is quasidiagonal 0 introduction we study essential extensions of the following form 0 a f c x 0 where a is a j unital nonunital simple c algebra of real rank zero and stable rank one and x is finite cw complex the brown douglas fillmore bdf theory bdf1 and bdf2 gives a classification of these extensions up to unitary equivalence in the case that a k the c algebra of compact operators on an infinite dimensional separable hubert space since then the theory of c algebra extensions developed rapidly it is very difficult to give a complete list we refer the reader to bl for references while using of theory ext c x a have been computed for the most interesting cases however ext c x a does not provide enough information in general to classify extensions up to unitary equivalence in fact as shown in ln6 and lnl2 there are usually many different unitary equivalence classes of trivial extensions and an extension r with r 0 in ext c x a may not be trivial we will only consider simple c algebras that share some properties with c we consider only those with real rank zero stable rank one and unique quasi trace up to scalar multiples there is an additional property that c has namely its corona algebra m k k the calkin algebra is simple we also as sume that m a a is simple it has been studied when a nonunital but cr unital simple c algebra a has the property that m a a is simple see lnl rrl and zh2 etc it is shown in lnl that a simple c algebra a has the property that m a a is simple if and only if a has continuous scale

inductive limits of subhomogeneous c algebras with hausdorff spectrum we consider unital simple inductive limits of generalized dimension drop c algebras they are so called ash algebras and include all unital simple ah algebras and all dimension drop c algebras suppose that a is one of these c algebras we show that a q has tracial rank no more than one where q is the rational uhf algebra as a consequence we obtain the following classification result let a and b be two unital simple inductive limits of generalized dimension drop algebras with no dimension growth then a b if and only if they have the same elliott invariant

incompressible navier stokes solutions by a triangular spectral p element projection method the application of the fractional step projection method recently proposed by guermond and quartapelle to the numerical approximation of unsteady navier stokes solutions by means of a spectral p element method is considered in particular we illustrate the second order pressure correction technique and evaluate its accuracy properties in some test cases stability with respect to the compatibility condition between the approximation spaces for velocity and pressure is also addressed the high spectral accuracy in space and the second order accuracy in time are verified by two simple test cases with analytical solution a more interesting problem is solved showing the ability of the method to produce very accurate results also for problems in complex geometries

short note a primal formulation for the helmholtz decomposition in 1999 jean paul caltagirone and jerome breil have developed in their paper caltagirone j breil sur une methode de projection vectorielle pour la resolution des equations de navier stokes c r acad sci paris 327 serie ii b 1999 1179 1184 a new method to compute a divergence free velocity they have used the grad div operator to extract the solenoidal part of a given vector field in this contribution we explain how this method can be considered as a real helmholtz decomposition and we present a stable approximation in the framework of spectral methods numerical results are presented to illustrate the efficiency of this approach

classification of homomorphisms and dynamical systems let a be a unital simple c algebra with tracial rank zero and let x be a compact metric space suppose that h 1 h 2 c x a are two unital monomorphisms we show that h 1 and h 2 are approximately unitarily equivalent if and only if h 1 h 2 in kl c x a and o h 1 f o h 2 f for every f c x and every trace r of a inspired by a theorem of tomiyama we introduce a notion of approximate conjugacy for minimal dynamical systems let x be a compact metric space and let x x be two minimal homeomorphisms using the above mentioned result we show that two dynamical systems are approximately conjugate in that sense if and only if a k theoretical condition is satisfied in the case that x is the cantor set this notion coincides with the strong orbit equivalence of giordano putnam and skau and the k theoretical condition is equivalent to saying that the associate crossed product c algebras are isomorphic another application of the above mentioned result is given for c dynamical systems related to a problem of kishimoto let a be a unital simple ah algebra with no dimension growth and with real rank zero and let a aut a we prove that if r fixes a large subgroup of k 0 a and has the tracial rokhlin property then ax z is again a unital simple ah algebra with no dimension growth and with real rank zero

asymptotic unitary equivalence and classification of simple amenable c algebras let c and a be two unital separable amenable simple c algebras with tracial rank at most one suppose that c satisfies the universal coefficient theorem and suppose that 1 2 c a are two unital monomorphisms we show that there is a continuous path of unitaries u t t 0 of a such that lim t to infty u t varphi 1 c u t varphi 2 c quad mbox for all c in c if and only if 1 2 in kk c a varphi 1 ddag varphi 2 ddag varphi 1 t varphi 2 t and a rotation related map overline r varphi 1 varphi 2 associated with 1 and 2 is zero applying this result together with a result of w winter we give a classification theorem for a class mathcal a of unital separable simple amenable c algebras which is strictly larger than the class of separable c algebras with tracial rank zero or one tensor products of two c algebras in mathcal a are again in mathcal a moreover this class is closed under inductive limits and contains all unital simple ash algebras for which the state space of k 0 is the same as the tracial state space and also some unital simple ash algebras whose k 0 group is and whose tracial state spaces are any metrizable choquet simplex one consequence of the main result is that all unital simple ah algebras which are mathcal z stable are isomorphic to ones with no dimension growth

legendre spectral methods for the grad div operator this paper describes two legendre spectral methods for the grad div eigenvalue problem in r 2 the first method uses a single grid resulting from the p n circle times p n discretization in primal and dual variational formulations as is well known this method is unstable and exhibits spectral pollution effects increased number of singular eigenvalues and increased multiplicity of some eigenvalues belonging to the regular spectrum our study aims at the understanding of these effects the second spectral method is based on a staggered grid of the p n circle times pn 1 discretization this discretization leads to a stable algorithm free of spurious eigenmodes and with spectral convergence of the regular eigenvalues eigenvectors towards their analytical values in addition divergence free vector fields with sufficient regularity properties are spectrally projected onto the discrete kernel of grad div a clear indication of the robustness of this algorithm c 2007 elsevier b v all rights reserved

on topologically finite dimensional simple c algebras we show that if a simple c algebra a is topologically finite dimensional in a suitable sense then not only k0 a has certain good properties but a is even accessible to elliott s classification program more precisely we prove the following results

non commutative shifts and crossed products abstract when a is a unital simple af c algebra and has a unique tracial state it is shown that the crossed product of the two sided infinite tensor product z a by the shift is a tracially af c algebra a similar result is given to the crossed product of a certain non unital two sided infinite tensor product by the shift applying a far reaching classification result of such c algebras by h lin we obtain an example of a one parameter automorphism group on some af c algebra which is not approximately inner a counter example to the af version of the so called powers sakai conjecture 23

the classification of simple separable unital z stable locally ash algebras let a be a unital simple separable locally approximately subhomogeneous c algebra locally ash algebra it is shown that a qa q can be tracially approximated by unital elliott thomsen algebras with trivial k1k1 group where q is the universal uhf algebra in particular it follows that a is classifiable by the elliott invariant if a is jiang su stable

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

on the structure of simple c algebras tensored with a uhf algebra ii let d be a simple unital c algebra let b be a uhf algebra and put a b d it is proved that if p q a are projections and p q for all quasitraces on a then p q in the sense of murray and von neumann a more general result involving positive operators in a is also proved if d has finitely many extremal quasi traces and the projections in d k separate these then it is proved that a has real rank zero finally it is proved that provided d is stably finite then each positive state on k0 d lifts to a quasi trace

lifting kk elements asymptotic unitary equivalence and classification of simple c algebras let a and c be two unital simple c algebras with tracial rank zero suppose that c is amenable and satisfies the universal coefficient theorem denote by kke c a the set of those in kk c a for which k0 c 0 k0 a 0 and 1c 1a suppose that kke c a we show that there is a unital monomorphism c a such that suppose that c is a unital ah algebra and is a continuous affine map for which t p t p for all projections p in all matrix algebras of c and any tt a where t a is the simplex of tracial states of a and is the convex set of faithful tracial states of c we prove that there is a unital monomorphism c a such that induces both and suppose that h c a is a unital monomorphism and hom k1 c aff a we show that there exists a unital monomorphism c a such that h in kk c a t t h for all tracial states t and the associated rotation map can be given by denote by kkt c a the set of compatible pairs where kle c a and is a continuous affine map from t a to together with a result on asymptotic unitary equivalence in h lin asymptotic unitary equivalence and asymptotically inner automorphisms arxiv math 0703610 2007 this provides a bijection from the asymptotic unitary equivalence classes of unital monomorphisms from c to a to where is a subgroup related to vanishing rotation maps as an application combining these results with a result of w winter w winter localizing the elliott conjecture at strongly self absorbing c algebras arxiv 0708 0283v3 2007 we show that two unital amenable simple stable c algebras are isomorphic if they have the same elliott invariant and the tensor products of these c algebras with any uhf algebra have tracial rank zero in particular if a and b are two unital separable simple stable c algebras with unique tracial states which are inductive limits of c algebras of type i then they are isomorphic if and only if they have isomorphic elliott invariants

generalized inductive limits of quasidiagonal c algebras if a is a unital quasidiagonal c algebra we construct a generalized inductive limit ba which is simple unital and inherits many structural properties from a if a is the unitization of a non simple purely infinite algebra e g the cone over a cuntz algebra then ba is tracially af which among other things lends support to a conjecture of toms

1 n expansion for the yukawa potential revisited using the form prescribed by moreno and zepeda for the n dimensional yukawa potential and employing the method of 1 n expansion we have obtained in a recent paper the energies of the ground state and the first excited state of a three dimensional yukawa potential in the present addendum we introduce a modified prescription for the n dimensional yukawa potential which enables us also to calculate the energies of the higher angular momentum states our results are in very good agreement with the accurate numerical values

spectral discretization of the vorticity velocity and pressure formulation of the stokes problem we consider the stokes problem in a square or a cube provided with nonstandard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity we write a variational formulation of this problem with three independent unknowns the vorticity the velocity and the pressure next we propose a discretization by spectral methods which relies on this formulation and since it leads to an inf sup condition on the pressure in a natural way we prove optimal error estimates for the three unknowns we present numerical experiments which are in perfect coherence with the analysis

simple nuclear c algebras of tracial topological rank one we give a classification theorem for unital separable nuclear c algebras with tracial rank no more than one let a and b be two unital separable simple nuclear c algebras with tr a tr b 1 which satisfy the universal coefficient theorem we show that a b if and only if there is an order and unit preserving isomorphism 0 1 2 k0 a k0 a 1a k1 a t a k0 b k0 b 1b k1 b t b where 2 1 x 0 x for each x k0 a and t b

asymptotically unitary equivalence and asymptotically inner automorphisms let c be a unital ah algebra and let a be a unital separable simple c algebra with tracial rank zero suppose that phi 1 phi 2 colon c to a are two unital monomorphisms we show that there is a continuous path of unitaries u t colon t in 0 infty of a such that lim t to infty u t phi 1 a u t phi 2 a quad hbox rm for all quad a in c if and only if phi 1 phi 2 in kk c a tau circ phi 1 tau circ phi 2 for all tau in t a and the rotation map tilde eta phi 1 phi 2 associated with phi 1 and phi 2 is zero in particular an automorphism alpha on a unital separable simple c algebra a in cal n with tracial rank zero is asymptotically inner if and only if alpha rm id a quad rm in quad kk a a and the rotation map tilde eta phi 1 phi 2 is zero let a be a unital ah algebra not necessarily simple and let alpha in aut a be an automorphism as an application we show that the associated crossed product a rtimes alpha bbb z can be embedded into a unital simple af algebra if and only if a admits a strictly positive alpha invariant tracial state

the range of a class of classifiable separable simple amenable c algebras we study the range of a classifiable class a of unital separable simple amenable c algebras which satisfy the universal coefficient theorem the class a contains all unital simple ah algebras we show that all unital simple inductive limits of dimension drop circle c algebras are also in the class this unifies some of the previous known classification results for unital simple amenable c algebras we also show that there are many other c algebras in the class we prove that for any partially ordered simple weakly unperforated rationally riesz group g0 with order unit u any countable abelian group g1 any metrizable choquet simplex s and any surjective affine continuous map r s su g0 where su g0 is the state space of g0 which preserves extremal points there exists one and only one up to isomorphism unital separable simple amenable c algebra a in the classifiable class a such that k0 a k0 a 1a k1 a t a a g0 g0 u g1 s r

on error estimates of projection methods for navier stokes equations first order schemes in this paper projection methods or fractional step methods are studied in the semi discretized form for the navier stokes equations in a two or three dimensional bounded domain error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method a modified projection scheme which leads to improved error estimates is also proposed

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

mathbb z actions on ah algebras and mathbb z 2 actions on af algebras we consider mathbb z actions single automorphisms on a unital simple ah algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the rohlin property under some technical assumptions moreover two mathbb z actions with the rohlin property on such a c algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent we also prove that locally approximately inner and uniformly outer mathbb z 2 actions on a unital simple af algebra with a unique trace have the rohlin property and classify them up to cocycle conjugacy employing the orderext group as classification invariants

regularity properties in the classification program for separable amenable c algebras we report on recent progress in the program to classify separable amenable c algebras our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank strict comparison of positive elements and z stability and on the importance of the cuntz semigroup we include a brief history of the program s successes since 1989 a more detailed look at the villadsen type algebras which have so dramatically changed the landscape and a collection of announcements on the structure and properties of the cuntz semigroup

extended supersymmetry for the bound states of the generalized hulthen potential hierarchy using the associated hypergeometric differential equation we analytically solve the bound states corresponding to a hierarchy of the radial potential v0 e r 1 e r c e r 1 e r 2 as a generalization of the hulth n potential then an analytic solution corresponding to a special case for which the parameter c is expected to be in terms of l l 1 is also derived meanwhile without introducing a superpotential and in the framework of supersymmetric quantum mechanics it is shown that these bound states can be calculated by two different algebraic methods based on these two approaches it is noted that the bound states realize an extended supersymmetry structure

stability of finite elements under divergence constraints a finite dimensional stability test for checking velocity pressure finite element trial spaces is presented applications are made to a new class of element pairs proposed in this paper as well as to existing spaces

polynomial approximation of divergence free functions etude de la meilleure approximation d une fonction sans divergence par un polynome algebrique ou trigonometrique sans divergence etablissement d une estimation optimale

the automorphism group of a simple tracially ai algebra the structure of the automorphism group of a simple tai algebra is studied in particular we show that frac overline rm inn a overline rm inn 0 a is isomorphic as a topological group to an inverse limit of discrete abelian groups for a unital simple ah algebra with bounded dimension growth consequently frac overline rm inn a overline rm inn 0 a is totally disconnected

crossed products by minimal homeomorphisms let x be an infinite compact metric space with finite covering dimension and let h x x be a minimal homeomorphism we show that the associated crossed product c algebra a 1 4 c z x h has tracial rank zero whenever the image of k0 a in a t a is dense as a consequence we show that these crossed product c algebras are in fact simple ah algebras with real rank zero when x is connected and h is further assumed to be uniquely ergodic then the above happens if and only if the rotation number associated to h has irrational values by applying the classification result for nuclear simple c algebras with tracial rank zero we show that two such dynamical systems have isomorphic crossed products if and only if they have isomorphic scaled ordered k theory

isomorphism and morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of sl2 z abstract let be irrational numbers and a b be matrices in s l 2 z of infinite order we compute the k theory of the crossed product a a z and show that a a z and a b z are isomorphic if and only if mod z and i a 1 is matrix equivalent to i b 1 combining this result and an explicit construction of equivariant bimodules we show that a a z and a b z are morita equivalent if and only if and are in the same g l 2 z orbit and i a 1 is matrix equivalent to i b 1 finally we determine the morita equivalence class of a f for any finite subgroup f of s l 2 z

renormalization group solutions for yukawa potential the self similar renormalization group is used to obtain expressions for the spectrum of the hamiltonian with the yukawa potential the critical screening parameter above which there are no bound states is also obtained by this method the approach presented illustrates that one can achieve good accuracy without involving extensive numerical calculations but invoking instead the renormalization group techniques

the tracial rokhlin property for actions of finite groups on c algebras we define tracial analogs of the rokhlin property for actions of finite groups approximate representability of actions of finite abelian groups and approximate innerness we prove the following four analogs of related nontracial results bullet the crossed product of an infinite dimensional simple separable unital c algebra with tracial rank zero by an action of a finite group with the tracial rokhlin property again has tracial rank zero bullet an outer action of a finite abelian group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property if and only if its dual is tracially approximately representable and is tracially approximately representable if and only if its dual has the tracial rokhlin property bullet if a strongly tracially approximately inner action of a finite cyclic group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property then it is tracially approximately representable bullet an automorphism of an infinite dimensional simple separable unital c algebra a with tracial rank zero is tracially approximately inner if and only if it is the identity on k 0 a mod infinitesimals

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

an improved calculation for screened coulomb potentials in rayleigh schrodinger perturbation theory earlier works on screened coulomb potentials using rayleigh schrodinger perturbation theory have been re examined instead of working with the usual hulthen potential as the unperturbed hamiltonian the authors propose that a scaled hulthen potential with modified strength and screening coefficient represents the lowest order approximation for the static screened coulomb and exponential cosine screened coulomb potentials the scale parameter appearing in the new hulthen potential is then determined from the notion of the virial theorem and intuitive physical arguments it is found that the accuracy of the predicted energy eigenvalues for the bound s states improves significantly even when the screening parameter is large and quite close to its critical values for which the quantum state becomes just bound in spite of the simplicity of the approach the numerical results compare fairly well with those obtained from rigorous analytic approximation methods